Active Electrokinetic Transport Control in a Nanofluidic Device with Embedded Surface

Electrodes

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Marie J. Fuest

Graduate Program in Mechanical Engineering

The Ohio State University

2016

Dissertation Committee:

Professor Shaurya Prakash “Advisor”

Professor Carlos Castro

Professor A.T. Conlisk

Professor Steven Ringel

Marie J. Fuest

2016

Abstract

Since the 1990s, lab-on-a-chip (LoC) systems, or miniaturized devices that perform several unit operations that typically require bench top sized equipment on an integrated platform have been developed for applications in biotechnology, chemical and biological reactors, energy conversion systems, separation and filtration systems, and medical, pharmaceutical, and environmental monitoring. The success of LoC technology relies on the ability to manipulate ions and molecules in increasingly small volumes of fluid (nL and less). With decreasing critical length scales for devices made possible by advances in microfabrication and nanofabrication, the device surface-area-to volume ratio has made the role of surface properties critical to operation and novel functionality of many of these devices. Of the various surface properties, surface charge presents a unique parameter with broad applicability for engineering new device functionalities.

Gated nanofluidic devices, geometrically analogous to semiconductor field-effect transistors, feature a nanofluidic channel with a “gate” electrode embedded in the nanochannel wall, providing an active, tunable region for manipulation of local surface charge. Specifically, an independently controlled potential applied to the embedded gate electrode allows systematic manipulation of the surface charge density at the dielectric-electrolyte interface. Fabrication protocols for gated nanofluidic devices with sub-20 nm critical length scales were developed that rely on UV lithography, wet etching,

ii and oxygen plasma bonding techniques. Active control over ionic transport through the nanochannel was monitored by changes in current as a function of gate potential, electrolyte type, electrolyte concentration, and solution pH. The measured current was referenced with respect to the ungated or intrinsic case, or the case when only an axial potential was applied with no gate potential.

In this dissertation, it was experimentally verified that the gate electrode additionally alters the electric field in the nanochannel by modifying the potential in the nanochannel near the gate electrode/dielectric/solution interface. In the surface charge governed transport regime, the gate electrode was used to switch off the measured current for a fixed axial potential, where repeatable on/off switching was demonstrated.

Local variation of surface charge by the gate electrode on transport of multivalent aqueous electrolytes and electrolyte mixtures, which form the basis for biological or practical applications, was investigated as a function of cation type. In agreement with previous anomalous transport reports, no significant difference was observed for the intrinsic nanochannel conductance of KCl compared to NaCl. Conductance decreased for

MgCl2 and CaCl2 at concentrations typically associated with surface charge governed transport for monovalent electrolytes, suggesting a decrease in the total surface charge due to divalent cation adsorption at the negatively charged walls. Data from KCl and

2+ CaCl2 electrolyte mixtures clearly indicated that Ca in the mixture is the dominating ion as determined by a decrease in surface charge density when CaCl2 was added and a surface charge density that was independent of KCl concentration for %CaCl2 > 25%.

Cation adsorption to the charged walls regulates the surface charge density thus limiting

iii the ability of the gate electrode to alter the net surface charge and consequently modulate nanochannel conductance as a function of cation type.

Dedication

This document is dedicated to Ciana Marie Pinti.

Acknowledgments

I would like to thank my advisor, Shaurya Prakash, for his guidance and support throughout my PhD. I would like to thank Professor A.T. Conlisk for his insight and useful suggestions that have helped guide the work in this dissertation. I would also like to thank my committee members, Professor Carlos Castro and Professor Steven Ringel, for their useful insights into my work.

I would like to thank the staff at Nanotech West laboratories for their assistance with equipment during fabrication and characterization of nanofluidic device. I want to thank all of my fellow lab mates for their hard work and the many things that I have learned from them over the years. Special thanks to Caitlin Boone, whose dedication and enthusiasm have made her a true pleasure to work with over the past year. I would also like to thank Kaushik Rangharajan for his work developing COMSOL models to describe ionic transport behavior in the nanofluidic device presented here. Past and current undergraduate researchers, Neil Ramirez, David Horner, Kyle Wellmerling, and Bowen

Wang, who assisted with experimental setup and worked on projects related to this work, are acknowledged for their hard work, creativity, and insightful questions. I would also like to thank Professor Harvey Zambrano for useful conversations that gave me a fresh perspective at different stages of this project. Eugene Sosnov is acknowledged for providing me with initial training in clean room processes. Special thanks to Karen

Bellman Lowe for helping me transition from Physics to Mechanical Engineering, for her unconditional support, and her invaluable friendship.

Finally, I would like to thank my parents for their unconditional love and support and their reassurance throughout my academic career. Special thanks to Frederik Fuest for his encouragement and support.

I would like to acknowledge partial financial support for this research from the

US Army Research Office (ARO) through grant number W911NF09C0079 and the

National Science Foundation through grant CBET-1335946. I would also like to thank the National Science Foundation for support through their Graduate Research Fellowship

Program (GRFP) and the Ohio State University for their support through the

Distinguished University Fellowship for my first year and dissertation year.

vii

Vita

May 2006 ...... Charles F. Brush High School

2010...... B.S. Physics, John Carroll University

2014...... M.S. Mechanical Engineering, Ohio State

University

2010 to present ...... Graduate Research Fellow, Department of

Mechanical Engineering, The Ohio State

University

Publications

1. Marie Fuest, C. Boone, A.T. Conlisk, and S. Prakash; Cation Dependent Surface

Charge Regulation in Gated Nanofluidic Devices. 2015, (submitted).

2. K. K. Rangharajan, Marie Fuest, A.T. Conlisk, S. Prakash; Transport of

Multicomponent, Multivalent Electrolyte Solutions across Nanocapillaries.

Microfluidics and Nanofluidics, 2015, (in review)

3. S. Prakash, H. A. Zambrano, Marie Fuest, C. Boone, E. Rosenthal-Kim,

N. Vasquez, and A.T. Conlisk; Electrokinetic Transport in Silica Nanochannels

viii

with Asymmetric Surface Charge. Microfluidics and Nanofluidics, 2015, 19 (6),

1455-1464.

4. Marie Fuest, C. Boone, A.T. Conlisk, and S. Prakash; Cation Dependent

Transport in a Field Effect Nanofluidic Device. Technical Digest of the 18th

International Conference on Solid-State Sensors, Actuators and Microsystems

Transducers 2015, Anchorage, Alaska, 6/21-25/2015 Transducers Research

Foundation, Cleveland (2015).

5. Marie Fuest, C. Boone, K. K. Rangharajan, A.T. Conlisk, S. Prakash; A Three-

State Nanofluidic Field Effect Switch. Nano letters, 2015, 15 (4), pp 2365–2371.

6. Marie Pinti (Fuest), H.A. Zambrano, K.K. Rangharajan, B. Wang, A.T. Conlisk,

and S. Prakash; Active surface charge control for artificial ion pumps, Technical

Digest of the Hilton Head Workshop 2014: A Solid-State Sensors, Actuators and

Microsystems Workshop, Hilton Head, South Carolina, 6/8-12/2014 Transducers

Research Foundation, Cleveland (2014), pp. 315-317.

7. Marie Pinti (Fuest), T. Kambham, B. Wang, S. Prakash; Fabrication of

centimeter long, ultra-low aspect ratio nanochannel networks in borosilicate glass

substrates. Journal of Nanotechnology in Engineering and Medicine, 2013, 4,

pp. 021003 (1-7).

8. Marie Pinti (Fuest), S. Prakash. (2013). Fabrication of Hybrid Micro-

Nanofluidic Devices with Centimeter Long Ultra-Low Aspect Ratio

Nanochannels. 2013 Proceedings of the 2013 ASME International Mechanical

Engineering Congress and Exposition, San Diego, California.

9. H A Zambrano, Marie Pinti (Fuest), A. T. Conlisk, S Prakash; Electrokinetic

transport in a water–chloride nanofilm in contact with a silica surface with

discontinuous charged patches. Microfluidics and Nanofluidics, 2012, 13(5),

735-747.

10. V. V. Swaminathan, L. R. Gibson II, Marie Pinti (Fuest), S. Prakash, P. W.

Bohn, M.A. Shannon; Ionic transport in nanocapillary membrane systems.

Journal of Nanoparticle Research, 2012, 14(8), 951-965.

11. S. Prakash, Marie Pinti (Fuest), K. Bellman; Variable cross-section nanopores

fabricated in silicon nitride membranes using a transmission electron microscope.

Journal of Micromechanics and Microengineering, 2012, 22 067002.

12. S. Prakash, Marie Pinti (Fuest), B. Bhushan; Theory, Fabrication and

Applications of Microfluidic and Nanofluidic Biosensors. Philosophical

Transactions of the Royal Society A, 2012, 370, 2269-2303.

13. Marie Pinti (Fuest), S. Prakash. (2011). A Two-Step Wet Etch Process for the

Facile Fabrication of Hybrid Micro-Nanofluidic Devices. 2011 ASME

International Mechanical Engineering Congress and Exposition, Denver,

Colorado.

14. A.F. Lotus, S.N. Tacastacas, Marie J. Pinti (Fuest), L.A. Britton, N. Stojilovic,

R.D. Ramsier, G.G. Chase; Fabrication and Characterization of TiO2-ZnO

Composite Nanofibers. Physica E, 2011, 43, 857-861.

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... ii

Dedication ...... v

Acknowledgments ...... vi

Vita ...... viii

Publications ...... viii

Fields of Study ...... xi

Table of Contents ...... xii

List of Figures ...... xx

Chapter 1: Introduction ...... 1

1.1 Motivation ...... 1

1.2 Specific Aims of this Research ...... 4

Chapter 2: Background ...... 8

2.1 Nanofluidics ...... 8

2.2 Gated Fluidic Devices ...... 29

2.3 Nanofluidic Device Fabrication ...... 45

xii

2.4 Fabrication of Gated Nanofluidic Devices ...... 77

Chapter 3: Fabrication of a Gated Nanofluidic Device ...... 96

3.1 Device Design ...... 98

3.2 Channel Network Fabrication ...... 101

3.2.1 Substrate Cleaning ...... 103

3.2.2 Metal Etching Mask...... 104

3.2.3 UV lithography ...... 107

3.3 Embedded Electrode Array ...... 114

3.4 Device Bonding ...... 118

3.5 Device Characterization ...... 127

3.6 Chapter Summary ...... 136

Chapter 4: Current Switching in a Gated Nanofluidic Device ...... 138

4.1 Gated Nanofluidic Devices for Fluidic Logic Circuits ...... 138

4.2 Experimental Design ...... 141

4.2.1 Electrode Location ...... 143

4.2.2 Gate Leakage Current ...... 145

4.3 Current Switching ...... 147

4.4 Axial and Gate Potential Dependence ...... 155

4.5 Gate Location ...... 160

xiii

4.6 Electrolyte Concentration ...... 162

4.7 Chapter Summary ...... 163

Chapter 5: Cation Dependent Surface Charge Regulation in Gated Nanofluidic Devices

...... 165

5.1 The role of surface charge in ionic transport ...... 165

5.2 Methodology for Cation Dependence Study ...... 169

5.3 Dependence of Nanochannel Conductance on Ion Type ...... 173

5.4 Cation Dependent Transport of Electrolyte Mixtures ...... 181

5.5 Surface Charge Regulation...... 188

Chapter 6: Summary, Conclusions, and Contributions ...... 216

6.1 Summary and Conclusions ...... 216

6.2 Contributions ...... 222

Chapter 7: Future Work ...... 224

7.1 Pumping against a concentration gradient ...... 224

7.2 Ion transport selectivity based on valence of the cation...... 225

7.3 PDMS v. Silica as the Gate Dielectric Material ...... 227

References ...... 229

Appendix A: Nomenclature and Abbreviations ...... 246

A.1 Alphabetical List of Abbreviations ...... 247

xiv

A.2 Nomenclature ...... 249

A.3 Units ...... 253

Appendix B: Device Characterization ...... 254

B.1 SEM images of the etched channel network ...... 255

B.2 Microchannel Etch Plot ...... 259

B.3 Channel Fabrication Challenges ...... 259

B.4 Electrode Characterization ...... 261

B.5 Characterization of Electrical Testing Station ...... 262

B.6 Device Testing Protocols ...... 264

B.7 Device Design Changes ...... 265

Appendix C: Process Sheets ...... 269

C.1 Fabrication of Gated Nanofluidic Device ...... 270

C.1.1 Channel Network Fabrication ...... 270

C.1.2 Process for Fabricating Electrode Covers ...... 282

C.2 Processes for Gated Nanofluidic Device Testing ...... 293

C.2.1 Preparation for Device Testing ...... 293

C.2.2 Device Testing ...... 298

C.3 Supplementary Process Sheets ...... 304

Appendix D: Matlab Codes ...... 309

Appendix E: Permission to Reprint ...... 313

xvi

List of Tables

Table 1: Summary of advantages and limitations of several common deposition

techniques as described in this section...... 55

Table 2: Summary of various fabrication techniques organized by category and their

respective advantages and limitations...... 74

Table 3: Select device dimensions, fabrication materials, and fabrication methods from

previously reported gated nanopore devices. All of the devices listed here feature

gate-all-around geometries except Karnik et al. (Karnik et al. 2005) and Fan et

al.(Fan et al. 2008) who used sacrificial layer etching techniques to define

nanopores and sputter deposition and lithography to define gate electrodes along the

length on the outside of the nanopores. All device schematics are used or adapted

(some labels removed) from the cited references. Device schematics reproduced

with permission, as indicated in the footnotes...... 85

Table 4: Select device dimensions, fabrication materials, and fabrication methods from

previously reported gated nanofluidic devices. All of the devices listed here feature

nanofluidic channels with a rectangular cross section. The gate electrode forms part

of the length of the channel along one wall or in the case of Maleki et al., two walls.

All device schematics are used from the cited references. Device schematics

reproduced with permission, as indicated in the footnotes...... 94 xvii

Table 5: Resistance measurements across various paths of a micro- nanofluidic device

filled with 1 mM KCl. Microchannel resistances were nearly 3 orders of magnitude

lower than nanochannel resistances. Microchannels were therefore considered

equipotential for subsequent analysis with the entire potential drop occurring across

the nanofluidic channels. Two wire resistance measurements across various paths

confirm channel network symmetry post fabrication. The corresponding paths are

labeled in the schematic of the channel network in Figure 36...... 125

Table 6: The table shows the time exposed to 10:1 buffered oxide etchant, the measured

depth of the un-bonded nanochannel and the aspect ratio of the nanofluidic channel

after bonding. The aspect ratio of 0.0005 is the lowest previously reported in

literature that incorporates polymers in fabrication ...... 127

Table 7. Debye Length as a function of electrolyte concentration for 1:1 (KCl and NaCl)

and 2:1 (CaCl2 and MgCl2) electrolytes...... 172

Table 8: A summary of electrolyte compositions and the corresponding prepared

concentrations...... 182

Table 9: Measured and estimated values for the conductance as a function of electrolyte

composition. Conductance values are given as a ratio of the conductance at a given

electrolyte composition over the conductance of the 0% CaCl2 (i.e. 100% KCl case).

Predicted values of the conductance are calculated using Equation 48 under the

assumptions that the proportion of the cations in the nanochannel is equal to the

relative proportion of cation concentration in the bulk and that the surface charge is

constant across cases. The conductance values calculated from Equation 48 failed to

xviii

predict the measured conductance indicating the constant surface charge assumption

is invalid...... 185

Table 10: Summary of the adsorption reactions between a negatively charged surface and

cations in the electrolyte solution for a 1:1 and a 2:1 electrolyte. The corresponding

equilibrium constants for each reaction are listed in terms of the bulk species

concentrations...... 195

Table 11: Values of the surface charge density as a function of pH used in COMSOL

simulations for 1 mM KCl. The values indicated by the “*” were calculated from the

site binding model described above for (푝퐾1 = 8.5 and 푝퐾푀 = 4.5). The surface

charge density predicted by the site binding model is given by 𝜎푆퐵...... 204

Table 12: Values of the surface charge density as a function of pH used in COMSOL

simulations for 0.33 mM CaCl2. Only the homogenous case was considered for

CaCl2 where 𝜎푃퐷푀푆 = 𝜎𝑔푙푎푠푠 = 𝜎푆퐵 and 𝜎푆퐵 is the surface charge density

predicted by the site binding model for (푝퐾1 = 8.5, 푝퐾퐷1 = 2.5, and 푝퐾퐷2 = 5.8).

...... 205

Table 13. A summary of device design parameters for Design 1 and Design 2. Gray

shading indicates a value that changed between designs...... 267

xix

List of Figures

Figure 1: A schematic of the general geometry of a gated nanofluidic device. A

nanofluidic channel is positioned to between an inlet and outlet reservoir. The height

of the channel (ℎ) ranges from 1-100 nm. The length of the nanochannel (퐿) can

range from 100’s of nm to mm. A gate electrode embedded in the nanochannel wall

is separated from the fluid in the channel by a dielectric layer...... 3

Figure 2: The isoelectric point, or the point where the net surface charge density is zero,

as a function of bandgap energy. Due to the high surface area to volume ratio in

nanofluidic flows, ionic transport through the nanofluidic architectures is governed

by the surface charge, which is a function of pH. Insulating materials are desired for

nanofluidic substrates to avoid extraneous current paths during current

measurements. Materials with a higher bandgap are better insulating materials.

Reprinted with permission from Cheng, L.J. and L. J. Guo (2009). Ionic Current

Rectification, Breakdown, and Switching in Heterogeneous Oxide Nanofluidic

Figure 3: A schematic representation of the Gouy-Chapman-Stern model of the electric

double layer. The Stern layer is comprised of adsorbed ions followed by bound,

hydrated, and partially hydrated ions. The diffuse layer consists of mobile hydrated

ions. The potential at the interface between the Stern and diffuse layers is known as xx

the zeta 휁 potential. Reprinted with permission from Prakash, S., A. Piruska, E. N.

Gatimu, P. W. Bohn, J. V. Sweedler and M. A. Shannon (2008). Nanofluidics:

Figure 4: A schematic representation of overlapped and non-overlapped electric double

layers. The plots represent the K+ and Cl- concentration and the potential in the

nanochannel with 0.1 mM KCl for the overlapped case and with 100 mM KCl for

the non-overlapped case generated using COMSOL Multiphysics. In the case of

overlapped electric double layers, the concentration of K+ ions exceeds the

concentration of the Cl- through-out the depth of the nanochannel. The potential at

the channel centerline is not electrically neutral. In the non-overlapped case there is

an excess of cations near the wall, but the concentrations of K+ and Cl- are

equivalent to their bulk values at the channel centerline. The channel is electrically

neutral at the centerline. Plots used with permission from Kaushik K. Rangharajan.

...... 17

Figure 5: A representative schematic showing the direction for each individual flux term

(here 퐽 rather than 푁) for a positively charged particle (methylene blue) in a

nanopore. The darker blue color indicates a higher concentration of methylene blue

(MB). In this case, diffusive flux is expected to occur from left to right (high

concentration to low concentration). Positively charged particles migrate towards the

cathode under the influence of an electric field (electromigration, left to right). Since

the channel is positively charged, there are an excess of negative ions compared to

positive ions in the channel. The bulk fluid flow and, therefore, the convective flux

xxi

is from right to left. If we consider the same system but substitute a negatively

charged particle for the MB, the direction of convection and diffusion would remain

the same, but the direction of electromigration would be reversed (towards the

anode). Schematic used with permission from the authors of K. K. Rangharajan,

Marie Fuest, A.T. Conlisk, S. Prakash (2015). Transport of Multicomponent,

Multivalent Electrolyte Solutions across Nanocapillaries. Microfluidics and

Nanofluidics, (in review)...... 22

Figure 6: The conductance through nanofluidic channels of various heights as a function

of bulk electrolyte concentration (KCl). The conductance is independent of

-3 concentration at low bulk electrolyte concentration 푐푏푢푙푘 < ~10 M). At low

concentration the number of charge carriers and therefore the conductance is

determined the total surface charge. At high concentration the conductance has a

linear dependence on both height and concentration as expected from bulk fluid

properties and the channel dimensions. The transition between the bulk transport and

surface charge governed transport regimes occurs at the critical concentration,

-3 푐푡 ≈ 10 M. . Adapted with permission from Stein, D., M. Kruithof and C. Dekker

(2004). Surface-Charge-Governed Ion Transport in Nanofluidic Channels. Phys.

Rev. Lett. 93(3): 035901. Copyright American Physical Society...... 28

Figure 7: Schematic representation of a gated nanochannel and a gated nanopore device.

The gated nanochannel device features two microchannels that serve as fluidic

reservoirs to a nanochannel. The cross section of the microchannels and the side

view of the nanochannel are shown in blue. Gold gate electrodes are embedded in

xxii

the roof of the nanochannel and isolated from the fluid by a dielectric layer (pink).

The gated nanopore device shows a silicon handle wafer (green) with a silicon

nitride (light green) insulation layer. A fluidic reservoir was etched into the silicon

handle wafer. The gate electrode (gray) forms the entire circumference over a

certain length of the pore. The gate dielectric layer is shown in blue. Schematics

were prepared using SolidWorks 2014. The geometries shown are an interpretation

of the two general geometries found in literature. A review of specific device

geometries and fabrication procedures is given in Section 2.4...... 30

Figure 8: A schematic representation of the hypothesized change in ion concentration in

the nanochannel during gating to maintain electroneutrality. (A) Under ungated

conditions with overlapped electric double layers the nanochannel walls are

negatively charged and there is an excess of positively charged ions compared to

negatively charged ions in the nanochannel. (B) When a positive potential is applied

to the embedded gate electrodes fewer net number of positive of ions are required to

maintain electroneutrality. (C) As the positive potential to the gate electrode is

further increased, an excess of negative ions would be required...... 33

Figure 9: An equivalent circuit model for a gated microfluidic channel (Horiuchi et al.

2006). The gate voltage, 푉푔, and axial voltage, here labeled 푉푑, are shown in the

schematic.푅푏1 and 푅푏2 represent the resistance of the portion of the microchannel

before and after the gate electrode. 푅푙푒푎푘 represents the resistance of the gate

dielectric. 퐶푡표푡푎푙 represents the capacitance of the electric double layers and the gate

dielectric. It should be noted there is a second smaller microchannel located above

xxiii

the gate electrode. The resistance of the smaller microchannel above the gate

electrode is given by 푅푏3. In this study the gate dielectric modeled as an equivalent

capacitor and resistor in parallel. Here 퐶푤푎푙푙 = 퐶𝑖푛푠. Reproduced from Horiuchi, K.

and P. Dutta (2006). Electrokinetic Flow Control in Microfluidic Chips Using a

Field-Effect Transistor. Lab Chip 6: 714-723 with permission of The Royal Society

of Chemistry...... 36

Figure 10: Translocation of positively charged avidin protein as a function of gate

potential. Negative gate bias allows translocation of avidin from reservoir to

reservoir while under positive bias the translocation is not observed. Reprinted with

permission from Karnik, R., K. Castelino and A. Majumdar (2006). Field-effect

control of protein transport in a nanofluidic transistor circuit. Appl. Phys. Lett. 88:

Figure 11: Schematic representation of UV lithography process for a glass substrate and

positive tone photoresist. Photoresist is spun onto the glass substrate. The

photoresist is selectively exposed to UV light using a photomask. The photomask

has dark (chromium) regions that prevent exposure and transparent (glass) portions

that all the UV light to reach the photoresist. The UV light breaks the bonds in the

polymer chains of the positive photoresist, causing the exposed region of photoresist

to selectively dissolve in the developer solution...... 57

Figure 12: Schematic representation of nanoimprint lithography. A master, often made of

silicon, is patterned using lithography and etching. The silicon master is pressed into

a polymer substrate and cured. The black dash-dot line indicates the cut line to

xxiv

generate the cross section view. The master is then removed and the negative of the

pattern is then imprinted into the polymer substrate...... 63

Figure 13: Schematic representation of a lift off process for patterning metal features. A

pattern is defined in photoresist using lithography. A metal layer is evaporated on

top of the patterned photoresist. Perfect step coverage is not desired so that solvent

can reach the photoresist layer. The photoresist sidewall profile should be greater

than or equal to 90° and the deposition should not be conformal. The angle of the

photoresist sidewall profile is 90° in the schematic. After exposure to solvents the

photoresist and metal layer on top of the photoresist is “lifted off” leaving the metal

in the form of the original pattern...... 64

Figure 14: Schematic representation of isotropic and anisotropic etching profiles using

SiO2 as an example. Wet etching with HF or buffered oxide etchant (BOE) is

isotropic leading to undercutting of the photoresist layer. Reactive ion etching is

anisotropic...... 66

Figure 15: Schematic representation of sacrificial layer etching. A sacrificial layer is

deposited and patterned on the substrate. A capping layer is deposited and then

etched to gain access to the sacrificial material. The sacrificial layer is selectively

etched to release sealed channels. Black dash-dot lines indicate cut lines used to

generate cross section views. The capping layer is shown transparent through until

the final device schematic for clarity...... 71

Figure 16: An example of a process flow chart for gated nanopore device taken from

Nam et al. (2009). Fabrication begins with a membrane stack including a silicon

xxv

handle wafer (gray), Si3N4 insulting layers, SiO2 insulating layers, and a conducting

TiN gate electrode. UV lithography and wet etching with KOH were used to etch

reservoirs in the silicon handle wafer. E-beam lithography and reactive ion etching

(RIE) were used to define the nanopores in the membrane stack, since the gate

electrode material (TiN) was compatible with RIE. Other groups who used Cr or

other metal used FIB or TEM milling to define the nanopores in the membrane

stack. The pore is then insulated using a conformal ALD technique. Other deposition

technique for the gate dielectric are described below. Reprinted

with permission from Nam, S. W., M. J. Rooks, K. B. Kim and S. M. Rossnagel

(2009). Ionic Field Effect Transistors with Sub-10 nm Multiple Nanopores. Nano

Figure 17: A sacrificial layer process (Figure 15) adapted to include gate electrodes. After

patterning the sacrificial layer, an insulating or capping layer is applied. A metal

layer is deposited on the capping layer and patterned to form a gate electrode.

Another lithography and etch step is performed to gain access to sacrificial layer.

The sacrificial layer is selectively etched to release nanofluidic channels...... 90

Figure 18: A flow chart for the process developed by Oh et al. (Oh et al. 2008). A SiO2

mask (blue in b) is applied to a clean Si wafer (a) to allow selective doping of the Si

substrate with boron (green). Panel (c) shows the boron doped region of the silicon

substrate that will serve as the gate electrode. A photoresist and anti-reflective mask

is applied to the Si (d) and patterned using interferometric lithography to create an

evenly spaced array of parallel nanochannels (e). A Cr layer is applied (f) and a lift

xxvi

off process is used to form the negative image of the channels in Cr (g). The

nanochannels are then etched into the Si substrate by reactive ion etching (h). The

Cr etch mask is then removed and an oxide layer is thermally grown to insulate the

gate electrode (green, boron doped Si) and the semiconducting Si substrate.

Reproduced from Oh, Y.-J., T. C. Gamble, D. Leonhardt, C.-H. Chung, S. R. J.

Brueck, C. F. Ivory, G. P. Lopez, D. N. Petsev and S. M. Han (2008). Monitoring

FET flow control and wall adsorption of charged fluorescent dye molecules in

nanochannels integrated into a multiple internal reflection infrared waveguide. Lab

Chip 8: 251-258 with permission of The Royal Society of Chemistry...... 93

Figure 19: (A) The schematic shows an exploded view of the gated nanofluidic device

design. The fluidic network consisted of two 8 μm deep x 50 μm wide x 3.2 cm long

microchannels connected by a bank of three 16 nm deep x 30 μm wide x 5 mm long

nanofluidic channels etched into borosilicate glass. An array of asymmetrically

spaced, individually addressable gold gate electrodes (25 nm high x 25 μm wide)

were patterned on a second glass substrate (cover). The cover with the patterned gate

electrodes was bonded to the substrate with the channel network using an

intermediate PDMS layer (red). The PDMS layer isolated the gate electrodes from

the fluid in the nanochannels. (B) The side view schematic shows the potential

difference applied along the nanochannel length (axial potential, 푉푎). The direction

of net fluid flow in the un-gated case (no potential applied to the embedded gate

electrode) is marked by the red arrow. The gate electrode is used for active, tunable

control over ionic transport through the nanofluidic channels, with changes in ionic

xxvii

transport characterized by changes in measured current. A full description of the

experimental setup is provided below. Reprinted with permission from Fuest, M., C.

Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State

American Chemical Society...... 99

Figure 20: Flow chart of the channel network fabrication procedures (Pinti et al. 2013).

Organic contaminates were removed from the borosilicate substrate with a Piranha

solution (4:1 sulfuric acid to hydrogen peroxide). A chrome adhesion layer,

followed by an inert Au metal mask layer was deposited on the Piranha cleaned

substrate. Shipley 1813 positive tone photoresist was spun onto the metal mask, then

exposed and developed to form the microchannel pattern. The substrate was exposed

to gold etchant followed by chromium etchant to transfer the microchannel pattern

into the metal etch mask. The microchannel pattern was then transferred, or etched,

into the substrate using a 4:1 solution of DI water to 49% HF. The photoresist was

stripped and a second UV lithography process with a spin process adapted for the

non-planar substrate was used to pattern the nanofluidic channels. The nanochannels

were etched with 10:1 buffered oxide etch. After the nanochannel pattern was

transferred into the substrate, the metal mask was removed. Each step in the

fabrication process is discussed in detail below. Reprinted with permission from

Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013). Fabrication of Centimeter

Long, Ultra-Low Aspect Ratio Nanochannel Networks in Borosilicate Glass

xxviii

Figure 21: Surface roughness of the borosilicate substrates measured before and after

Piranha cleaning using an Asylum MFP-3D AFM. The RMS surface roughness

decreased from 0.316 nm before cleaning to 0.076 nm after cleaning. The reduction

of surface roughness was attributed to removal of contaminates on the glass surface

during the cleaning process. The AFM scan size was 10 μm x 10 μm...... 103

Figure 22: Comparison of a microfluidic channel etched using only photoresist as the

masking layer (left panel) to a microfluidic channel etched with a photoresist layer,

an inert Au metal layer, and a Cr adhesion layer as an etch mask (right panel). Both

samples were exposed to a 4:1 DI water to 49% HF etching solution for 8 minutes.

(A) SEM images of a microchannel etched without using a metal etch mask. The

inset shows the irregular shape of the sidewall profile. (B) SEM images of a

microchannel etched with a Cr/Au metal etch mask. The sidewall profile has a clear

“step” from the substrate surface to the bottom of the microchannel. The inset shows

the curved sidewall profile expected from an isotropic etch. The metal mask was not

removed before the image in the inset was taken. SEM imaging confirmed that after

etching the metal mask was still intact. (C) A profilometer scan of the microchannel

etched without the metal mask. (D) A profilometer scan of the microchannel etched

with the metal mask. A clear step is observed for the channel etched with the metal

mask, in contrast to the channel etched without. The microchannel etched with the

metal mask was ~ 8 µm deep in contrast to the channel etched without the metal

mask which was ~ 1.5 µm deep. The difference in depth for the same exposure time

to HF indicates that the mask fully delaminated after about ~1.5 µm of etching and

xxix

the HF solution began uniformly etching the substrate and the channel rather than

increasing the depth of the channel relative to the substrate surface...... 105

Figure 23: An SEM image of the micro- and nanochannel interface of a 55 nm deep

nanofluidic channel. The inset shows a zoomed in view of the nanochannel sidewall.

The zoomed in image was taken at the location denoted by the red dashed box.

Semi-circular “notch” defects in the nanochannel sidewall were caused by stress

gradients at the edge of the Cr/Au metal mask. Stress gradients at the mask edges

cause the mask to break as the isotropic etch progresses...... 107

Figure 24: SEM images of an un-even layer of photo active polymer (photoresist). The

photoresist was spun onto the substrate containing two previously fabricated

microchannels. The “bright” regions represent uncoated glass on the edge of the

microchannel that will be etched upon exposure to 10:1 buffered oxide etchant. (A)

The full width of the microchannel is shown as well as an uncoated “ridge” that

connects the nanochannels near their entrances. Note that an earlier design has

100 µm wide microchannels. All device testing data reported in this dissertation is

for 50 µm wide microchannels. (B) A higher magnification of the area marked by

the box in A. The top portion of the microchannel wall remains uncoated with

photoresist. After etching, this will result in an undesired ~4 μm wide edge channel

that created a perpendicular fluidic path connecting adjacent nanochannels. Fluid

can flow between nanochannels on the path indicated by the red arrow. The dashed

red line indicates the desired edge of the photoresist, which would ensure the

microchannel was the only path between nanochannels...... 109

xxx

Figure 25: SEM image of two parallel nanofluidic channels connected by an etched ridge

or “edge channel”. The edge channel runs parallel to the microfluidic channel and

resulted from undesired exposed regions of the non-planar substrate following the

nanochannel lithography step. The nanochannels shown in this image are 227 ±

6 nm deep. As the ridge is a defect that occurred during the nanochannel lithography

step, the edge channel is the same depth as the nanochannels (Pinti et al. 2013).

Fluid can flow between adjacent nanochannels along the path indicated by the red

arrows. Reprinted with permission from Pinti, M, and S. Prakash (2011). A Two-

Step Wet Etch Process for the Facile Fabrication of Hybrid Micro-Nanofluidic

Devices. 2011 ASME International Mechanical Engineering Congress and

Figure 26: SEM image of the micro- nanochannel interface in a properly fabricated

device. The ridge and subsequent edge channel produced after wet etching was

eliminated by adding a third spin step to the typical two-step photoresist spin recipe

and reducing the spin acceleration by 1.5 orders of magnitude compared to standard

recipes. Reprinted with permission from Fuest, M., C. Boone, A.T. Conlisk, and S.

Prakash; Cation Dependent Transport in a Field Effect Nanofluidic Device.

Technical Digest of the 18th International Conference on Solid-State Sensors,

Actuators and Microsystems Transducers 2015, Anchorage, Alaska, 6/21-25/2015

Figure 27: An etch plot showing the depth of the un-bonded nanofluidic channel as a

function of time exposed to 10:1 buffered oxide etchant. Depths ranged from 16 ±

xxxi

1 nm for a 20 second etch time to 227 ± 6 nm for a 300 second etch time. The

nanochannel depth was measured with an Asylum MFP-3D AFM. Reprinted with

permission from Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013).

Fabrication of Centimeter Long, Ultra-Low Aspect Ratio Nanochannel Networks in

Borosilicate Glass Substrates. J. Nanotechnol. Eng. Med.. 4(2): 020905. Copyright

2013 ASME...... 113

Figure 28: (A) An AFM line scan of an un-bonded nanochannel after 20 second exposure

to 10:1 buffered oxide etchant. The depth was 16 ± 1 nm and the width was 31 ±

1 μm. Reprinted with permission from Pinti, M, and S. Prakash (2013 Fabrication of

Hybrid Micro-Nanofluidic Devices with Centimeter Long Ultra-Low Aspect Ratio

Nanochannels. 2013 Proceedings of the 2013 ASME International Mechanical

ASME. (B) A 3-D image of the 16 nm deep x 31 μm wide un-bonded nanochannel.

The AFM scan area was 40 μm x 40 μm...... 113

Figure 29: A schematic representation of the glass cover with the patterned Au/Cr

electrode array is shown in the center of the image. Insets show actual images of

respective positions of the electrodes. (A) A micrograph image of the center of the

electrode array showing the asymmetric placement of the six individually

addressable electrodes. The image was taken using a 10x objective. (B) The

micrograph image, taken using a 4x objective, shows curves in the electrodes needed

to make the connections between the portion of the electrode over the nanochannels

and the electrical contact pad. (C) An SEM image of the connection between an

xxxii

electrode and an electrical contact pad. The contact pads were used to make

connections between the gate voltage power supply and the electrodes. (D) An SEM

image of a bend in one of the electrodes...... 115

Figure 30: (A) A bonded device with a discontinuous PDMS film. The regions of missing

PDMS near the fluidic channels caused leaking. (B) Reducing the maximum spin

speed of the liquid PDMS from 5000 rpm (device in A) to 1000 rpm (device in B)

resulted in a continuous polymer film and a leak-free bond...... 117

Figure 31: A micrograph image of PDMS partially collapsed into the microfluidic

channel. Partial PDMS collapse can prevent or obstruct flow. Fully curing the spun-

on PDMS layer prior to bonding prevented partial PDMS collapse. To prevent

collapse the PDMS layer was cured on a hot plate for at least 12 hours at 70°C. The

image was taken using a 4x objective...... 118

Figure 32: A schematic representation of the bonding mechanism of oxygen plasma

treated polydimethyl siloxane with a glass substrate (Sun et al. 2007 ). PDMS

generally has surface methyl groups (– Si(CH3)2). Exposure to oxygen plasma

oxidizes the PDMS surface resulting in surface silanol groups (SiOH) (Hillborg et

al. 2000; Sun et al. 2007 ; Qin et al. 2010). The surface silanol groups on the

oxidized PDMS surface and the silanol groups on the glass surface have a

condensation reaction when placed in contact forming Si-O-Si covalent bonds

between the two surfaces. Reproduced from Sun, Y. and J. A. Rogers (2007).

Structural forms of single crystal semiconductor nanoribbons for high performance

xxxiii

stretchable electronics. J. Mater. Chem. 17: 832–840 with permission of The Royal

Society of Chemistry...... 119

Figure 33: (A) A cross section SEM image of a 227 nm deep x 31 μm wide nanofluidic

channel. The PDMS layer here was measured to be ~2 μm thick. The inset shows a

zoomed in view of the area marked by the white box. Reprinted with permission

from Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013). Fabrication of

Centimeter Long, Ultra-Low Aspect Ratio Nanochannel Networks in Borosilicate

(B) A cross section SEM image of a 16 nm deep x 31 μm wide nanofluidic channel.

The PDMS layer here was measured to be ~0.5 μm thick. Note that the entire

channel width cannot be visualized in one frame. The cross section SEM images

confirm that the nanofluidic channels are bonded and open for flow. Reprinted with

permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S.

Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4):

Figure 34: Time elapsed micrograph images of the interface of the KCl electrolyte and

unfilled gas/vapor region of the 22 nm deep nanofluidic channels. The KCl

electrolyte solution filled the channel with time, providing further evidence that the

channel was bonded and open for flow. The images were taken using a 10x

objective. Reprinted with permission from Pinti, M, and S. Prakash (2013).

Fabrication of Hybrid Micro-Nanofluidic Devices with Centimeter Long Ultra-Low

Aspect Ratio Nanochannels. 2013 Proceedings of the 2013 ASME International

xxxiv

Mechanical Engineering Congress and Exposition, San Diego, California.

Figure 35: Micrograph images taken of bonded devices with different spacings between

the nanochannels. The white arrows denote the spacing between two adjacent

nanochannels. The nanochannels were 50 μm apart in A resulting in leaking devices.

The channel spacing was increased to 200 μm in B resulting in properly bonded

devices. The images were taken using a 10x objective...... 124

Figure 36: Paths used for resistance measurements. For example, a two wire resistance

measurement from 1-3 measures the resistance of the left microchannel...... 125

Figure 37: A fluorescence image of three 57 nm nanofluidic channels and one 8 µm deep

microchannel filled with 100 μM Rhodamine B fluorescent dye. No visible leaks

were observed adding further evidence to support micrograph images, SEM images,

and resistances measurements that indicate the devices were properly bonded. The

image was taken using a 10x objective...... 126

Figure 38: Schematic representation of the experimental set-up for current measurements.

Red is used to denote connections to the axial voltage source, purple is used to

denote connections to the picoammeter, and green is used to denote connections to

the gate voltage source. The color scheme was preserved in all three panels. (A) A

schematic of the instruments used for current measurements and the connections

between instruments. All potentials were applied with respect to the same ground for

a common reference (black connections). Gold wires were used to connect the axial

voltage source and picoammeter to the fluid in the microchannel reservoirs. The

xxxv

measurements were conducted in an Earth grounded Faraday cage to minimize

electrical noise. (B) An exploded view schematic of the micro- and nanofluidic

device with labeled connections to axial voltage source, gate voltage source, and

picoammeter. (C) Nanochannel side view schematic generated from slicing (B)

along the red dashed line. Connections to instruments are labeled...... 128

Figure 39: Measured current as a function of applied axial potential for 16 nm deep

nanofluidic channels. The measured current has a linear dependence on applied axial

potential in the range 0 V to 150 V. The limiting regime where measured current is

constant with applied potential occurs for axial potentials ranging from 150 V to

240 V and the overlimiting regime begins at an applied axial potential of 240 V.

This curve shows expected concentration polarization behavior for these devices.

Subsequent tests are performed with an axial potential 푉푎 ≤ 15 V to ensure that

effects of concentration polarization do not have a significant effect on the data. . 130

Figure 40: Nanochannel conductance for the un-gated case is shown as a function of KCl

concentration. Conductance was independent of concentration at “low”

concentration and follows a linear trend at “high” concentrations in agreement with

previous reports (Stein et al. 2004; Karnik et al. 2005; Schoch et al. 2005) The

transition between these two regimes occurs near the critical concentration of ~

1 mM, with general agreement in published reports that the low concentration

regime (푐푏푢푙푘< 1 mM) is the surface charge governed transport regime for

nanofluidic channels. The dashed blue line is the conductance calculated from the

analytical equation for the bulk conductance of KCl through 18 nm deep x 30 µm

xxxvi

wide x 5mm long channels (퐺푏푢푙푘, Equation 33). The experimentally measured

conductance agrees with a 2-D Poisson-Nernst-Planck model for a 16 nm deep

nanochannel, confirming successful device operation according to established theory

of ionic transport in nanofluidic channels...... 132

Figure 41: A schematic of the micro- nanofluidic system modeled with COMSOL

multiphysics. Due to the low aspect ratio of the nanochannel (width >> height) the

system can be modeled in two dimensions (Conlisk 2013). The inlet and outlet

reservoirs, which correspond to microchannels in the fabricated device, were

100 nm long and 250 nm tall. The size of the channel in the model was 16 nm deep

x 5 mm long to match the dimensions of the fabricated device. The KCl

concentration in the inlet and outlet reservoirs was set to the bulk electrolyte

concentration (ranging from 0.01 mM to 100 mM). Modeling the reservoirs

accounts for the difference in concentration of species in the bulk electrolyte and in

the nanochannel. The inlet microchannel was set to 5V while the outlet

microchannel was grounded. The location where the concentration and potential

boundary conditions were imposed is indicated with the red arrow in the schematic.

A surface charge density of -2 mC/m2, consistent with previously reported values for

glass at pH 7 (Guan et al. 2011; Jin et al. 2011), was imposed on all surfaces marked

with the dark grey line (reservoirs and nanochannel)...... 133

Figure 42: (A) An exploded view schematic of the fabricated gated nanofluidic device.

The fluidic network consisted of two 10 μm deep x 50 μm wide x 3.2 cm long

microchannels connected by a bank of three 16 nm deep x 30 μm wide x 5 mm long

xxxvii

nanochannels wet-etched into borosilicate glass. Gold gate electrodes (20 nm high x

25 μm wide) were patterned on a second glass substrate (cover) and bonded to the

substrate with the channel network using an intermediate PDMS layer. The PDMS

layer isolated the gate electrodes from the fluid in the nanochannels. (B) A scanning

electron microscope (SEM) image of the bonded nanochannel cross section. The

complete nanochannel width of 30 μm does not permit imaging the entire cross

section in one frame. From the SEM image, the PDMS dielectric layer was ~ 500

nm thick. (C) An exploded side view of the device. The red dash-dot line in Figure

42A indicates the cut-line (A-A’) used to generate the side view schematic. (D) The

assembled side view schematic shows the experimental set-up with the applied axial

(Va) and gate (Vg) potentials. Only one electrode is shown as only one electrode was

active at a given time. The direction of fluid flow in the un-gated case (Vg = 0 V) is

marked by the red arrow. The axial and gate potentials are referenced to the same

ground. The location of a given electrode is the relative distance of the center of the

electrode from the nanochannel inlet as indicated in the schematic by L1. The light

green dashed line indicates the region where the gate electrode is expected to alter

the surface charge density, as described below. Reprinted with permission from

Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A

Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371.

Figure 43: A micrograph image of the 6 individually addressable electrodes. The

electrodes are labeled with their relative location along the nanochannel length

xxxviii

퐿 = 5 mm. The location of the nanofluidic channels is marked with white dashed

lines. The device can also be rotated 180°, changing the relative locations from 푥퐿 to

(퐿 − 푥퐿). Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan,

A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch.

Figure 44: A representative image showing gate leakage current measurement for 1 mM

KCl referenced to the axial current for Va = 3 V. The axial voltage range of 1-5 V

and gate sweeps from -2 to +2 V were used in all reported data for 1 mM KCl to

meet the threshold for gate leakage current at Va = 1 V, as described above.

Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T.

Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch.

Figure 45: The plot shows the measured current as a function of gate voltage with the

overall trend showing evidence for operation of a nanofluidic field effect device as a

3-state ionic current switch. A current of 0.106 nA was measured through the

nanofluidic channels for Va = 3 V, Vg = 0 V. For Vg = 0 V to – 2 V, the measured

current decreased from 0.106 nA to -0.026 nA with no measureable current at Vg = -

1.4 V. Here +2 V applied to the gate electrode results in 0.220 nA of current. From

the un-gated conductance for 1 mM KCl (Figure 40), achieving the same current,

i.e., 0.220 nA purely from Va requires Va = 7.0 V. Reprinted with permission from

Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A

xxxix

Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371.

Figure 46: Current switching for 0.1 mM KCl indicating the gate voltage can be tuned to

produce the desired current. The current is 0.024 ± 0.002 nA for Va = 3 V, Vg = 0 V

and switched off for Va = 3 V, Vg = -3 V. Reprinted with permission from Fuest, M.,

C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State

American Chemical Society...... 150

Figure 47: A visual representation of the change in potential induced by the gate

electrode. Inlet and outlet channels are labeled with respect to un-gated flow and are

designated in this way for reference. The gate potential is referenced to the

outlet/grounded microchannel. Application of a gate voltage changes the potential in

the nanochannel, and necessarily the electric field, where the potential in the

nanochannel below the gate will be proportional to the gate voltage 훼푉푔. The

location dependent potential profile will be significantly complicated compared to

the un-gated case. The proportionality factor, 훼, will depend on a variety of factors

dielectric material (Karnik et al. 2005), dielectric thickness (Guan et al. 2011; Singh

et al. 2012), gate electrode location (Jin et al. 2011; Singh et al. 2011; Singh et al.

2012), gate electrode position (Jin et al. 2011; Singh et al. 2011), and electrolyte

concentration (Liu et al. 2010). Reprinted with permission from Fuest, M., C.

Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State

American Chemical Society...... 155

Figure 48: A representative plot showing current modulation in a nanochannel filled with

1 mM KCl as a function of gate voltage for three test axial potentials. In all three

cases the slope, 푑퐼/푑푉푔, remained constant with a value of 0.060 ± 0.003 nA/V. It is

worth noting that in the same device for a given electrolyte concentration, the

measured current can be switched off for different combinations of Va and Vg. In

addition, current reversal was also be obtained by systematically tuning Vg with

respect to Va. Reprinted with permission from Fuest, M., C. Boone, K. K.

Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field

Society...... 157

Figure 49: A representative plot showing gate leakage current (GLC) for 1 mM KCl

plotted alongside the data shown in Figure 48. The measured axial current is higher

than the measured gate leakage current, particularly in the forward current state.

Finite gate leakage current may contribute to the change in the electric field, likely

enhancing the effect of the gate electrode relative to the ideal dielectric case.

Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T.

Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch.

Figure 50: A representative plot which demonstrates that the current modulation depends

on the additive or subtractive effect of the electric field induced by the gate electrode

xli

with respect to the axial field. The gate electrode was located at 0.57 L. For Va = +3

V a negative gate voltage (-Vg) decreases the magnitude of the current while for Va =

-3 V the same negative gate voltage (-Vg) increases the magnitude of the current.

Here, current was switched off for Va = +3 V with Vg = -1.4 V, and Va = -3 V with

Vg = +1.8 V, consistent with modeling results that showed changes to the electric

field induced by the gate electrode dramatically decrease ionic current when Va and

Vg were of opposite sign. Reprinted with permission from Fuest, M., C. Boone, K.

K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic

Chemical Society...... 160

Figure 51: Current modulation increases as the relative distance of the gate electrode

from the channel inlet, L1, increases, in agreement with the proposed hypothesis.

The increase in modulation for the representative case of 1 mM KCl (Va = 3 V) is

demonstrated by the increase in the slope as shown in the plots above going from the

left to right panels. Reprinted with permission from Fuest, M., C. Boone, K. K.

Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field

Society...... 161

Figure 52: The plot shows dependence of current modulation on bulk KCl concentration

for a representative axial potential of Va = 3 V. Error bars were smaller than the

markers and are therefore not shown explicitly. Current modulation was observed to

decrease as bulk KCl concentration increases likely due to enhanced screening of the

xlii

gate electrode. Reprinted with permission from Fuest, M., C. Boone, K. K.

Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field

Society...... 163

Figure 53: (A) Schematic showing the layers of the nanofluidic device. Two

microchannels (8 µm deep x 50 µm wide x 3 cm long) served as reservoirs to a bank

of three nanochannels (16 nm deep x 30 µm wide x 2.5 mm long). The micro- and

nanochannel network was fabricated on a borosilicate glass substrate with

individually addressable gold (Au) gate electrodes patterned on the glass cover. A

polydimethyl siloxane (PDMS) dielectric layer supported on the glass cover isolated

the gate electrodes from the aqueous electrolytes in the nanochannels. (B) Side-view

schematic of the nanochannel, showing the active gate electrode for the data

reported. Electrical connections are shown with yellow lines. An axial potential

difference, 푉푎, was applied between the two microchannel reservoirs. An

independently controlled gate potential, 푉푔, applied to the gate electrode modified

the local surface charge density and the local electric field at the

dielectric/electrolyte interface enabling field-effect control over ionic transport

through the nanochannel. Changes in ionic transport were quantified through a

current (퐼) measurement with all potentials applied with respect to the same ground.

The gate electrode was located at a distance 퐿푔 = 0.43 ± 0.02 퐿, where 퐿 is the total

nanochannel length and 퐿푔 is the relative distance from the gate electrode to the

grounded microchannel (Fuest et al. 2015). (C) Scanning electron microscope

xliii

(SEM) image of an open nanochannel cross section. The slit-like channel cross

section lies between the arrows. The dashed red lines denote the locations on the

device where the SEMs were taken. The channel height was ~16 nm, as expected

from previous reports on device fabrication and characterization (Pinti et al. 2013;

Fuest et al. 2015). (D) SEM image of PDMS bonded to glass in regions where no

channel is expected...... 171

Figure 54: (A) The intrinsic nanochannel conductance, measured with the gate electrode

floating (푉푔 = 0 V) , was independent of concentration at low concentration for

monovalent electrolytes KCl and NaCl indicating surface charge governed transport.

The conductance depended linearly on concentration at high concentrations, in

agreement with general previous trends reported (Stein et al. 2004; Karnik et al.

2005; Schoch et al. 2005; Duan et al. 2010). (B) The intrinsic nanochannel

conductance for divalent electrolytes MgCl2 and CaCl2 shows surface charge

governed behavior similar to monovalent electrolytes for (푐푏푢푙푘 < ~0.1 mM. The

conductance decreased at 푐푏푢푙푘 ≈ ~1 mM for MgCl2 and 푐푏푢푙푘 ≈ ~3.33 mM for

CaCl2. The decrease in conductance is likely due to adsorption of divalent cations to

the negatively charged walls as described in the main text. The dashed lines are

intended as eye-guides only...... 174

Figure 55: A representative plot of the measured current v. gate voltage as a function of

cation type for 10 mM KCl, 10 mM NaCl, 3.33 mM CaCl2, and 3.33 mM MgCl2.

The ionic strength of the electrolyte solutions was matched to ensure consistent

xliv

values of the Debye length or the characteristic screening length of the surface

potential, across cases. For all cases 푉푎 = 3 V...... 177

Figure 56: The conductance ratio as a function of cation type. The conductance ratio

퐺푔/퐺푎 is a non-dimensional parameter that compares the gated nanochannel

conductance, 퐺푔, to the intrinsic nanochannel conductance, 퐺푎. For all

measurements, the gate was located at 퐿푔= 0.43 ± 0.02 (Fuest et al. 2015). (A) The

maximum conductance ratio was observed at the transition concentration for KCl

and NaCl, in agreement with previous reports for KCl and HCl (Fan et al. 2008;

Nam et al. 2009). (B) Local minimums of the conductance ratio for divalent ions

correspond to the transition concentration where cation adsorption reduced the

magnitude of 𝜎 (c푎 = 0.1 mM for MgCl2 and c푎 = 1 mM for CaCl2). Cation

adsorption to the charged glass (and PDMS) walls regulates the surface charge

density thus preventing the gate electrode from altering the surface charge density.

The dashed lines are intended as eye-guides only...... 180

Figure 57: (A) The measured intrinsic nanochannel conductance as a function of

electrolyte composition for a fixed ionic strength of 1 mM. The estimated values are

based on the intrinsic nanochannel conductance of 1 mM KCl assuming a constant

surface charge density and that the ratio cations in the bulk is preserved in the

nanochannel (Equations 44 to 48). The constant surface charge assumption fails to

predict experimentally measured conductance (B) The deduced surface charge

density ratio as a function of electrolyte composition calculated using the measured

intrinsic nanochannel conductance at each electrolyte composition and Equations 46,

xlv

47, and 49. The surface charge density for each electrolyte composition (𝜎퐸퐶) is

shown relative to the surface charge density for the 0% CaCl2, or 1 mM KCl, case

2+ (𝜎0). The surface charge density decreases with the introduction of Ca and

+ remained constant with K concentration for % CaCl2 ≥ ~25%...... 183

Figure 58: The gated conductance and conductance ratio (퐺푔/퐺푎) as a function of

electrolyte composition at a fixed ionic strength of 1 mM. (A) The gated

nanochannel conductance decreased as % CaCl2 was increased from 0% to 25%,

consistent with the trend for intrinsic conductance as a function of electrolyte

composition. Similar to the decrease in intrinsic conductance, decrease in gated

conductance was attributed to Ca2+ adsorption. The drop in gated conductance

between 0% CaCl2 (1 mM KCl) and 25% CaCl2 was only 43% compared to 68% for

the intrinsic nanochannel conductance. (B) The conductance ratio (퐺푔/퐺푎) showed

that gate modulation decreased with % CaCl2 greater than 25%, with an

approximately constant value of 퐺푔/퐺푎 beyond 25% CaCl2, suggesting that with

surface charge regulated by ion adsorption, the gate is limited in modulating the

dielectric/fluid potential...... 187

Figure 59: The surface charge density calculated from the SBM for a 1:1 and a 2:1

electrolyte solution (A) The predicted surface charge density for a 1:1 electrolyte

using KCl as representative case. The case of only surface site deprotonation (black

line) is compared to a site binding model that accounts for neutralization of surface

sites via adsorption of K+ ions (green, red, blue curves). For a given 푝퐾1, ion

adsorption becomes significant at more basic pH as 푝퐾푀 increases. (B) The xlvi

predicted surface charge density for a 2:1 electrolyte using CaCl2 as a representative

case. Site binding reactions between Ca2+ either neutralize a surface site or reverse

the polarity of an individual surface site. The black curve considered only surface

site deprotonation while the pink, green, and blue curves consider both adsorption

2+ mechanisms of Ca . For a given 푝퐾1 = 8.5, 푝퐾퐷1 = 2.5, ion adsorption becomes

significant at more basic pH as 푝퐾퐷2 increases. Note, equilibrium constants for most

surface reactions are unknown and were therefore used as fit parameters to

experimental data (Sverjensky 2006; Datta et al. 2009)...... 196

Figure 60: Use of solution pH to modify surface charge density and the effect on intrinsic

and gated nanochannel conductance. (A) Intrinsic nanochannel conductance as a

function of pH for 1 mM KCl and 0.33 mM CaCl2 with equivalent ionic strength for

both solutions. Since conductance is proportional to the surface charge density,

Equation 39 was used to calculate the intrinsic conductance using the calculated

surface charge density from the site binding model (SBM). Equilibrium constants

used as fit parameters for the model are listed in the legend (Sverjensky 2006; Datta

et al. 2009). The site binding model accurately described the conductance behavior

of the nanochannel for 1 mM KCl and 0.33 mM CaCl2 at pH ≥ 6. Below pH 6 the

experimental conductance of CaCl2 filled channel increased as pH decreased to 2.

The site bonding model combined with Equation 39 for 퐺푎 considering only

2+ conductance of Ca failed to predict the observed increase in conductance for CaCl2

at pH = 2. However, a numerical model with 4 ionic species that includes mobility

+ of H captured the increase in 퐺푎 for CaCl2 as discussed below. The model with 4

xlvii

ionic species yields incorrect theoretical prediction for the anomalous transport of

KCl, which does not show an increase in conductance at highly acidic pH (pH = 2).

(B) Gated conductance as a function of pH for 1 mM KCl and 0.33 mM CaCl2. A

local maximum for the gate conductance was observed at pH = 8. The gated

conductance increased between pH 4 and pH 2 for CaCl2 in agreement with

observed trends for intrinsic nanochannel conductance as a function of pH. The

dashed lines are intended as eye-guides only...... 198

Figure 61: A schematic of the micro- nanofluidic system modeled with COMSOL

multiphysics. Due to the low aspect ratio of the nanochannel (width >> height) the

system can be modeled in two dimensions (Conlisk 2013). The inlet and outlet

reservoirs, which correspond to the near-infinite reservoirs represented by the

microchannels in the fabricated device, were 500 nm long and 250 nm tall. The size

of the channel in the model was 16 nm deep x 2.5 mm long to match the dimensions

of the fabricated device. The concentration in the inlet and outlet reservoirs was set

to the bulk electrolyte concentration with all four species considered (that is K+, Cl-,

- + 2+ - - + OH , and H for KCl and Ca , Cl , OH , and H for CaCl2) for ionic transport. Inlet

microchannel was set to 5V while the outlet microchannel was grounded to match

the experimental case for 푉푎 = 5V. The location where the concentration and

potential boundary conditions were imposed is indicated with the red arrow in the

schematic. The surface charge density for each pH was imposed on all surfaces

marked with the dark grey line (reservoirs and nanochannel) with the magnitude set

according to the site binding model (SBM) as discussed below...... 201

xlviii

Figure 62: The calculated conductance from COMSOL Multiphysics. The surface charge

density used for each of the three cases for KCl are given in Table 11 while the

surface charge density used for the CaCl2 case is given in Table 12. No difference

was observed between the homogenous case (𝜎푃퐷푀푆 = 𝜎푆𝑖푙𝑖푐푎 = 𝜎푆퐵) and the case

where the average surface charge density was preserved ((𝜎푃퐷푀푆 + 𝜎푆𝑖푙𝑖푐푎)/2 =

𝜎푆퐵)...... 206

Figure 63: The micro-nanochannel gated device has been considered analogous to solid-

state electronic devices, therefore, the gate electrode-dielectric-electrolyte interface

was modeled in terms of capacitors in series, similar to a previous report by Jiang

and Stein (Jiang et al. 2010)...... 209

Figure 64: Predicted values of the surface charge at the dielectric-electrolyte interface

from the gated nanochannel model with and without ion adsorption. The non-

linearity in the surface charge density v. gate voltage plot is caused by surface

buffering. Surface buffering is a shift in the equilibrium deprotonation state of the

surface. The gate electrode is tuning the point of zero charge to a higher pH

compared to pH in the ungated case, consistent with results from Jiang et al.(Jiang et

al. 2010) A clear maximum change in the slope of the surface charged density v.

gate voltage plot was observed for the pH 2 and 4 case. The case of surface site

deprotonation with the possibility of monovalent ion adsorption. Surface buffering is

not observed for pH 2 and pH 4...... 212

xlix

Figure 65. A schematic representation of the channel network. The color coded and

labeled locations are used to identify the location where SEM and micrograph

images were taken in the following figures...... 255

Figure 66. An SEM image of the fluidic reservoir etched into the borosilicate substrate.

The location of the reservoir is marked by box A in Figure 65...... 256

Figure 67. An SEM image of the interface between the fluidic reservoir and the

microfluidic channel. The location of the reservoir is marked by box A in Figure 65.

...... 256

Figure 68. An SEM image of the bend in the microchannel. The location of the

microchannel bend is denoted by box B in the schematic shown in Figure 65...... 257

Figure 69. An SEM image of the bend in the microchannel. The location of the

microchannel bend is denoted by box B in the schematic shown in Figure 65...... 257

Figure 70. An SEM image of the micro- and nanochannel interface showing two 227 nm

deep nanochannels. The small etched region on the bottom of the microchannel

denoted by the two light blue arrows occurs when the nanochannel is slightly

misaligned. The photoresist in the microchannel is then exposed and the bottom of

the microchannel is etched to the same depth of the nanochannel. Despite the slight

misalignment, this channel slide had nanochannels that connected the right and left

microchannels...... 258

Figure 71. SEM image of a microfluidic channel etched for 8 minutes in 4:1 DI water to

49% HF...... 258

Figure 72. Micochannel etch plot. The depth of the microchannel was measured after

exposure to 4:1 DI Water to 49% HF with a profilometer...... 259

Figure 73. Patches of unetched SiO2 after exposure to 10:1 buffered oxide etchamt. The

etched channel was 16 nm deep. The Cr/Au metal etch mask was not removed. A

notch defect in the metal etch mask can be observed in the upper inset. The unetched

areas occur from “micromasking” from portions of the Cr/Au metal mask that were

not completely removed during lithography and Au/Cr etching of the nanochannel

pattern. The image demonstrates the necessity of over etching Au/Cr masking

layers...... 260

Figure 74. The electrode height was measured with an Asylum MFP-3D AFM. The

electrode height was 29 ± 2 nm (nominal height 25 nm). The scan size was 4 μm x

5 μm ...... 261

Figure 75. An SEM image of a patterned electrode on a glass substrate that has been

sliced to expose the thickness of the metal layers. The locations of the electrode, the

glass substrate, and the cut line are labeled on the image...... 261

Figure 76. An SEM image of a patterned electrode on a glass substrate that has been

sliced to expose the thickness of the metal layers. The image was taken near the cut

line in Figure 75...... 262

Figure 77. Axial voltage sweep performed for an “open” circuit. Instruments and test

leads were all connected with test leads placed inside an Earth grounded Faraday

cage. The test leads were not connected to the micro- and nanofluidic device. The

average “noise” current was 0.15 ± 0.02 pA...... 263

Figure 78. A gate voltage sweep was performed on a dry micro- and nanofluidic device to

characterize the noise of the measurement system. Gold wires were inserted into the

dry reservoirs and a potential of 3V was set to the axial power supply. The gate

electrode was connected to the gate power supply and the gate potential was swept

from 0 to 10V and then from 0V to -10V. The current does not show any

dependence on the applied gate potential and has an average value of 0.14 ± 0.08

pA. The noise measurement confirms that there are not any unexpected current paths

inherent to the experimental setup...... 264

Figure 79. Rinsing a micro- nanofluidic device with 1 mM KCl. The previous data run

was done with DI water. Data was used after rinsing the channel 3x with 1 mM KCl

to ensure the nanofluidic channels were filled with the appropriate electrolyte

concentration ...... 265

Figure 80: Exploded view schematics of the two major device designs used in this

dissertation. Design 1 was used in Chapters 3 and 4 while Design 5 was used in

Chapter 5. It should be noted fabrication processes detailed in Chapter 3 and

Appendix C were not affected by the design change...... 266

lii

Chapter 1: Introduction

1.1 Motivation

Since the 1990s, there has been a growing interest in developing lab-on-a-chip systems, or miniaturized devices that perform several processes that would typically require bench top sized equipment on a single chip, for applications such as biodetection, biotechnology, chemical and biological reactors, and medical, pharmaceutical, and environmental monitoring (Harrison et al. 1993; Kopp et al. 1998; Prakash et al. 2012;

Swaminathan et al. 2012; Guan et al. 2014). The success of lab-on-a-chip technology relies on the ability to manipulate ion and molecules in increasingly small volumes of fluid (nL and less). Many technological demonstrations have shown manipulation of ions and biomolecules at femtoliter volumes (Karnik et al. 2005) for biosensing (Huo et al.

2011; Prakash et al. 2012), sample concentration (Kim et al. 2010), molecular sorting (Ai et al. 2010), and separations (Kim et al. 2010; O’Hern et al. 2014) moving towards the still elusive goal of mimicking the exquisite ion transport control found in biological systems (Siwy et al. 2002; Gouaux et al. 2005; Sparreboom et al. 2009; Guan et al.

2011).

Ion channels and ion-pumps form the basis of nearly all cellular communication and electrolyte transport for maintaining essential cell functions (Huo et al. 2011; Duan et

al. 2013 ). Numerous efforts have been made to develop ‘smart’ nanostructures to understand and implement operational principles of their biological counterparts with applications in bio- and chemical sensing (Stern et al. 1997), drug delivery (Duan et al.

2013 ), and energy conversion systems (Wen et al. 2010). Ion channels have three essential capabilities i.) ion selectivity, ii.) preferential direction of charge transport (i.e. ion current rectification), and iii.) gating or the ability to switch on and off transport (Huo et al. 2011; Duan et al. 2013 ). Transport through nanoscale conduits is governed by surface fluid interactions due to the high surface area to volume ratio. Efforts to capture exquisite ion transport control therefore rely on modification of surface properties such as surface charge as well as conformal changes to functionalized molecules on the nanopore/nanochannel wall that alter the internal pore geometry (Hou et al. 2011;

Tagliazucchi et al. 2015).

Several previous efforts have focused on chemical surface modification of nanofluidic elements (nanochannels or nanopores) to achieve ion transport control, where the modified surface responds to pH, temperature, pressure, or light among other parameters to initiate the flow modulation. Voltage-gated nanofluidic devices, geometrically analogous to semiconductor field effect transistors, are an attractive platform for applications that involve transport control over charged species in a small volume of fluid as electrodes embedded in nanofluidic elements can be used to actively tune surface properties post-fabrication over a short time scale (~ µs) (Hou et al. 2011).

Ion selectivity has been achieved by sign of the charged species in voltage-gated

nanofluidic pores (Nishizawa et al. 1995) and modulation of nanochannel conductance (a fundamental step towards channel gating) was first experimentally demonstrated by

Karnik et al.(Karnik et al. 2005) with current switching or full gating demonstrated by

Fuest et al. (Fuest et al. 2015).

A schematic of the general geometry of a voltage-gated nanofluidic device is shown in Figure 1. A gate electrode is embedded in the nanochannel wall, separated from the fluid in the channel by a dielectric layer. The nanochannel height ranges from

1-100 nm while the length may be 100’s of nm to mm. A potential applied to the gate electrode tunes the electrostatic properties at the dielectric / electrolyte interface thus enabling control over ionic transport through the nanofluidic conduit.

Gate Gate Dielectric

Inlet Outlet h Reservoir Reservoir

Figure 1: A schematic of the general geometry of a gated nanofluidic device. A nanofluidic channel is positioned to between an inlet and outlet reservoir. The height of the channel (ℎ) ranges from 1-100 nm. The length of the nanochannel (퐿) can range from 100’s of nm to mm. A gate electrode embedded in the nanochannel wall is separated from the fluid in the channel by a dielectric layer.

1.2 Specific Aims of this Research

Before specific applications can be realized, reliable fabrication techniques for gated nanofluidic devices that are versatile enough to incorporate various elements of device design need to be developed. In addition, further insight into the physical mechanism of ionic transport regulation in a gated nanofluidic device is required. The primary goal of this dissertation is to fabricate, characterize, and report on a voltage- gated nanofluidic device for active, tunable ion transport control. Ion transport was quantified in terms of the measured current through the gated nanofluidic device.

Changes in electrokinetic transport were determined by monitoring changes in the measured current caused by the gate electrode.

The nanofluidic device layout is based on the hypothesis that a gate electrode isolated from the fluid by a dielectric layer can be used to control the electric field and, therefore, the ionic transport through the nanofluidic channels. Initial device testing was performed with a monovalent symmetric electrolyte (KCl) to test the hypothesis by systematically altering the applied axial and gate potentials and the location of the gate electrode. The ability of the gate electrode to influence the ionic transport was further investigated as a function of the Debye length, or the characteristic screening length of the nanochannel surface potential.

Ionic transport through gated and ungated devices was then investigated as a function of cation type of the electrolyte solution. Nearly all reports to date on ionic transport through gated nanofluidic devices have used monovalent symmetric electrolytes

with the majority of experimental and modeling studies focusing on transport of KCl

(Karnik et al. 2005; Fan et al. 2008; Kalman et al. 2009; Liu et al. 2010; Liu et al. 2010;

Jin et al. 2011; Shin et al. 2012; Singh et al. 2012; Pardon et al. 2013; Guan et al. 2014;

Lee et al. 2015), and limited evaluation of HCl (Fan et al. 2008; Joshi et al. 2010) and glycine-based buffer solutions (Jiang et al. 2011). The effect of local variation of electrostatic properties in nanoscale conduits on transport of polyvalent electrolytes and electrolyte mixtures, which form the basis for most actual biological systems or practical applications, has not yet been reported. A systematic investigation was performed on two monovalent electrolytes (KCl, NaCl), two divalent electrolytes (MgCl2 and CaCl2), and electrolyte mixtures of KCl and CaCl2 to investigate the effect of local changes in the electrostatic surface state on ionic transport as a function of cation type.

The specific aims of this dissertation are:

1. Develop a fabrication sequence for gated nanofluidic devices that relies on UV

lithography, wet etching, and oxygen plasma bonding techniques to yield sealed

channels with a sub-20 nm critical length scale. The device layout incorporates

multiple electrodes at engineered locations along the nanochannel length.

2. Use an embedded surface electrode that is isolated from the fluid by an

electrically insulating layer to demonstrate control of ionic transport in the

electrolyte solution through flow gating. Flow gating will be demonstrated

through switching the current on and off for a fixed axial potential using an

embedded gate electrode.

3. Perform a parametric study to test the hypothesis that a gate electrode isolated

from the fluid by a dielectric layer can be used to control the electric field and,

therefore, the ionic transport through the nanofluidic channels. Parameters that

will be investigated include the Debye length, or characteristic screening length of

the surface potential, the ratio of the transverse electric field from the gate

electrode to the axial electric field, the magnitude of the applied potential to the

gate electrode, and the electrode location along the channel length.

4. Demonstrate cation dependent transport based on the magnitude of the cation

valence (i.e. greater flux of K+ compared to Ca2+ flux through the nanochannel).

The ion dependent transport will be shown through current measurements of

single electrolyte solution (KCl, NaCl, CaCl2, and MgCl2) and mixtures.

5. Develop a site binding model to investigate the role of ion adsorption in

regulating the surface charge density in both gated and ungated nanofluidic

channels as a function of cation type and pH.

6. Perform a parametric study to investigate the change in measured current induced

by the gate electrode as a function of cation type for single electrolytes and

electrolyte composition of mixtures. The parametric study will test the hypothesis

that the surface charge is regulated by ion adsorption as a function of cation type.

Ion adsorption, therefore, limits the ability of the gate electrode to modulate the

ionic transport.

This dissertation is organized as follows. Background information is provided in

Chapter 2. Chapter 3 contains a description and the rational for the device layout as well as details on the development of the fabrication procedures. Characterization of the functional micro- nanofluidic device with embedded surface electrodes is given at the end of Chapter 3. Current switching, or the ability to control both the magnitude and the direction of the current through the nanochannels for a fixed axial potential by tuning the potential applied to the embedded electrode is presented in Chapter 4. The dependence of the current switching behavior on KCl concentration, the magnitude of the applied axial and gate potential, and the gate location is discussed. Chapter 5 contains a study on cation dependent transport through gated nanofluidic channels. Individual electrolytes (KCl,

NaCl, CaCl2, and MgCl2) are studied along with electrolyte mixtures and solution pH. A site binding model is presented, verifying ion adsorption has a significant effect on the magnitude of the surface charge density as a function of cation type and pH. Conclusions and contributions are found in Chapter 6. Finally, suggested future work is given in

Chapter 7. For convenience, a summary of the abbreviations and nomenclature used in this dissertation is given in Appendix A.

Chapter 2: Background

This dissertation focuses on the fabrication and characterization of a gated nanofluidic device for active, tunable control of electrokinetic transport through the nanofluidic channels. Before discussing the device layout and open questions based on state-of-art knowledge in the published literature, a brief background on essential concepts in nanofluidics is presented. Next, an overview of previous studies on ionic transport control in gated nanofluidic devices is presented. The discussion on functionality of nanofluidic devices is followed by an overview of common fabrication procedures used to realize nanofluidic devices and how those procedures have been adapted to incorporate embedded electrodes.

2.1 Nanofluidics

Nanofluidics is defined as the transport of fluid in or around objects with at least one dimension between 1-100 nm (Prakash et al. 2008; Prakash et al. 2014) . In this dissertation, nanoscale conduits or nanofluidic architectures are broadly classified into nanopores and nanochannels. Nanopores have an elliptical or circular cross section with at least one dimension between 1-100 nm. Nanopores are generally cylindrical, conical, or cigar-shaped, where the nanopore length can vary from 100’s of nm to 100’s of µm.

Nanochannels have a rectangular cross section with one dimension (typically the height)

ranging from 1-100 nm. The width of the nanochannel can be on the same order as the height (aspect ratio of ~1), much greater than the nanochannel height, typically on the order of a few µm’s (low aspect ratio channels), or the height can be on the order of µm’s and the width ranging from 1-100 nm (high aspect ratio channels).

Due to the characteristic length scale in nanofluidic channels, steric and hydration effects (~ 1-2 nm) (Qiao et al. 2003), van der Waals interactions (~ 1-50 nm) (Singh et al.

2011; Singh et al. 2012), and electrostatic interactions (Debye length ~ 1-100 nm) can effect overall system behavior, resulting in deviations from the macroscale fluid behavior. The high surface area to volume ratio characteristic of nanofluidic channels leads to dominance of surface-fluid interactions which govern net transport through the nanochannels. This chapter begins with a summary of relevant theory of ionic transport at the nanoscale.

2.1.1 Surface Charge

Deprotonation / Protonation of Oxide Surfaces

Surfaces in contact with an aqueous solution often attain a net surface charge by dissociation of surface groups or through adsorption of ions from the solution

(Israelachvili 1992). SiO2, which is a commonly used material for micro- and nanofluidic devices, including devices discussed in this dissertation, attains a net negative surface charge when placed in contact with an aqueous solution through the dissociation of silanol groups (Israelachvili 1992; Conlisk 2013). The general form of deprotonation/

protonation reactions for oxides in contact with an aqueous electrolyte solution is given by (Parks 1965; Israelachvili 1992)

−푀푂− + 퐻+ ⇔ 푀푂퐻 (1)

−푀푂 + 퐻+ ⇔ 푀푂퐻+ (2)

- + Using SiO2 as an example, surface silanol groups (SiOH) deprotonate to form SiO and H .

The concentration of protons ions relative to OH- determines the pH of the solution

(Behrens et al. 2001).

For a glass or silica surface, the net surface charge density is a function of the pH of the aqueous solution in contact with the surface. The presence of H+ at the silica- solution interface determines the extent of surface silanol group dissociation, dictated by the dissociation constant (pK). The pH at which the number of positively charged surfaces cites is equal to the number of negatively charged surface cites is known as the isoelectric point, with the surface presenting no net charge (Cheng et al. 2009). At pH greater than the isoelectric point the surface has a net negative charge and below it has a net positive charge. The isoelectric points of several oxide materials are summarized in

Figure 2 (Cheng et al. 2009).

Fluid flows through micro- and nanofluidic channels are generally driven by an electric field making insulating substrates preferable for device fabrication to avoid

extraneous current paths. The isoelectric points are therefore plotted as a function of energy band gap where materials with higher band gaps are better insulating materials.

Figure 2: The isoelectric point, or the point where the net surface charge density is zero, as a function of bandgap energy. Due to the high surface area to volume ratio in nanofluidic flows, ionic transport through the nanofluidic architectures is governed by the surface charge, which is a function of pH. Insulating materials are desired for nanofluidic substrates to avoid extraneous current paths during current measurements. Materials with a higher bandgap are better insulating materials. Reprinted with permission from Cheng, L. J. and L. J. Guo (2009). Ionic Current Rectification, Breakdown, and Switching in Heterogeneous Oxide Nanofluidic Devices. ACS Nano 3(3): 575–584. Copyright 2009 American Chemical Society.

Origin of surface charge of polymers

In contrast to oxides, the surfaces of polymers such as poly dimethylsiloxane

(PDMS), polycarbonate (PC), and polymethylmethacrylate (PMMA) were thought to be electrically neutral at pH 7. Experimental measurements of the zeta potential in

microfluidic channels, however, indicated that the surface charge is negative with an isoelectric point between pH 2 and 4, similar to SiO2. The exact charging mechanism of hydrophobic polymer substrates has been the subject of debate, as experimental measurements give the magnitude and sign of the diffuse layer or surface charge, but do not allow direct measurement of the chemical charging mechanism.

Empirical experimental results along with molecular dynamics (MD) simulations suggest polymers obtain a net negative charge through the adsorption of hydroxide ions to the channel walls. MD simulations indicate that water molecules at the interface between water and a hydrophobic surface are orientated with their hydrogen atoms pointing towards the low dielectric phase (polymer), creating an electric field gradient in the first several layers of water (Dang et al. 2002; Mamatkulov et al. 2004; Vacha et al.

2008). The electric field leads to enhanced autolysis of water, or the breakdown of H2O

+ - molecules to hydronium (H3O ) and hydroxide ions (OH ) ions (Beattie 2006). Under the influence of the electric field, the hydroxide ions are attracted to the surface and the protons are repelled, generating a net negative surface charge density due to the adsorption of the hydroxide ions to the surface (Beattie 2006; Vacha et al. 2008).

While the mechanism by which polymers obtain a net surface charge density is not well described as a function of pH, several efforts have focused on measuring the surface charge density under a variety of experimental conditions. Experimental measurements, reviewed by Kirby et al. (Kirby et al. 2004), indicate that the surface charge of silica and poly dimethylsiloxane (PDMS) are approximately equivalent as a

function of pH. Therefore, in this dissertation, the surface charge density of glass and

PDMS, which comprise the surfaces of the nanofluidic channels exposed to the electrolyte solution, is assumed to be equivalent.

2.1.2 Electric Double Layer

To compensate for the surface charge, a region of counter ions with an opposite polarity to the surface charge develops at the solid-liquid interface (Schoch et al. 2008;

Pardon et al. 2013). The region of the electrolyte where the concentration of counter ions exceeds the concentration of co-ions is known as the electric double layer (Sparreboom et al. 2009). The Gouy-Chapman model of the electric double layer assumes that the surface charge is a continuous average value over the entire surface, the ions are treated as point charges, and the solvent is a dielectric medium with constant permittivity (Schoch et al.

2008). Stern added to this model a layer adjacent to the charged surface to account for the finite size of ions and the fact that the ions closest approach to the surface is on the order of the ionic radius. The Stern layer consists of ions adsorbed to the channel wall and bound, hydrated or partially hydrated ions (Prakash et al. 2008; Schoch et al. 2008;

Pardon et al. 2013). The inner Helmholtz plane is defined as the average position of the charge center of adsorbed ions which is approximately one ionic radius from the surface

(Pardon et al. 2013). The outer Helmholtz plane is the averaged position of the charge center of hydrated and partially hydrated ions at their closest approach to the charged surface (Pardon et al. 2013). Together the adsorbed and bound, hydrated or partially

hydrated ions comprise the Stern layer in the classical description of the electric double layer.

Outside of the Stern layer is the diffuse layer, which is comprised of mobile, hydrated counterions and co-ions. The potential drops from the surface across the inner and the outer portions of the Stern layer are linear (Schoch et al. 2008; Pardon et al.

2013). The potential at the interface between the Stern and diffuse layers is defined as the zeta (ζ) potential, where the potential decays exponentially across the diffuse layer to the electrically neutral “bulk” region (Prakash et al. 2008; Prakash et al. 2012; Conlisk 2013;

Prakash et al. 2014). The structure of the electric double layer as described by the Gouy-

Chapman-Stern model is shown schematically in Figure 3 (Prakash et al. 2008; Prakash et al. 2014).

The characteristic length scale of the electric double layer (EDL) is the Debye length. The Debye length (Abgrall et al. 2008) is the distance from the surface where the potential has dropped by 1/푒1, given by

휀 푅푇 푒 (3) 휆퐷 = √ 2 퐹 퐼푆

where 휀푒 is the permittivity of the medium (often water), 푅 is the universal gas constant,

푇 is the temperature, 퐹 is Faraday’s constant, and 퐼푆 is the ionic strength of the electrolyte. Here, the ionic strength of an electrolyte solution is

푚 2 퐼푆 = ∑ 푧𝑖 푐𝑖 (4) 𝑖=1

where 푚 is the number of charged species in the electrolyte, 푧𝑖 is the valence of a species

𝑖, and 푐𝑖 is the concentration of a species 𝑖 (Conlisk 2013).

Figure 3: A schematic representation of the Gouy-Chapman-Stern model of the electric double layer. The Stern layer is comprised of adsorbed ions followed by bound, hydrated, and partially hydrated ions. The diffuse layer consists of mobile hydrated ions. The potential at the interface between the Stern and diffuse layers is known as the zeta (휁) potential. Reprinted with permission from Prakash, S., A. Piruska, E. N. Gatimu, P. W. Bohn, J. V. Sweedler and M. A. Shannon (2008). Nanofluidics: Systems and Applications. IEEE Sens. J. 8(5): 441-450. Copyright 2008 IEEE.

Typical Debye lengths range from about 0.1 nm-100 nm with larger Debye lengths corresponding to lower concentrations (Abgrall et al. 2008). From Equation (3,

the Debye length has an inverse square root dependence on bulk ionic strength. The thickness of the electric double layer, defined as the distance from the charged surface to the electrically neutral “bulk” electrolyte solution, is approximated as 3-4x 휆퐷 (Conlisk

2013; Prakash et al. 2014).

As channel sizes decrease, the EDL extends through a larger portion of the channel. In nanofluidic channels with critical dimensions between 1-100 nm, the EDLs can interact from each wall at low (≤ ~10 mM, as function of nanochannel size) concentrations and the resulting potential charge in the bulk is no longer neutral. In the case of strongly overlapped EDLs, co-ions are excluded from the channel (Donnan 1995) leading to ion-permselectivity. A detailed discussion on the effect of the overlapped or interacting electric double layers on ionic flux is discussed in Section 2.2. This section further details how electric double layer overlap affects the operation of gated nanofluidic devices.

A schematic representation of the electric double layer under overlapped and non-overlapped conditions is shown in Figure 4. Bulk electrolyte concentrations of

0.1 mM KCl and 100 mM KCl were used for the representative cases of overlapped and non-overlapped EDLs respectively. Plots of the concentration of K+ and Cl- as well as the potential along the y-direction in a negatively charged channel were generated using

COMSOL Multiphysics.

Overlapped Electric Double Layers Non-Overlapped Electric Double Layers

y -0.081 3.5 0 108 x + + K 106 K -0.082 3 - -

Cl ) Cl (mM) -0.083 (mM) 2.5 -0.0004 104

(V) 102 -0.084 2 -0.0008 100 -0.085 1.5 98 -0.086 1 -0.0012 96

-0.087 0.5 (V Potential 94 Potential

-0.088 0 -0.0016 92 Concentration Concentration -8 -3 2 7 Concentration -8 -3 2 7 -8 -3 2 7 -8 -3 2 7 Height (nm) Height (nm) Height (nm) Height (nm)

Figure 4: A schematic representation of overlapped and non-overlapped electric double layers. The plots represent the K+ and Cl- concentration and the potential in the nanochannel with 0.1 mM KCl for the overlapped case and with 100 mM KCl for the non-overlapped case generated using COMSOL Multiphysics. In the case of overlapped electric double layers, the concentration of K+ ions exceeds the concentration of the Cl- through-out the depth of the nanochannel. The potential at the channel centerline is not electrically neutral. In the non-overlapped case there is an excess of cations near the wall, but the concentrations of K+ and Cl- are equivalent to their bulk values at the channel centerline. The channel is electrically neutral at the centerline. Plots used with permission from Kaushik K. Rangharajan.

In the case of non-overlapped electric double layers, the potential in the channel decays from a negative value at the charged wall to zero in the bulk, where there is an equivalent concentration of potassium and chloride ions. In contrast, in the case of overlapped electric double layers, the channel has a higher concentration of potassium ions in the entire nanochannel depth, and the potential at the channel centerline has a net negative value. The potential drop between the surface and the nanochannel centerline is much smaller in the case of overlapped double layers, with values of 5 mV and 16 mV for the overlapped and non-overlapped cases respectively. The implications of the smaller

potential drop between the nanochannel surface and the centerline for operation of gated nanofluidic devices will be discussed further in Chapter 4.

2.1.3 Donnan Potential

The ion selective nanofluidic architecture is in chemical equilibrium with the reservoir where the concentration of the electrolyte is equal to the bulk prepared concentration. In order for the chemical potentials to be equal, an electric potential difference arises between the charge-selective nanofluidic architecture and the reservoir.

This electrochemical equilibrium is known as Donnan equilibrium. The electrical potential difference between the reservoir and the charge selective nanochannel is given by (Schoch et al. 2008)

푏푢푙푘 푅푇 푐𝑖 휙퐷푂푁 = 푙푛 ( 푛푎푛표) (5) 푧𝑖퐹 푐𝑖

or in terms of the surface charge (𝜎) for a monovalent symmetric electrolyte such as KCl

(Chang et al. 2012)

푅푇 𝜎 푅푇 𝜎 𝜎 2 휙 = 푎푠𝑖푛ℎ ( ) = 푙푛 ( + √( ) + 1) (6) 퐷푂푁 퐹 퐹ℎ푐푏푢푙푘 퐹 퐹ℎ푐푏푢푙푘 퐹ℎ푐푏푢푙푘

When a concentration gradient exists across the charge selective nanofluidic architecture a membrane potential develops. The membrane potentials is comprised of the two Donnan potentials that exist at the interface of the channel with each respective reservoir and the diffusion potential which arises from differences in transference numbers of ions in the membrane. In this dissertation, the microchannel reservoirs are filled with electrolyte solutions of equal concentration. However, measurement of the potential difference between two reservoirs can be used to monitor the concentration difference between those two reservoirs (Li et al. 2015). Further discussion on the importance of the Donnan potential for experimental investigations in gated nanofluidic devices is given in the Chapter 7.

2.1.4 Ionic Transport through Nanofluidic Channels

Continuum approximation for modeling nanofluidic transport

The continuum approach for modeling nanofluidic transport relies on the Nernst-

Planck equation to describe mass transport, Poisson equation for the electric potential, and Navier-Stokes equation for the fluid velocity, where ions are considered point charges within the fluid. These three equations are highly coupled with mass transport depending on fluid velocity and species concentration, species concentration determined by the gradient in the electric field, and the fluid velocity dependent on the concentration of species and the electric field. The continuum approach is generally considered valid experimentally for channels greater than 10 nm deep and for simulated channels larger than 6 nm deep. Some studies impose the additional restriction that the channel depth

must be greater than two Debye lengths for the continuum approach to be valid for simulations (Singh et al. 2011; Singh et al. 2012).

In channels that fall outside of these limitations, molecular dynamics simulations are required to accurately model ionic transport. Generally, discrepancies between continuum and MD simulations are most evident near the channel walls (Zambrano et al.

2012). Discrepancies are likely caused by surface roughness and interactions of ions and molecules with the wall which can enhance effects related to the finite size of ions, the discrete nature of water molecules, hydration and partial hydration of ions, and the polar nature of water which are not captured in continuum calculations (Qiao et al. 2004;

Zambrano et al. 2012). MD and continuum calculations generally agree well in the

“bulk” fluid or in the first few nanometers away from the wall (Zambrano et al. 2012), leading to the overall limitation for continuum calculations to channels greater than 6 nm.

The nanochannels used in this dissertation have a depth greater than or equal to 16 nm, which falls within the continuum description of ionic transport.

Mass Flux

In electrically driven flows, there are three transport mechanisms which determine the total flux through the nanofluidic architecture: a diffusive term resulting from a gradient in species concentration, an electromigration term accounting for motion of charged particles under the influence of an electric field, and a convective component which originates from the bulk fluid flow. The total flux of the ith species, Ni, is given by

(Jin et al. 2007; Singh et al. 2012; Conlisk 2013)

푁𝑖 = −퐷𝑖∇푐𝑖 − 휇𝑖푧𝑖퐹푐𝑖∇휙 + 푐𝑖푢⃗ (7)

where 퐷𝑖 is the coefficient of diffusion, ∇푐𝑖 is the concentration gradient, 휇𝑖 is the ionic mobility, 푧𝑖 is the valence, 푐𝑖 is the concentration of each species i in the nanochannel, and 퐹 is Faraday’s constant, ∇휙 is the electric field, and 푢⃗ is the velocity of the fluid flow. The ionic mobility is given by Einstein’s relation, 휇𝑖 = 퐷𝑖퐹/푅푇, where 푅 is the universal gas constant, and 푇 is the temperature. The direction of the flux due to diffusion, electromigration, and convection are schematically shown in Figure 5 for the representative case of a positive particle in a positive nanopore.

The electric potential distribution, 휙, is governed by the Poisson equation (Jin et al. 2007; Singh et al. 2012; Conlisk 2013)

𝜌푒 ∇ ∙ (휀푅∇휙) = − (8) 휀0

where 휀푅 is the relative permittivity of the electrolyte solution, 휀0 is the permittivity of free space, and 𝜌푒 is the net space charge density.

Figure 5: A representative schematic showing the direction for each individual flux term (here 퐽 rather than 푁) for a positively charged particle (methylene blue) in a nanopore. The darker blue color indicates a higher concentration of methylene blue (MB). In this case, diffusive flux is expected to occur from left to right (high concentration to low concentration). Positively charged particles migrate towards the cathode under the influence of an electric field (electromigration, left to right). Since the channel is positively charged, there are an excess of negative ions compared to positive ions in the channel. The bulk fluid flow and, therefore, the convective flux is from right to left. If we consider the same system but substitute a negatively charged particle for the MB, the direction of convection and diffusion would remain the same, but the direction of electromigration would be reversed (towards the anode). Schematic used with permission from the authors of K. K. Rangharajan, Marie Fuest, A.T. Conlisk, S. Prakash (2015). Transport of Multicomponent, Multivalent Electrolyte Solutions across Nanocapillaries. Microfluidics and Nanofluidics, (in review).

The net space charge density is defined by (Jin et al. 2007; Conlisk 2013)

푚

𝜌푒 = 퐹 ∑ 푧𝑖푐𝑖 (9) 𝑖=1 where m is the total number of molecules of a species i. The potential distribution of the channel is a function of the externally applied axial potential and the surface charge density which will alter the net space charge density in the nanofluidic channel to satisfy

system electroneutrality (Jin et al. 2011). The gate potential embedded in the wall of the gated nanofluidic devices alters the surface charge density at the dielectric / electrolyte interface. To maintain electroneutrality, the gate electrode also alters the net space charge density in the channel (Karnik et al. 2005; Jin et al. 2011), as described in detail in

Section 2.2.

In electrically driven low Reynold’s number flows, such as in micro- and nanofluidics, the Stokes equation for fluid flow and the continuity equation for an incompressible fluid are used to describe the flow velocity and are given by (Jin et al.

2007; Conlisk 2013)

2 −∇푝 + 휂∇ 푢⃗ − 𝜌푒∇휙 = 0 (10)

∇ ∙ 푢⃗ = 0 (11)

where 휂 is the fluid viscosity and ∇푝 is the pressure gradient. In electrically driven flows in nanofluidic channels there is not typically an applied pressure difference. The gradient in pressure arises from gradients in concentration of species, particularly if the device design features an interface between micro- and nanofluidic channels, or an embedded gate electrode.

The Nernst-Planck equation describes the mass transfer of each species and is given by (Jin et al. 2007; Conlisk 2013)

훿푐 𝑖 = −∇ ∙ 푁 (12) 훿푡 𝑖

where the change in concentration with time will be zero for the steady-state case. In numerical simulations of nanofluidic transport the coupled Poisson (Equation (8), Nernst-

Planck (Equations (7 and 12), and Stokes equations (Equation (10) are solved to obtain the electric potential, ionic concentration, velocity, and pressure profiles in the system.

For comparison with experimental measurements, the current through the channel is calculated by integrating the ionic fluxes over the nanochannel cross section, (Jin et al.

2007) that is,

퐼 = ∫ ∑ 푧𝑖퐹푁𝑖푑푆 (13) 푆 𝑖

where S is the nanochannel cross section. Note the equations for ionic transport through nanofluidic channels detailed in this section (Equations (7 to 13) were solved using

COMSOL Multiphysics, with the calculated current (Equation 13) compared to experimental measurements to verify successful fabrication and operation of the micro- and nanochannel device reported in this dissertation (Chapter 3).

2.1.5 Velocity and Potential Profiles in Micro and Nanofluidic Channels

Due to the high surface area to volume ratio in both micro- and nanofluidics, the viscous forces dominate over the inertial forces, with Reynold’s number typically much smaller than 1. Stokes’ flow, which assumes the fluid is a continuum, the fluid is

Newtonian, and the fluid is incompressible, applies for channels larger than ~10 nm

(Sparreboom et al. 2010). For the case of Stokes flow driven by an electric field, the velocity profile follows the same profile as the potential along the depth of the nanochannel

(Conlisk 2013). In the thin electric double layer case, such as in microchannels, this leads to a plug-like velocity profile. For nanofluidic channels with overlapped electric double layers and a non-electrically neutral bulk the velocity profile is more parabolic.

Under the assumptions of laminar flow with constant fluid properties and thin electric double layers the electroosmotic velocity outside of the EDL is proportional to the zeta potential according to the Helmholtz-Smoluchowski equation (Conlisk 2013; Prakash et al. 2014)

휀 퐸 푢 = 푒 푥 (휁 − 휙) (14) 푥 휂

where 푢푥 is the fluid velocity along the channel length, 퐸푥 is the electric field applied along the channel length, 휙 is the potential in the fluid, and 휂 is the fluid viscosity which is usually assumed to be the viscosity of water. Since 휙 ≈ 0 in the bulk of the electrolyte solution, in the thin electric double layer limit the electroosmotic velocity is proportional

to the zeta potential. Micro- or nanoparticle image velocimetry (nPIV) is routinely used to measure the flow velocity in microchannels and subsequently estimate the zeta potential (Horiuchi et al. 2006; Datta et al. 2009).

Experimental measurements in nanofluidic devices are generally reported in terms of current (퐼) or nanochannel conductance (퐺푎) (the ratio of the current to the applied axial potential 퐼/푉푎) rather than in terms of velocity or flow rate. Due to the length scale of nanofluidic devices, optically based techniques used for measuring flow velocity in microfluidic channels are not practical. Particle image velocimetry (PIV) is limited by the wavelength typically to imaging in microchannels (Joseph et al. 2005). While imaging of the flow front of a fluorescent dye has been used to measure flow velocity in larger

(≥ ~ 100 nm) nanochannels (Oh et al. 2009), the fluorescence signal strength decreases with the amount of dye in the channel. Long exposures, on the order of 10’s of seconds, are required for fluorescence imaging of 30 nm channels (Karnik et al. 2005), which does not allow for an accurate measurement of flow velocity. The measured current is, therefore, the main quantifiable metric used to characterize the ionic transport through nanofluidic devices, where the relation between the current and ionic flux is given by

Equation 13.

Generally, experimental data is reported in terms of conductance (퐺푎), rather than current. At sufficiently low applied axial potentials where entrance effects at the reservoir

/ nanochannel interface do not have a significant impact on ionic transport (푉푎 < 150 V for the device reported in this dissertation), the current depends linearly on the applied

axial potential. Thus reporting the data in terms of conductance rather than current allows comparison of measurements taken at different axial potentials. More information on characterization of linear and non-linear 퐼/푉푎 regimes in nanofluidic devices is given in

Chapter 3.

2.1.6 Conductance of nanofluidic channels

Figure 6 (Stein et al. 2004) shows the conductance (퐺푎) of nanofluidic channels with various channel heights as a function of bulk electrolyte (KCl) concentration. KCl is a commonly used electrolyte solution for experimental and theoretical studies in nanofluidics because it is a monovalent symmetric electrolyte and the ionic mobility of

K+ and Cl- are approximately equivalent, which simplifies the analysis of results. The plot shows that there are two distinct conductance regimes. At “low” concentration

-3 (cbulk < ~10 M) conductance is independent of concentration while at high

-3 concentrations (cbulk > ~10 M) the conductance has a linear dependence on concentration as expected from bulk properties. The transition between the bulk transport and surface charge governed transport regimes occurs at the critical concentration,

-3 푐푡 ≈ 10 M.

From bulk properties the conductance is

(휇 + + 휇 −)퐹푐 푤ℎ 퐺 = 퐾 퐶푙 푏푢푙푘 (15) 푏푢푙푘 퐿

+ - where 퐺푏푢푙푘 is the bulk conductance, 휇퐾+ and 휇퐶푙− are the ionic mobilities of K and Cl respectively, 퐹 is Faraday’s constant, 푐푏푢푙푘 is the bulk electrolyte concentration, 푤 is the width of the nanofluidic channel, ℎ is the height of the nanofluidic channel, and L is the length of the nanofluidic channel. From the bulk properties the conductance is expected to increase linearly with channel height. Interestingly, the conductance in the low concentration regime only has a weak dependence on the channel height (Figure 6).

Figure 6: The conductance through nanofluidic channels of various heights as a function of bulk electrolyte concentration (KCl). The conductance is independent of concentration -3 at low bulk electrolyte concentration (푐푏푢푙푘 < ~10 M). At low concentration the number of charge carriers and therefore the conductance is determined the total surface charge. At high concentration the conductance has a linear dependence on both height and concentration as expected from bulk fluid properties and the channel dimensions. The transition between the bulk transport and surface charge governed transport regimes occurs -3 at the critical concentration, 푐푡 ≈ 10 M. . Adapted with permission from Stein, D., M. Kruithof and C. Dekker (2004). Surface-Charge-Governed Ion Transport in Nanofluidic Channels. Phys. Rev. Lett. 93(3): 035901. Copyright American Physical Society.

To maintain electroneutrality, the net charge in the nanochannel volume must be equal and opposite to the total charge on the nanochannel walls. In the low concentration

regime the number of charge carriers needed to maintain electroneutrality exceeds the bulk electrolyte concentration. The number of charge carriers in the nanofluidic channel, and therefore, the conductance is determined by the surface charge at low concentration according to the relation

2푤휇 + |𝜎| 퐺 = 퐾 (16) 푆퐶퐺 퐿

for KCl filled channels with a negative surface charge density, 𝜎. The relation 2푤𝜎/퐿 gives the total surface charge which must be balanced by equal and opposite net charge in the fluid volume. The total conductance (퐺푎) is given by the sum of Equations 15 and 16, where the dominant term will be determined by the bulk electrolyte concentration (Guan et al. 2014).

2.2 Gated Fluidic Devices

Gated fluidic devices, sometimes referred to as fluidic field effect devices, are micro- or nanofluidic devices that have a “gate” electrode in embedded in the wall of the fluidic architecture. For slit-like or rectangular channels the electrode is planar, forming a select portion of the length of the channel, located on one or, less commonly, two walls of the nanochannel. For cylindrical or conical pores, the gate electrode is annular, comprising the entire circumference over a certain length of the pore. The gate electrode is separated from the electrolyte solution in the channel by a dielectric layer. A potential applied to the gate electrode locally modifies the surface potential at the dielectric-

electrolyte interface. Since transport in micro- and nanofluidic channels can be controlled via the surface properties, the gate electrode allows tunable control over ionic transport in the fluidic channels. A schematic representation of a gated nanopore and a gated nanochannel device are given in Figure 7.

Gated Nanochannel Device Glass

Fluidic Channels

Gate Electrode

Gate Dielectric Gated Nanopore Device Silicon Wafer

Si3N4

Gate Electrode

Gate Dielectric

Figure 7: Schematic representation of a gated nanochannel and a gated nanopore device. The gated nanochannel device features two microchannels that serve as fluidic reservoirs to a nanochannel. The cross section of the microchannels and the side view of the nanochannel are shown in blue. Gold gate electrodes are embedded in the roof of the nanochannel and isolated from the fluid by a dielectric layer (pink). The gated nanopore device shows a silicon handle wafer (green) with a silicon nitride (light green) insulation layer. A fluidic reservoir was etched into the silicon handle wafer. The gate electrode (gray) forms the entire circumference over a certain length of the pore. The gate dielectric layer is shown in blue. Schematics were prepared using SolidWorks 2014. The geometries shown are an interpretation of the two general geometries found in literature. A review of specific device geometries and fabrication procedures is given in Section 2.4.

Gated microfluidic devices, or microfluidic field effect devices, were first introduced for modulation of electroosmotic velocity (Schasfoort et al. 1999). The potential applied to the gate electrode modifies the local surface potential and subsequently the local zeta potential which, in the thin EDL limit, is proportional to the electroosmotic velocity (Equation 14). Sufficiently high potential reverses the polarity of the zeta potential from negative to positive causing reversal of the electroosmotic velocity

(Schasfoort et al. 1999; Polson et al. 2000). The electroosmotic flow (EOF) was manipulated using two gate electrodes in a T-junction channel for flow valving, demonstrating the capability to manipulate fluidic transport using gated devices.

Gated microfluidic devices are limited to control over interfacial effects as the modulation of the surface potential does not typically affect the electrically neutral bulk

(Karnik et al. 2005). The potential needed to reverse the EOF increases with surface charge density. Generally, gated microfluidic devices are therefore limited to control over low pH electrolyte solutions because of the low surface charge density associated with low pH (Figure 2) (Schasfoort et al. 1999), thus limiting their applicability. In nanofluidics, the electric double layers overlap at low concentrations, leading to a smaller potential drop between the surface and the center of the nanochannel (Pardon et al. 2013)

(Figure 4). At low concentrations the conductance of nanofluidic channels is determined by the surface charge (Stein et al. 2004; Schoch et al. 2005), therefore, manipulation of the surface property can lead to direct electrostatic manipulation of ions throughout the depth of the nanofluidic channel (Karnik et al. 2005). Karnik et al. (Karnik et al. 2005)

presented the first experimental demonstration of a gated nanofluidic device with a gate electrode embedded in the wall of the nanofluidic architecture. The gate electrode modulated the conductance of both slit-like nanochannels and nanopores as a function of gate potential with a linear relationship between current and applied gate voltage. Further studies on concentration dependence of current modulation in gated nanofluidic devices found that the gate electrode is most effective at modifying the current at concentrations in the surface charge governed regime or near the critical concentration (Fan et al. 2008;

Nam et al. 2009; Guan et al. 2011; Fuest et al. 2015), supporting the hypothesis that the control over ionic transport via the gate electrode is maximized in conditions of electric double layer overlap.

The change in nanochannel conductance observed in gated nanofluidic devices was attributed to the change in the number of charge carriers (Karnik et al. 2005), or the concentration of species in the nanochannel. The gate potential alters the surface charge density at the dielectric-electrolyte interface (Singh et al. 2011; Xue et al. 2012; Yeh et al. 2012; Pardon et al. 2013). To maintain electroneutrality, the concentration of ions in the channel is altered (see Figure 8 for a schematic representation).

Karnik et al. (Karnik et al. 2005) qualitatively verified local changes in the concentration through fluorescence imaging of dye collection beneath an active gate electrode. The current voltage behavior followed a similar trend, where lower conductance corresponded to lower concentration of dye while a higher conductance corresponded to a higher concentration of dye in the channel. However, in contrast to the

linear current-gate potential relationship, the change in concentration of dye with gate potential was highly non-linear with nearly no change in concentration of negatively charged dye at negative gate potentials and significant increase in dye concentration with positive gate potential (Karnik et al. 2005).

Figure 8: A schematic representation of the hypothesized change in ion concentration in the nanochannel during gating to maintain electroneutrality. (A) Under ungated conditions with overlapped electric double layers the nanochannel walls are negatively charged and there is an excess of positively charged ions compared to negatively charged ions in the nanochannel. (B) When a positive potential is applied to the embedded gate electrodes fewer net number of positive of ions are required to maintain electroneutrality. (C) As the positive potential to the gate electrode is further increased, an excess of negative ions would be required.

Changes in concentration, particularly in the region of the channel below the gate electrode, were confirmed by modeling studies (Joshi et al. 2010; Guan et al. 2011; Jin et

al. 2011; Singh et al. 2011) with one report indicating the net space charge density could be reversed from positive (cation selective nanochannel) to negative (anion selective nanochannel) by the gate electrode (Jin et al. 2011). The reversal of pore selectivity from cation to anion selective was first experimentally demonstrated by Nishizawa et al.

(Nishizawa et al. 1995) in uninsulated gold coated nanopore membranes and recently deomonstrated by Lee et al. (Lee et al. 2015) who used a Al2O3 insulation layer on their gate electrode. The isoelectric point of Al2O3 is near pH 7 (Figure 2). The relatively low surface charge density enhanced the effect of the gate electrode compared to SiO2 channels, allowing the device to be tuned from cation to anion selective based on the polarity of the gate electrode.

2.2.1 Equivalent Circuit Analysis

Gated nanofluidic devices are sometimes analyzed in terms of an equivalent electrical circuit to perform analytical analysis of experimentally observed trends

(Albrecht 2011; Rutkowska et al. 2013). The gate electrode-dielectric-electrolyte geometry is considered an ideal capacitor where the entire gate potential, Vg, drops across the dielectric layer. The charge stored by the gate electrode-dielectric-electrolyte capacitor represents a change in concentration of charge carriers in the nanofluidic channel thus modulating the ionic current by altering the number of available charge carriers. The capacitance of a parallel plate capacitor is given by 퐶 = 휀푅휀0퐴푒/푡 and the total charge stored or change in concentration by 푄 = 퐶푉푔. For a given dielectric material, the effect of the capacitive coupling of the gate electrode and the nanofluidic

channel will be enhanced by increasing the area of the wall covered by the gate electrode,

Ae, decreasing the thickness of the dielectric layer, t, and increasing the potential difference applied Vg.

Real dielectrics, however, permit a finite gate leakage current, or a current path from the nanofluidic channel through the dielectric layer to the gate electrode. Horiuchi and Dutta (Horiuchi et al. 2006) showed that in a gated microfluidic device the gate dielectric should be considered as a capacitor and resistor in parallel (Figure 9). The total capacitance was considered as three capacitors in series accounting for the capacitance of the wall (dielectric material), the Stern layer capacitance, and the capacitance of the diffuse layer. The Stern layer is much smaller than the diffuse layer so the Stern layer capacitance is usually neglected (Schasfoort et al. 1999; Horiuchi et al. 2006). The other capacitors are written as

퐶𝑖푛푠 = 휀푅휀0퐴푒/푡 (17)

휀 휀 퐴 푧퐹휉 퐶 = 푅 0 푒 푐표푠ℎ ( ) (18) 퐸퐷퐿 휆 2푅푇

The derivation for the electric double layer capacitance assumes that the entire potential drop occurs across the wall and the electric double layer and that the channel is electrically neutral in the bulk region outside of the electric double layer. This is a good approximation for microfluidic channels which generally fall in the limit of thin electric

double layers for most electrolyte concentrations used in experimental studies. However, in nanofluidic channels with interacting electric double layers the center of the channel is no longer electrically neutral, resulting in a smaller potential drop between the nanochannel wall and the nanochannel center (Pardon et al. 2013). In the case of gated nanofluidic channels generally the entire potential is assumed to drop across the oxide layer and the change in concentration is estimated by the charge stored by the gate- dielectric-electrolyte-capacitor (Guan et al. 2011).

Figure 9: An equivalent circuit model for a gated microfluidic channel (Horiuchi et al. 2006). The gate voltage, 푉푔, and axial voltage, here labeled 푉푑, are shown in the schematic. 푅푏1 and 푅푏2 represent the resistance of the portion of the microchannel before and after the gate electrode. 푅푙푒푎푘 represents the resistance of the gate dielectric. 퐶푡표푡푎푙 represents the capacitance of the electric double layers and the gate dielectric. It should be noted there is a second smaller microchannel located above the gate electrode. The resistance of the smaller microchannel above the gate electrode is given by 푅푏3. In this study the gate dielectric modeled as an equivalent capacitor and resistor in parallel. Here 퐶푤푎푙푙 = 퐶𝑖푛푠. Reproduced from Horiuchi, K. and P. Dutta (2006). Electrokinetic Flow Control in Microfluidic Chips Using a Field-Effect Transistor. Lab Chip 6: 714-723 with permission of The Royal Society of Chemistry.

Rutkowska et al.(Rutkowska et al. 2013) used an equivalent circuit model to qualitatively explain data trends observed for a nanopore with a Au electrode that is uninsulated in the center of the nanopore. Their study allows for variation in the resistance of the path from the center of the nanopore to the gate electrode known as the charge transfer resistance, Rct. In this case the value of Rct is not the resistance of the gate dielectric layer (as there isn’t one), but rather accounts for Faradaic reactions due to charge transfer between the gate electrode and the electrolyte solution in the nanopore.

While equivalent circuit analysis allows for qualitative interpretations and is useful for rational design of gated nanofluidic devices, the quantitative agreement between theoretical analysis and experimental data is relatively poor (Rutkowska et al.

2013). Experimentally measured intrinsic nanopore resistance and electrolyte solution resistance had to be adjusted by 1-6 orders of magnitude to quantitatively match experimental data. Equivalent circuit analysis is limited in its capability to explain geometrically analogous fluidic components as solid state analysis does not fully capture all the effects relevant in nanofluidic devices. Specifically, the type, concentration and distribution of charge carriers (“+” or “-”) are altered by the gate electrode in a fluidic device while a solid-state device is either n-type or p-type based on the physical doping of the substrate (Guan et al. 2011; Pardon et al. 2013; Guan et al. 2014). The

+ - + - concentration and type of charge carriers (i.e. H3O , OH , K , Cl ) is coupled to the solution pH and surface charge density in gated nanofluidic devices.

2.2.2 pH dependence and modulation of surface charge

The gate electrode alters the surface potential resulting in a change in concentration of charge carriers (both K+ and Cl-) in the nanofluidic channel to maintain electroneutrality (Karnik et al. 2005; Guan et al. 2011; Jiang et al. 2011; Jin et al. 2011;

Singh et al. 2011). In addition to change in concentration of K+ and Cl-, high electric

+ − fields can change solution pH through autoprotolysis of water (퐻3푂 + 푂퐻 ↔ 퐻2푂) and charge transfer / Faradaic reactions at the gate electrode (i.e. gate leakage current).

The shift in pH alters the deprotonation state of the silica channel, further resulting in change in the electric field by modifying the surface charge (Fan et al. 2008;

Pardon et al. 2013; Rutkowska et al. 2013). The change in surface charge necessarily alters concentration and type of charge carriers in the channel to maintain system electroneutrality. Further, autoprotoylsis of water from high electric fields and charge

+ - transfer/ Faradaic reactions at the gate electrode introduce more H3O or OH ions altering the relative concentration and type of charge carriers (Oh et al. 2009; Pardon et al. 2013). Reduction at a gate electrode with a positive polarity (+푉푔) is given by (Oh et al. 2009)

+ − 2퐻2푂 → 푂2 + 4퐻 + 4푒 (19)

+ + 4퐻 + 4퐻2푂 → 4퐻3푂 (20)

+ − 퐻 + 푂퐻 ↔ 퐻2푂 (21)

thus lowering the pH of the electrolyte solution. Oxidation at a gate electrode with a negative bias (−푉푔) is given by

− − 2퐻2푂 + 2푒 → 퐻2 + 2푂퐻 (22)

− − 푂2 + 2퐻2푂 + 2푒 → 4푂퐻 (23)

+ − 2퐻 + 2푒 → 퐻2 (24)

+ thus increasing the pH of the electrolyte solution. The relative concentration of H3O ,

OH-, K+, and Cl- can change the dominant charge carrier and reverse the direction of electroosmotic flow (i.e. fluid velocity) that would be expected from an analysis based on

K+ and Cl- alone (Oh et al. 2009).

The value of the surface charge has been recently shown by a detailed modeling study to be a complex function of the local electric field and concentration of carriers

+ - + - (H3O , OH , K , Cl ), making a dynamic surface charge model the most appropriate choice for gated nanofluidic devices (Pardon et al. 2013). Upon application of a gate potential chemically reactive surfaces act as a buffer. For example, in response to a negative gate potential the effective surface charge on a chemically inert surface (i.e. a surface that does not protonate / deprotonate) would increase in magnitude compared to the negative native surface charge. A surface which protonates / deprotonates, such as

- SiO2, will attract protons to the surface which will then combine with SiO surface groups to form electrically neutral SiOH surface groups (Jiang et al. 2010; Jiang et al. 2011;

Guan et al. 2014). The buffering action reduces the change in the net surface charge density induced by the gate electrode and thus reduces the modulation of the surface state by the gate electrode (Guan et al. 2014).

The ionic current through the nanofluidic channel, therefore, depends on the concentration, type, and distribution of charge carriers as well as the electric field within the nanofluidic channel which are inherently coupled. The above listed parameters will depend on the gate voltage, the dielectric material, and the concentration of the prepared electrolyte solution, among other factors. The effect of the pH and, therefore, the surface charge density on the operation of the gated nanofluidic device as a function of cation type is discussed in Chapter 5.

2.2.3 Controlled Translocation of Molecules

Gated nanofluidic devices are desired for control over transport of biomolecules for applications such as DNA (deoxyribonucleic acid) sequencing and molecular sorting

(Ai et al. 2010; Paik et al. 2012). Through discrimination of the current signals, electrophoretic translocation (electromigration) of DNA is a promising technique for measuring the order of nucleotide bases in a single DNA nanoparticle. However, one major challenge is that the DNA molecules translate through the pore too fast, requiring extremely high temporal measurement resolution. Gated nanofluidic devices are desired to selectively deliver the DNA molecules at a controlled rate for current based ordering of nucleotides bases. Simply reducing the axial voltage may result in a current too close to the noise limit that cannot be resolved. Tuning the gate potential in the gated nanofluidic

device is desired to selectively control the rate of nucleic acid delivery in real time.

Further, studies on translocation of biomolecules in gated nanofluidic devices give fundamental information of the net ionic flux of positively and negatively charged species through the nanofluidic channel. The flux will depend on the degree of electric double layer overlap and the gate potential, as described next.

DNA has a net negative charge with a positive electric double layer. Under pure axial bias (푉푔= 0 V), DNA is electrostatically excluded from a negatively charged nanopore or nanochannel and no DNA passes through to the other reservoir. When a positive bias is applied to the gate electrode the DNA can enter the nanofluidic architecture and capture is observed in the opposite reservoir. The DNA capture threshold or the magnitude of the bias needed to capture DNA is a function of surface charge density, which depends on pH. Lower pH corresponds to lower surface charge density and thus a lower threshold potential.

While translocation of DNA has been the focus of most studies, the control of translocation events can be utilized for other charged biomolecules. A similar modulation of positively charged protein molecules in a gated nanofluidic device was demonstrated by Karnik et al. (Karnik et al. 2006). Figure 10 shows translocation of fluorescently tagged avidin under negative gate bias with no transport observed at positive gate bias.

Figure 10: Translocation of positively charged avidin protein as a function of gate potential. Negative gate bias allows translocation of avidin from reservoir to reservoir while under positive bias the translocation is not observed. Reprinted with permission from Karnik, R., K. Castelino and A. Majumdar (2006). Field-effect control of protein transport in a nanofluidic transistor circuit. Appl. Phys. Lett. 88: 123114 (1-3). Copyright 2006, AIP Publishing LLC.

2.2.4 Dependence of transport on relative EDL thickness

The translocation event is controlled by adjusting the relative contributions of electroosmotic and electrophoretically (electromigration) driven flow (see discussion of

Equation (7). In the case of a negatively charged channel filled with KCl, the K+ ions are eletrophoretically driven to the cathode. Since K+ ions are the majority carrier and the mobility’s of K+ and Cl- are nearly equivalent, the bulk velocity or electroosmotic flow will also be towards the cathode. Negatively charged ions will have an electrophoretic force towards the anode but an electroomotic force towards the cathode. The relative magnitude of these forces determines the direction which the negative ions are transported.

Using DNA as an example, in negatively charged channels the native nanochannel/nanopore is highly cation selective. While the negatively charged DNA has an electrophoretic force towards the anode (i.e. against the flow of cations) there is a hydrodynamic force acting on the DNA molecule towards the cathode caused by the flow of cations (majority carrier) towards the cathode. This adverse force prevents the DNA from entering the channel. This balance of forces is visualized in a modeling study by a hydrodynamic force pushing the DNA away from the pore entrance for zero and low positive gate potential (100 mV) and reduction of this adverse force at higher positive gate potential (500 mV) (Paik et al. 2012). See Figure 5 for a representative schematic that shows the direction of electrophoresis (electromigration) compared to electroosmosis

(convection).

The relative size of the Debye length compared to the channel plays a crucial role in the dominating ion transport mechanism, because the extend of electric double layer overlap determine if the nanochannels are cation selective, or if the concentration of positive and negative ions is equivalent in the nanochannel bulk (see Figure 4). When the

Debye length is small compared to the radius of the nanochannel (휅푎 ≥ 1 where 휅 is the inverse Debye length and a is the diameter of the channel) electromigration, the transport of ions under the influence of an electric field, is the dominant transport mechanism.

Thus cations migrate towards the cathode and anions towards the anode. If the electric double layer spans the width of the pore (휅푎 < 1) then electroosmotic flow, the bulk fluid

motion induced by an electric field, is the dominating transport mechanism (Kemery et al. 1998).

In conditions of strong electric double layer overlap, the channel is permselective with primarily counter-ions in the nanochannel. The DNA translocation event and the magnitude of the potential required to modulate translocation is thus a function of the prepared electrolyte concentration. Under non-overlapped EDL conditions, the electrostatic interaction between the DNA and the pore surface is negligible leading to dominance of electroosmotic flow. When the electrostatic interaction dominates over the hydrodynamic force from the EOF, the DNA can be trapped within the nanopore, which occurs at relatively low axial electric field and low 휅푎 (overlapped electric double layers)

(Ai et al. 2010).

In the case of non-overlapped EDLs or high axial electric field the DNA velocity is asymmetric with axial location due to the electrostatic interaction with the gate electrode (Ai et al. 2010). The particle-nanopore electrostatic interaction increases or decreases translocation velocity as a function of the polarity of the gate voltage and the location of the DNA in the nanopore. The electroosmotic flow has a global effect on the

DNA transport while the electrostatic effect is local, leading to an asymmetric velocity where the DNA accelerates towards a gate electrode with a positive bias and then the velocity slows after the DNA molecule passes the gate electrode, though the net velocity remains in the direction of EOF (Ai et al. 2010).

Oh et al.(Oh et al. 2009) showed that in conditions of weakly overlapped double layers in a gated nanofluidic device positive and negatively charged dyes migrate in the same direction (towards the cathode) under the influence of an electric field. The flow velocity of both dyes was modulated or even reversed with respect to the initial ungated flow velocity. The flow velocity of negatively charged Alexa 488 experienced a greater difference in flow velocity between the gated and ungated case compared to positively

Rhodamine B, indicating that the positively charged dye was more likely to adsorb to the wall. The migration of oppositely charged dyes in the same direction indicates dominance of electroosmotic behavior. In contrast Maleki et al. (Maleki et al. 2009) showed migration of negatively charged Fluospheres towards the anode in the thin EDL limit.

2.3 Nanofluidic Device Fabrication

While many interesting studies have demonstrated feasibility of control over transport of ions and molecules using gated nanofluidic devices, several challenges remain in reliable fabrication of desired device design. The next sections summarize general fabrication procedures for nanofluidic devices. Several excellent reviews have been published on fabrication of nanofluidic devices highlighting innovative advances in device fabrication (Mijatovic et al. 2005; Perry et al. 2006; Dekker 2007; Abgrall et al.

2008; Schoch et al. 2008; Duan et al. 2013). Here a brief overview of select patterning, etching, bonding, and other standard micro- and nanofluidic device fabrication techniques is presented, with the following section (2.4) detailing how those fabrication techniques have been adapted to incorporate embedded electrodes in the nanofluidic architecture.

2.3.1 Materials and substrates for nanofluidic device fabrication1

The most common substrates for microfluidic and nanofluidic devices are silicon, glass, and a variety of polymers. Substrate selection is important because it determines the fabrication procedures available and thus fundamental limitations placed on device design. Many mature, well characterized fabrication procedures exist for silicon due to its prevalent use in the semiconductor industry. Silicon itself, however, is not an ideal substrate for nanofluidic devices with electrokinetically driven flows (Duan et al. 2013).

An insulating silicon dioxide or silicon nitride layer is necessary on the surface of the channel to prevent current paths through the semiconducting substrate. Glass, Pyrex

(borosilicate or borofloat), and quartz have the advantage of being chemically stable and electrically insulating. Transparency of glass is particularly attractive when optical detection methods such as fluorescence or SPR are used. However, depending on the type of glass there can be large amounts of impurities or trace materials that may potentially interfere with device fabrication or operation. For example, soda lime glass is one the cheapest forms of glass, but it can contain a large amount of contaminants such as aluminum, which can introduce surface roughness through non-uniform etching due to the impurities and cause cracking during fusion bonding. Pyrex or borosilicate glass is often used in microfluidic and nanofluidic devices. The best optical properties are achieved in either fused silica or quartz.

1This section has been adapted and used with permission from Prakash, S., M. Pinti and B. Bhushan (2012). Theory, Fabrication and Applications of Microfluidic and Nanofluidic Biosensors. Phil. Trans. R. Soc. A 370(1967): 2269-2303. Copyright 2012 RSC Publishing.

One of the challenges with glass is the difficulty in bonding device layers to create sealed channels. Often high temperatures and/or large electric fields are needed and therefore fabrication methods for devices with specific applications such as devices that incorporate bio-materials have to be adapted to meet bonding requirements.

Polymers are attractive materials for substrates because of their low cost, disposability, and biocompatibility (Siegrist et al. 2010). Poly(dimethyl siloxane) (PDMS) is the most commonly used polymer for fabrication of fluidic channels (Easley et al. 2006; Choi et al. 2009; Lee et al. 2010; Buffi et al. 2011), though PMMA and polycarbonate based materials are also used (Chikkaveeraiah et al. 2009). The main challenges in working with polymers are related to the relatively lower Young’s modulus for these materials making polymer channels more prone to collapse and deformation than either silicon or glass. Further, many polymers also show non-specific adsorption of bio-materials and can therefore pose contamination challenges for biomedical applications such as biosensors.

2.3.2 Fabrication techniques and methods2

Fabrication methods are broadly classified in two categories, bottom-up methods that allow for device fabrication by using manipulation of individual blocks or fundamental building matter, and top-down approaches which use conventional and advanced materials machining techniques to develop devices. Bottom-up approaches such as self-assembly can be driven by a thermodynamic energy minimization processes

2This section has been adapted and used with permission from Prakash, S., M. Pinti and B. Bhushan (2012). Theory, Fabrication and Applications of Microfluidic and Nanofluidic Biosensors. Phil. Trans. R. Soc. A 370(1967): 2269-2303. Copyright 2012 RSC Publishing.

to develop polymer structures based on phase segregation. Other self-assembly methods use molecular assembly of alkanethiols to form organized monolayers that enable surface modification (Prakash et al. 2009), as discussed below. Other methods include pick-and- place approaches using advanced tools such as optical tweezers (Ashkin et al. 1989;

Svoboda et al. 1994), and atomic force microscopes (AFMs) (Bhushan 2010; Bhushan

2010; Stavis et al. 2011). Nearly all of these methods are application specific and have not been developed as generalized fabrication procedures.

Top down methods were developed primarily for processing of silicon and glass based on advances in microelectronics and microelectromechanical systems (MEMS).

These methods remain more common for fabrication of micro- and nanofluidic devices.

The majority of device fabrication begins with definition of channels or other features on a photoactive polymer layer using lithography, with UV lithography being the most commonly used method. The photoactive polymer is exposed to photons then developed to form the desired pattern in the photoresist. Lithography is followed by etching to transfer the patterned features into the substrate (Madou 1997). Other material addition (e.g., metals) may take place to add functionality to the devices. Essential fabrication techniques for micro- and nanofluidic devices such as material deposition, patterning, pattern transfer to the substrate, and device bonding are discussed next.

2.3.3 Deposition Techniques

Deposition techniques refer to the addition of layers of material to the substrate that may be utilized as part of the fabrication process (i.e. photoactive polymers, etching

masks, sacrificial layers, etc.) or as functional components of the final device (electrodes, insulation layers, wires, cantilevers, etc.). Common deposition techniques include thermal oxidation, spin coating, chemical vapor deposition, and physical vapor deposition.

Thermal oxidation consumes part of the substrate to form an oxide layer on the surface of the substrate. Spin coating refers to spinning of a liquid material to form a thin layer on the substrate. Chemical and physical vapor deposition methods use a gas, liquid, or solid source material to deposit the desired film. As the substrate material is not consumed in spin coating, chemical, or physical vapor deposition methods, they are available for deposition of a broader range of materials. The basic mechanism for each deposition technique is summarized next. Discussion of spin coating can be found in Chapter 3.

Thermal Oxidation

Thermal oxidation is most commonly used to form an insulation layer on a silicon substrate. In un-gated nanofluidic devices thermally grown oxides are often used to insulate the entire nanochannel wall to prevent current paths through the silicon substrate.

In gated nanofluidic devices thermally grown oxides are additionally used to form the gate dielectric (Joshi et al. 2010; Petrossian et al. 2010).

Thermal oxides can be grown in a dry (oxygen) or wet (water vapor) environment at temperatures ranging from 1000 - 1200°C. The Deal-Grove model is widely used for the prediction of the final oxide thickness grown under wet or dry conditions. The oxidation is broken into three steps consisting of diffusion of O2 to the Si surface, penetration and diffusion of the O2 through the surface oxide film, and reaction of the O2

with the underlying Si substrate (Prakash et al. 2014). The rate of the oxide growth slows as the thickness of the oxide layer increases. The reactions for wet and dry oxidation are given by (Madou 1997)

푆𝑖 + 2퐻2푂 → 푆𝑖푂2 + 퐻2 (푤푒푡) (25)

푆𝑖 + 푂2 → 푆𝑖푂2 (푑푟푦) (26)

The oxide growth rate from the Deal-Grove model is given by

푑푋 퐶 푘 표푥 = 𝑖 푠 (27) 푑푡 푁

where 푋표푥 is the oxide thickness, 퐶𝑖 is concentration of oxidant at the surface which is a function of 푋표푥, 푘푠, the partial pressure of the oxidant, and the diffusivity of the oxidant,

푘푠 is the silicon oxidation rate constant, 푁 is the number of molecules oxidant per unit volume of oxide, and 푡 is time. The predicted oxide thickness as a function of time is

퐴퐶 푡 + 휏 푋표푥(푡) = [(1 + 4퐵 2 ) − 1] (28) 2 퐴퐶

AC and B are rate limiting constants that depend on the temperature and oxidation conditions and 휏 is an initial time offset that accounts for the initial oxide thickness at

푡 = 0. The constants A and B are tabulated in many microfabrication textbooks. The quality and thickness of thermally grown SiO2 is a fundamental concern to semiconductor device performance leading to a high volume of work focusing on growth of thin, high quality, well controlled oxide layers. SiO2 layers need to be as thin as possible to allow efficient switching of transistors while minimizing losses from resistive heating and leakage current through the SiO2 layer.

Chemical Vapor Deposition

Chemical vapor deposition (CVD) utilizes a precursor gas which reacts at the surface of a heated substrate to produce a thin film on the surface of the substrate. The choice of precursor gas determines the deposited material. While CVD is based on chemical reactions, the deposition itself does not consume the substrate material, making

CVD a more generalizable deposition method than thermal oxidation. The precursor gases flow into the chamber and a boundary layer is formed as the precursor gases flow over the flat plate holding the substrates. The precursor gases diffuse to the substrate surface typically aided by a thermal gradient between the precursor gases and the substrate. The precursor gases adsorb to surface and react to form the desired material.

The substrates are often heated to 300°C and above to promote surface reactions, making

CVD unsuitable for materials with low melting points. Plasma enhanced chemical vapor deposition uses an RF plasma to provide energy to the precursor gas molecules rather

than relying primarily on a temperature gradient. The process can therefore run at lower temperatures reducing the stress of the final deposited film. Typically the substrate is placed on the grounded electrode to prevent excessive ion bombardment. Low pressure chemical vapor deposition (LPCVD) is performed at low pressure and high temperature

(800°C or higher). The diffusion coefficient is high at low pressures promoting transport of reactant species to the surface. LPCVD is limited by the surface reaction rate rather than the mass transfer rate of reactants. The surface reaction controlled nature of LPCVD leads to conformal coating of the substrate and allows many wafers to be uniformly coated at the same time, though LPCVD has the disadvantage of a low deposition rate.

Atomic layer deposition is a cyclic conformal chemical vapor deposition technique that uses precursor gases to deposit a monolayer of material with each cycle.

Each growth cycle consists of four steps which include exposure to the first precursor, purge of the reaction chamber, exposure to the second precursor, and finally purge of the reaction chamber. Using deposition of TiO2 as an example, TiCl4 is introduced into the chamber where it adsorbs to the surface of the substrate. The un-adsorbed TiCl4 is purged from the chamber. Water vapor is then introduced into the chamber where it reacts with the absorbed TiClx to form TiO2 with surface TiOH groups (Leskela et al. 2003). The process is limited to monolayer deposition due to limited possible adsorption sites to the surface of the substrate. Due to the cyclic nature chemical reactions between precursor gases are less of a concern than in other CVD techniques as multiple precursor can be introduced at different times. However, the cyclic nature makes the deposition technique

relatively slow with 1 cycle taking 0.5 to a few seconds and depositing between 0.1 and

3 Å depending on the deposition material (Leskela et al. 2003).

Physical Vapor Deposition

Evaporation and sputter deposition are two commonly used deposition techniques in fabrication of micro- and nanofluidic devices. Evaporation uses sublimation of a source material to transfer that material to a substrate (Madou 1997). The deposition is performed in a vacuum chamber to prevent contamination of the deposited layer and oxidation of the source material from exposure to air. In most modern evaporators, a high energy (~10kV) electron beam is magnetically focused on the source material

(non-magnetic source material). The source locally melts and the material evaporates and is deposited on the substrate. The mean free path, or the distance a particle can travel without being scattered by a collision with another particle, must be longer than the distance from the source to the substrate. The mean free path is inversely proportional to the chamber pressure. The deposition is performed in high vacuum to increase the mean free path and to prevent scattering of the evaporated particles through collisions with particles in the chamber between the source and the substrate. The number of particles

−푑푠−푠/휆푚푓 scattered by collisions (푛푠) is given by 푛푠 = 1 − 푒 where 푑푠−푠 is the distance between source and substrate and 휆푚푓 is the mean free path, or the distance a particle can travel before colliding with another particle. While evaporation allows deposition of thin films with low amount of contamination (Madou 1997), x-ray damage or even ion damage to the substrate is a concern due to x-ray emissions caused by the high energy

electron beam. Evaporation requires high local temperatures in the source material for deposition. High temperatures may lead to decomposition of some materials, limiting the range of available materials for deposition.

Sputter deposition uses kinetic energy transfer from an inert plasma (usually

Argon) to the surface atoms/molecules of the source material to deposit the material on the substrate. The sputtering target is at a high negative potential and is bombarded with positive ions created in a plasma, such as Ar+. The incident Ar+ ions transfer momentum to the ions on the surface of the source material which are then ejected from the source as neutral particles. The plasma must be inert and consist of relatively heavy ions. Ion bombardment energies range from 10 keV to 1 MeV. This is enough energy for the sputtered atoms to penetrate the first few atomic layer of the substrate, increasing the adhesion of the deposited material. When sputtering an oxide layer such as SiO2, an overpressure of a reactive gas such as oxygen can be used to help control the stoichiometry of the deposited layer, especially. For non-planar substrates, the step coverage of the deposited layer is determined by the angle of the sputtered atoms to the surface as they are deposited. Sputtered atoms arrive at a broader range of angles compared to evaporated atoms, leading to improved step coverage in layers deposited by sputtering (Madou 1997). Advantages and limitations of the deposition techniques discussed in this section are summarized in Table 1. Thermal oxidation techniques or

LPCVD are typically used in gated nanofluidic devices to insulate the silicon substrate.

Thermal oxidation, PECVD, LPCVD, sputter deposition, and ALD can be used to deposit

the gate dielectric (Section 2.4). Typically sputter deposition or e-beam evaporation are used to deposit metals used for the gate electrodes.

Table 1: Summary of advantages and limitations of several common deposition techniques as described in this section. Technique Advantages Limitations

Thermal Oxidation  High quality oxide film  Only applicable for oxidation with minimal of substrate material pinholes/defects  Well characterized process due to importance in semiconductor devices PECVD  Lower temperature  More pinholes compared CVD process to LPCVD  Good adhesion  Low pinhole density  Good step coverage LPCVD  High quality films with  High Temperature minimal pinholes  Relatively slow deposition rate  Conformal step coverage  High purity, uniform film deposited on many wafers simultaneously  Commonly used for SiO2 and Si3N4

ALD  High quality and high  Slow – Angstroms per second purity  Conformal, uniform films  Lower temperature than LPCVD (~400°C)

continued

Table 1 continued E-beam Evaporation  Low contamination of  Poor step coverage – deposited film advantage for lift off  X-ray damage to substrate  High temperature at source – possible decomposition of source material Sputter Deposition  Low temperature  Gas molecules can be compared to e-beam incorporated  Improved step coverage  Ionic bombardment of sample  Better Adhesion  Better preservation of stoichiometry

2.3.4 Patterning Device Features

The majority of device fabrication begins with definition of features using lithography, with photolithography being the most commonly used method. The photoactive or electron sensitive polymer is exposed to photons or electrons and then developed to form the desired pattern in the resist. Lithography is followed by etching to transfer the patterned features into the substrate (Madou 1997). Next, essentials of patterning and etching are discussed.

UV Lithography

Ultraviolet lithography (Figure 11) has been widely used by the semiconductor industry, due to the ability to simultaneously pattern features over a large surface area thus making the process compatible with large-scale manufacturing. Photoresist, a light sensitive polymer, is spun onto a clean substrate which is then soft-baked to remove excess solvents and to activate the photo-initiators in the resist. A photomask with the

desired pattern is placed over the substrate and then exposed to ultraviolet light. If the photoresist is a positive tone the photons break bonds of the molecular chains, reducing the molecular weight of the polymer in the exposed area. The photoresist in the exposed area will dissolve when placed in a developer solution forming a copy of the exposed pattern in the photoresist. In the case of a negative photoresist, the photons will cause crosslinking of the polymer chains in the exposed area. The unexposed area with lower molecular weight will dissolve in the developing solution and the negative of the exposed pattern will be formed in the resist (Madou 1997).

Glass Photoresist Chrome

Spun on Photoresist Expose Develop

Figure 11: Schematic representation of UV lithography process for a glass substrate and positive tone photoresist. Photoresist is spun onto the glass substrate. The photoresist is selectively exposed to UV light using a photomask. The photomask has dark (chromium) regions that prevent exposure and transparent (glass) portions that all the UV light to reach the photoresist. The UV light breaks the bonds in the polymer chains of the positive photoresist, causing the exposed region of photoresist to selectively dissolve in the developer solution.

Though UV lithography allows simultaneous patterning of many features such as nanochannels on a substrate (compared to direct writing techniques), problems with

uneven photoresist coverage often occur when patterning hierarchical structures as discussed in Chapter 3. Methods such as detachment lithography have been developed to replace standard methods that use spin coating to deposit the photoresist layer (Yeom et al. 2009). Detachment lithography is a photoresist contact printing technique used in the fabrication of three dimensional structures. A pre-patterned silicon substrate is brought into contact with a flat PDMS stamp that has been coated with photoresist. After annealing and rapid peeling, the protruding areas of the silicon substrate become coated with photoresist. The substrate can then be patterned using UV or other lithographic methods to produce more complicated structures (Yeom et al. 2009).

State of the art UV lithography systems in the semiconductor industry can achieve minimum feature sizes down to 22 nm (Duan et al. 2013). Modifications to the lithography system to achieve these feature sizes are generally cost-prohibitive for a research laboratory. Typical minimum feature sizes range from 1-2 μm without further modification to the lithography system. In the case of nanofluidic channels UV lithography is used to pattern a micron scale channel width with etching used to define the nanoscale depth into the substrate.

Interferometric Lithography

Interferometric lithography is a laser based lithographic method used to pattern periodic and semi-periodic nanoscale structures. Interferometric lithography does not require a photomask or specialized lithography systems (i.e. wafer stepper or aligner) which can be cost-prohibitive for a research laboratory when micro- and

nanomanufacturing facilities are not readily available. Two or more beams are used to expose a layer of photoresist and the interference pattern of the beams is patterned into the photoresist layer. The smallest feature for a single exposure is limited to 휆/4푛 where

휆 is the wavelength of the source light used for the exposure and 푛 is the refractive index of the medium through which the light is traveling, surpassing the limit of standard UV lithography by an order of magnitude or more.

In standard IL the medium is usually air, but the substrate can be immersed in a material with a high index of refraction, such as water, to decrease the limit. This is known as immersion IL. Two-beam interferometric lithography creates an array of uniformly spaced parallel lines. As more beams are added, complex interference patterns beyond simple gratings can be generated. As any function can be written as the sum of periodic functions, Fourier series analysis can be used to design the placement of lasers and optics, where the limiting factor to design complexity comes from the amplitude of the interference pattern i.e. having a clearing exposure dose in all desired areas of the wafer while not over exposing others. While some standardized procedures have been developed for common patterns such as an array of holes, as the complexity of the pattern grows the benefits of using IL over standard UV lithography are lost.

E-beam and Focused Ion Beam Lithographic Techniques

Direct writing techniques such as electron beam or focused ion beam lithography use a highly focused beam of electrons or ions to directly write a pattern into photoresist or, in the case of focused ion beam (FIB) lithography, directly into the substrate. Material removal is achieved by surface sputtering or a kinetic energy transfer between incident electrons or ions and the molecules on the surface of the substrate.

E-beam lithography is typically used to write a pattern into an electron sensitive polymer such as SU-8. The minimum feature size is limited by wavelength of electrons, the size of the beam spot, and the scattering of electrons after their initial collision with the surface. The wavelength of incident electrons is much smaller than the wavelength of

UV light allowing features as small as 10 nm or smaller to be patterned.

Focused ion beam lithography uses a focused beam of high energy ions (10-

100keV) to directly write into the substrate. The most commonly used incident ion is

Ga+. Pattern transfer is achieved through surface sputtering of ions. The incident ion collides with surface atoms on the substrate which provide enough energy to overcome surface binding leaving behind a patterned feature in the substrate. The minimum feature size is determined by the beam size and ion energy as well as by the depth of the feature.

Typically features broaden with continued exposure to the ion beam due to ion scattering after the initial collision. Focused ion beam milling has been used to pattern features on the order of 10 nm, but the minimum feature size depends on the depth of the milling.

A similar process for drilling nanopores in Si3N4 and SiO2 membranes has been performed using a transmission electron microscope (S. Prakash et al. 2012). Nanopores with diameters as small as 1-2 nm have been achieved in these materials, typically employing pore expansion/contraction procedures to further control the final pore diameter. While the ability to fabricate nanopores with controlled diameters down to a few nanometers has exciting possibilities for applications such as DNA sequencing devices, the process for removal of material with a TEM is also based on a surface sputtering mechanism. This limits the ability to drill pores with uniform cross sections in materials of higher molecular weight (Jiang et al. 2010).

Molding Techniques for Patterning Polymer Substrates

The compliant nature of polymers along with the ability to begin fabrication with an uncured polymer allows a broader range of fabrication procedures for polymers compared to silicon and glass. Nanoimprint lithography begins with a pre-patterned mold, typically made of silicon, that is pressed into a flat polymer sheet often made of

PMMA, SU-8, or a UV curable polymer. The mold is held in contact with the polymer under pressure and heated until the polymer has cured. The mold is then removed and the negative form of the mold has been imprinted into the polymer sheet. The device can be bonded to form sealed polymer-based channels (Abgrall et al. 2007) or if the polymer sheet was initially spun onto a silicon or glass substrate, the polymer can be used as a resist layer. The resist layer is etched with an oxygen plasma to ensure the underlying substrate is exposed for etching. Since plasma etching is an anisotropic technique, the

oxygen plasma etching preserves the imprinted pattern but reduced the resist thickness over the entire substrate (Figure 12).

A similar technique can be used to pattern channels with a circular cross section by using a silicon nanowire as the mold. Nanowires are hot embossed into a polymer substrate which is then bonded to a second silicon or glass substrate with prefabricated microfluidic channels. The nanowire forms its negative pattern in the polymer which serves at the nanopore connecting the two microfluidic reservoirs.

Soft lithography is a similar fabrication process, but instead of pressing the mold into a polymer sheet, liquid uncured polymer is poured over the mold. Once the polymer is fully cured it is detached from the master and the device is ready for bonding (Choi et al. 2009; Park et al. 2009). Both nanoimprint lithography and soft lithography have high- throughput capabilities. The master or mold is fabricated using e-beam or UV lithography and reactive ion etching depending on the desired minimum feature size. A master patterned using e-beam lithography is subject to the time constraint characteristic of direct writing processes, however, the mold can be re-used with all the features of the mold transferred at the same time. Nanoimprint lithography is commonly used for biomedical applications such as biosensors.(Maeng et al. 2008; Choi et al. 2009;

Mannoor et al. 2010; Buffi et al. 2011; Chen et al. 2011; Javanmard et al. 2011)

Polymer Substrate Silicon Master

Cure Under Pressure

Remove Master

Figure 12: Schematic representation of nanoimprint lithography. A master, often made of silicon, is patterned using lithography and etching. The silicon master is pressed into a polymer substrate and cured. The black dash-dot line indicates the cut line to generate the cross section view. The master is then removed and the negative of the pattern is then imprinted into the polymer substrate.

Lift Off

Lift off (Figure 13) is a patterning technique that combines lithography and deposition techniques to add features to a substrate. A photoresist layer is spun onto the device substrate and patterned using one of the patterning techniques listed above. A second material, such as metal, is deposited onto the photoresist layer generally using

PECVD or evaporation. The photoresist layer is removed, subsequently removing the metal layer on top of the photoresist. The metal layer deposited in the openings of the photoresist layer remains on the substrate. The sidewall profile of the resist becomes

important for lift-off processes. The resist layer should have a greater than 90° profile to prevent covering the edge of the photoresist during evaporation. Step coverage of the photoresist layer will prevent lift-off as a continuous layer of metal will form over the resist layer preventing solvent access to the underlying resist. Lift-off is a common technique used for patterning metal components such as electrodes. Nearly all of the patterning techniques described here have been implemented to fabricate gated nanofluidic devices, as discussed in Section 2.4.

Glass Substrate θ Photoresist Metal

Figure 13: Schematic representation of a lift off process for patterning metal features. A pattern is defined in photoresist using lithography. A metal layer is evaporated on top of the patterned photoresist. Perfect step coverage is not desired so that solvent can reach the photoresist layer. The photoresist sidewall profile should be greater than or equal to 90° and the deposition should not be conformal. The angle of the photoresist sidewall profile is 90° in the schematic. After exposure to solvents the photoresist and metal layer on top of the photoresist is “lifted off” leaving the metal in the form of the original pattern.

2.3.5 Pattern Transfer or Etching Techniques

Etching techniques are used to permanently transfer the pattern defined in the photoresist to the substrate. Etching techniques are classified as wet or dry etching techniques depending on whether the etch medium is a liquid or a vapor. Wet etching can be performed using hydrofluoric acid (HF) (Easley et al. 2006; Durand et al. 2009) or buffered oxide etch (BOE)(Gervais et al. 2011) for glass and KOH for silicon respectively. Hydrofluoric acid gives isotropic wet etching thus undercutting the masking layer and resulting in semi-circular sidewalls or sidewalls that taper downward. Depth of the features is controlled by the etch time. Continued exposure to HF required for etching deeper features can result in photoresist delamination. For this reason masking layers such as aluminum or gold with an intermediate chrome adhesion layer are used to protect the substrate (Zhu et al. 2009). In the case of silicon, KOH gives an anisotropic etch as it etches the <100> plane more than 100x faster than any other crystalline plane, resulting in sidewalls with a mirror-like finish. Patterns can also be transferred into the substrate through reactive ion etching (RIE). RIE is often used rather than wet etching because it is anisotropic (Yanik et al. 2010; Gervais et al. 2011). CF4 or CHF3 is typically used for etching glass while Cl3/BCl3 plasma is typically used for Si (Bang et al. 1991). Etching profiles for isotropic and anisotropic etching are shown schematically in Figure 14.

Isotropic Anisotropic

Photoresist Photoresist

SiO SiO 2 2

Figure 14: Schematic representation of isotropic and anisotropic etching profiles using SiO2 as an example. Wet etching with HF or buffered oxide etchant (BOE) is isotropic leading to undercutting of the photoresist layer. Reactive ion etching is anisotropic.

2.3.6 Bonding Techniques

Once device features have been fabricated on a substrate, the device must be bonded to create sealed channels. The features are often sealed using a cover layer with well-established bonding methods. Next, a discussion for several methods used in fabrication of nanofluidic devices is presented.

Anodic Bonding

Anodic bonding is used most often to bond silicon to glass in micro- or nanofluidic devices (Durand et al. 2009). Typically silicon devices are bonded with glass top covers because of the optical transparency of glass which is preferred for device testing and characterization. The silicon substrate and glass top cover are brought into physical contact and bonded by applying heat (temperatures on the order of 400°C), pressure (~ 100-500 kPa), and a voltage (~ several kV) across the device. The high voltage drives O2- ions from the glass to the silicon forming Si-O bonds between the substrates at elevated temperatures (~400°C).(Duan et al. 2013) The strong potential

difference applied across the device can cause the channels to bow due to strong electrostatic forces. If the aspect ratio for the channels is low the silicon and glass may come into contact in the center of the channel causing bonding due to elastic deformation of either the glass or the silicon. Once the surfaces come in contact the bond expands quickly down the channel, resulting in completely sealed off channels. Aspect ratios as low as 0.004 (channel depth of 20 nm and width of 5 μm) have been fabricated by this method.(Mao et al. 2005) The minimum channel height to avoid channel collapse during anodic bonding is given by (Duan et al. 2013)

2 1/2 푤휀0푉 ℎ푚𝑖푛 = ( ) (29) 퐸푒푓푓

where ℎ푚𝑖푛 is the minimum channel height, 푤 is the channel width, 푉 is the potential difference applied, 휀0 is the dielectric constant, and 퐸푒푓푓 is the effective Young’s modulus.

One way to overcome this limitation is to reduce the electrostatic attractive force that causes channel bowing and collapse by growing a thick oxide layer on the silicon before bonding. This modified anodic bonding technique was successfully employed by Duan et al.(Duan et al. 2010) to bond a 2 nm deep x 2 μm wide channel.

Fusion Bonding

Fusion bonding is typically used for glass to glass bonding. Glass is heated to a temperature near the glass transition temperature (~550°C) and placed under pressure.

Diffusion and plastic deformation at the interface create a bond as the substrate is cooled back to room temperature. Fusion bonding is limited to materials that have a similar glass transition temperature and coefficient of thermal expansion. Mismatched coefficients of thermal expansion will result in device cracking during heating or cooling. In the case of compatible substrates, the temperature and aspect ratio of the channels are the main factors that determine the survival of the channels. If the bonding temperature is too high, the channels tend to deform or collapse due to re-flow of glass. If the temperature is too low bonding will not occur (Mao et al. 2005). Sealed channels with depths as low as

5 nm (Haneveld et al. 2008) or 6 nm (Delft et al. 2007) were achieved in a Pyrex substrate. Small aspect ratios down to 0.0004 for 25 nm deep channels in Pyrex have been achieved (Mao et al. 2005).

Adhesive and Polymer Based Bonding Techniques

Typically PDMS devices are bonded to glass covers by simply placing the glass cover in contact with the PDMS and curing the PDMS while applying pressure (Easley et al. 2006; Park et al. 2009) or by applying pressure (Goral et al. 2006). PDMS can also be used as an intermediate layer for bonding other substrates. In stamp and stick bonding, a thin layer of adhesive polymer layer such as UV curable adhesive or PDMS is spun onto a wafer. A patterned substrate is then carefully brought into contact with the uncured adhesive. The adhesive layer is transferred from the silicon wafer to the protruding regions of the patterned substrate. A cover is then brought into contact with the patterned substrate. The adhesive is cured and the device is sealed.

Microfluidic networks formed in PDMS through nanoimprint or soft lithography are often bonded to glass covers using oxygen plasma bonding (Maeng et al. 2008;

Javanmard et al. 2011). Both the glass and PDMS are treated with an oxygen plasma and brought into contact. The bond forms instantaneously once the two substrates are mated, though oxygen plasma treatment decays with time, which can lead to locally unbonded regions (Leong et al. 2005). Adhesive or polymer based bonding techniques are often limited by the relatively lower Young’s modulus compared to silicon or glass substrates.

The lower Young’s modulus leads to channel deformation and collapse. Channels can collapse during bonding that employs uncured polymers as the uncured material can seep into the channel and seal it off. Generally techniques that use uncured adhesives or polymers are limited to channels that are larger than the thickness of the uncured polymer or adhesive layer.

Non-conformal Deposition for Sealing Nanochannels

Anodic, fusion, and adhesive bonding are typically used to seal low aspect ratio two dimensional nanochannels. In the case of relatively deep channels with a nanoscale width (high aspect ratio channels), non-conformal deposition methods can be used to apply a capping layer to trenches etched on a substrate. The non-conformal deposition shrinks the dimension of the trench as the deposition progresses. Since the process is non- conformal, the deposited material collects near the top of the trench sealing off the top while leaving a nanoscale opening for fluid flow in the center of the trench. Non- conformal deposition is a relatively fast and cost effective technique compared to anodic

and fusion bonding, however, it limits the ability to control the final channel dimension post fabrication (Duan et al. 2013).

2.3.7 Sacrificial Layer Releasing and Related Techniques

In the sacrificial layer technique (Figure 15) a sacrificial material such as amorphous/polysilicon, silicon dioxide, a metal, or polymer is deposited on the substrate.

The sacrificial material is patterned to form the negative of a nanotrench. A capping layer is deposited over the patterned sacrificial material. The capping layer is selectively etched to gain access to both ends of the sacrificial material. An etchant is used to selectively remove the sacrificial material which may be xenon diflouride for silicon, hydrofluoric acid for silicon dioxide, or an appropriate liquid metal etchant for metals. Polymer layers can be removed through plasma etching or in the case of some polycarbonate based polymers, the polymer sacrificial layer vaporizes when heated to 300-400° C. The availability of capping layers is limited for polymer sacrificial layers by the low glass transition temperatures, making polysilicon and silicon dioxide more popular choices.

While eliminating the need for a device bonding technique that preserves the channel dimension, sacrificial layer techniques are suitable for channels that are 10 nm of larger as they tend to collapse during etchant extraction or liquid etchant introduction

(Duan et al. 2013). Sacrificial layer etching uses diffusion based etching to remove the sacrificial layer, requiring long periods of time to release the sacrificial layer (about 15 hours for 0.66 mm long channels) (Tas et al. 2003). Huang et al. (X T Huang et al. 2010) modified the etching technique by using a non-conformal capping layer to leave the

sacrificial layer exposed from the side. Etching progressed along the nanochannel width, which is typically significantly shorter than the channel length. This allowed fabrication of centimeter long nanochannels in 90 seconds. However, the final channel cross section tends to deform from the designed rectangular shape during channel sealing / bonding.

Pattern Sacrificial Layer Deposit Capping Layer

Access Sacrificial Layer

Etch Sacrificial Layer

Substrate

Sacrificial Layer Capping Layer

Figure 15: Schematic representation of sacrificial layer etching. A sacrificial layer is deposited and patterned on the substrate. A capping layer is deposited and then etched to gain access to the sacrificial material. The sacrificial layer is selectively etched to release sealed channels. Black dash-dot lines indicate cut lines used to generate cross section views. The capping layer is shown transparent through until the final device schematic for clarity.

Pre-fabricated silicon nanowires can be used as the sacrificial material to create nanopores with circular or oval-shaped cross sections. The nanowire is coated with a capping material, such as SiO2 using an appropriate deposition technique for the capping material such as CVD in the case of SiO2. The nanowire is then released by selective etching, resulting in a SiO2 nanopore (Fan et al. 2003).

2.3.8 Surface Modification3

Surface modification is a common fabrication technique used to control surface properties in micro- or nanofluidic channels. As described above, transport in nanofluidic devices are governed by surface-fluid interactions. Surface modification techniques can therefore enable a broad range of device functionalities. Surface modification methods can be divided in two broad categories: physical and chemical methods. The definition of these broad categories depends on how the process affects the surface. Physical methods, in most cases, do not change the chemical composition of the surface but may alter physical characteristics such as surface roughness, grain sizes and grain boundaries, and faceting. Consequently, physical modification often uses tools such as lasers, plasmas, temperature, ion beams, and physical polishing and grinding to alter the surface state of a material of interest. Chemical methods are often classified as such because these methods introduce a change in the eventual chemistry or chemical composition at the surface of a material. The surface may possess chemical properties that are different from the bulk

3This section has been adapted and used with permission from Prakash, S., M. Pinti and B. Bhushan (2012). Theory, Fabrication and Applications of Microfluidic and Nanofluidic Biosensors. Phil. Trans. R. Soc. A 370(1967): 2269-2303. Copyright 2012 RSC Publishing.

material. Amongst these formation of surface layers, either covalently bonded or physisorbed, have been most common. Other chemical methods include treatment with

UV light and reactive plasmas. These changes can also introduce a change in the surface charge density or the surface energy.

Recent reviews have discussed in detail the methods for surface modification(Prakash et al. 2009) and operational physics behind modified surfaces.(Squires et al. 2008) Surface modification has been essential for biosensors to immobilize affinity tags for binding of target molecules to surfaces (Abbasi et al. 2001;

De Campos et al. 2003; Pijanowska et al. 2003; Krenkova et al. 2004; Rosi et al. 2005;

Deng et al. 2008). For example, several platforms for cell, protein, and DNA assays have been investigated (Sauberlich et al. 1999; Yang et al. 2002; Ayhan et al. 2003; Gray

2004; Tegenfeldt et al. 2004; Falconnet et al. 2006; Franks et al. 2007). Other examples include tissue engineering, bio-threat and environmental sensors (Danielsson 1990;

Cirino et al. 2004; Palchetti et al. 2008), biomimetic surfaces (Wu et al. 2005; Bhushan

2009), and development of myriad surface-based platforms for clinical diagnostics and applications (Bogunia-Kubik et al. 2002; Grayson et al. 2004; Langer et al. 2004; Freitas

2005; Rosi et al. 2005; Ciardelli et al. 2006; Herrmann et al. 2007). However, surface modifications techniques have the disadvantage that the surface property cannot be actively altered in real-time, reducing the range of applications. One way to control surface properties without the surface modification techniques described above is to embed electrodes into the nanochannel wall. The electrodes allow for active, tunable

control of the surface potential post-fabrication. Notably, surface modification techniques have been used to reduce the net surface charge density in gated nanofluidic device, allowing lower operating voltages while retaining the active, tunable control characteristic of gated devices.

This section has summarized a selection of the most relevant nanofluidic device fabrication techniques that have been used to develop fabrication protocols for gated nanofluidic devices. The various fabrication procedures and their respective advantages and disadvantages are listed by category in Table 2. All of the fabrication procedures listed in Table 2 have been adapted and implemented for fabrication of gated nanofluidic devices, or in the case of some of the polymer based techniques, for gated microfluidic devices. The next section discusses fabrication procedures for gated nanofluidic devices.

Table 2: Summary of various fabrication techniques organized by category and their respective advantages and limitations.4 Technique Advantages Limitations Patterning UV  High throughput  Most research lithography  Low cost after initial start systems limited to up features ≥ 1μm  Pattern samples over cm2  High start-up cost areas simultaneously  Inherently a 2-D  No additional effort based process on feature complexity for adjustments planar substrate required for non- planar substrates continued

4This table has been adapted and used with permission from Prakash, S., M. Pinti and B. Bhushan (2012). Theory, Fabrication and Applications of Microfluidic and Nanofluidic Biosensors. Phil. Trans. R. Soc. A 370(1967): 2269-2303. Copyright 2012 RSC Publishing.

Table 2 continued IInterferometric  Optical technique with  Interference Lithography lower start-up cost patterns used for  Potential for high patterning more throughput complex  Smallest feature is 34 nm structures lead to achieved by immersing uneven exposure substrate in water  Works very well for gratings E-beam  Excellent control of feature  Time consuming dimensions Focused Ion  Excellent control of feature  Time Consuming Beam dimensions – smallest achieved  Removes the need for a separate etching step Nanoimprint  High throughput while  Requires a master Lithography preserving feature sizes from master – may be made with direct writing process Soft  High throughput while  Limited to Lithography preserving feature sizes polymers from master – may be made with direct writing process Pattern Dry Etching  Anisotropic  Specialized Transfer  Reduced undercut equipment  User does not need to  Toxic Gases handle chemicals

Wet Etching  Simple with readily  Photoresist available equipment in delamination most labs during long  Helps remove particulate etches defects  May be isotropic

continued

Table 2 continued Bonding Anodic  High Bond Strength  Specialized  Successfully bonded 2 nm equipment deep nanochannels  Requires substrate planarity  Limited to glass- silicon bonding  High voltage can cause channel bowing and collapse Fusion  Strong Bond  High  Successfully bonded 5 nm Temperature deep channels  Collapse due to material re-flow  Requires matched coeff. of thermal expansion Adhesive  Relatively simply and fast  Collapse due to flow of un-cured polymer  Collapse from lower Young’s Modulus  Only for polymer based devices Capping  Relatively simple and fast  Poor control over final channel dimension  Generally for high aspect ratio channels Sacrificial Lithography +  Removes the need for  Channel collapse Layer etching bonding step post channel can occur due to Release etch capillary forces  Successful channels bond down to ~ 10 nm

2.4 Fabrication of Gated Nanofluidic Devices

Gated nanofluidic devices, or nanofluidic field effect devices, have a gate electrode embedded in the nanochannel wall. The fluidic architecture is either a nanopore that with an elliptical/ round cross section or a nanochannel with a rectangular cross section. Note in the relevant citations long nanopores (퐿 ≥ ~1 µm) nanopores are sometimes referred to as nanotubes. Fabrication procedures specific to each device geometry are described next. A summary of fabrication procedures as well as a schematic of the fabricated devices referenced here are shown at the end of each subsection in Table

3 (nanopore devices) and Table 4 (nanochannel devices).

2.4.1 Gated Nanopore Devices

Gated nanopore devices feature a gate-all-around geometry with a conducting annular gate electrode incorporated along a portion of the length of an insulating nanopore (schematic, Figure 7). The nanofluidic architecture has a circular or elliptical cross section, though the pore itself may be cylindrical (Joshi et al. 2010), conical

(Kalman et al. 2009), or hourglass shaped. The gate electrode spans the entire circumference of a certain length of the pore, where the position of the gate electrode along the length of the pore has been shown by modeling studies to affect the relative impact of the gate electrode on the ionic transport through the nanopore (Ai et al. 2011).

Gated nanopore devices are fabricated by either adding a gate electrode to an existing nanopore membrane (Kalman et al. 2009; Shin et al. 2012), or by etching nanoscale holes through a multi-layer membrane consisting of insulating and conducting layers (Nam et

al. 2009; Joshi et al. 2010; Jiang et al. 2011). After the formation of a gate electrode within the nanofluidic pore by either method, a dielectric layer is deposited on the gate electrode to isolate the gate electrode from the fluid in the pore during device operation.

Kalman et al. (Kalman et al. 2009) evaporated a Cr adhesion layer followed by a gold gate electrode on a PET membrane with pre-fabricated conical nanopores. A similar technique was employed by Shin et al. (Shin et al. 2012) who used sputter deposition to add an aluminum electrode to a commercially available porous alumina membrane.

While eliminating the need for development of fabrication protocols to form the nanofluidic architecture, additive metal deposition techniques such as e-beam evaporation or sputtering can locally alter the dimensions of the nanopore. Shin et al. (Shin et al.

2012) showed that after sputter deposition of 300 nm of aluminum the average diameter of the nanopores decreased from 320 nm to 28 nm. The metal deposition, however, does not alter the nanopore diameter through-out the entire length of the pore. The result was a

~300 nm long nanopore with a diameter of 28 nm followed by a 320 nm diameter pore that spans the remaining length of the alumina membrane. Using a pre-fabricated membrane, the gate electrode can be placed at either the entrance or the exit of the pre- fabricated pore.

Nanopores with gate electrodes integrated into the center of the nanopore are generally fabricated using a combination of e-beam lithography and reactive ion etching

(Nam et al. 2009; Joshi et al. 2010; Petrossian et al. 2010) or through milling of a membrane stack with a focused ion beam (Jiang et al. 2010; Jiang et al. 2011; Paik et al.

2012) or transmission electron microscope (Jiang et al. 2010). Generally, a SiNx layer deposited by low pressure chemical vapor deposition (LPCVD) (Nam et al. 2009; Jiang et al. 2010; Jiang et al. 2011; Paik et al. 2012) or a thermally grown SiO2 layer (Joshi et al. 2010; Petrossian et al. 2010) is added to insulate both sides of a silicon handle wafer.

A conducting layer to serve as the gate electrode is added to one side of the insulated wafer. Standard UV lithography is used to define large fluidic reservoirs (on the order of

100’s of microns, Figure 11). Reactive ion etching transfers the reservoir pattern into the top insulating layer followed by wet etching with KOH to create reservoirs in the silicon handle wafer. An example of a process flow chart from Nam et al. is given in Figure 16.

In the case where the gate electrode material is compatible with reactive ion etching (for example a doped Si (Joshi et al. 2010; Petrossian et al. 2010) or TiN (Nam et al. 2009) gate electrode) e-beam lithography was used to define the nanopore cross section with pattern transfer to the remaining insulation layer and gate electrode layer achieved through reactive ion etching (Nam et al. 2009; Joshi et al. 2010; Petrossian et al. 2010). The resulting nanopores with annular electrodes integrated along the length of the nanopore can be well controlled with diameters on the order of 10’s of nanometers, where the final pore has a cylindrical geometry (Nam et al. 2009; Joshi et al. 2010;

Petrossian et al. 2010).

Figure 16: An example of a process flow chart for gated nanopore device taken from Nam et al. (2009). Fabrication begins with a membrane stack including a silicon handle wafer (gray), Si3N4 insulting layers, SiO2 insulating layers, and a conducting TiN gate electrode. UV lithography and wet etching with KOH were used to etch reservoirs in the silicon handle wafer. E-beam lithography and reactive ion etching (RIE) were used to define the nanopores in the membrane stack, since the gate electrode material (TiN) was compatible with RIE. Other groups who used Cr or other metal used FIB or TEM milling to define the nanopores in the membrane stack. The pore is then insulated using a conformal ALD technique. Other deposition technique for the gate dielectric are described below. Reprinted with permission from Nam, S. W., M. J. Rooks, K. B. Kim and S. M. Rossnagel (2009). Ionic Field Effect Transistors with Sub-10 nm Multiple Nanopores. Nano Lett. 9(5): 2044-2048. Copyright 2009 American Chemical Society.

In the case of gate electrode materials such as Au, Al, Ti, Cu, Ni, etc., nanopores were patterned by milling a nanoscale diameter hole using focused ion beam milling

(Jiang et al. 2010; Jiang et al. 2011; Paik et al. 2012) or electron beam milling with a transmission electron microscope (Jiang et al. 2010). Focused ion beam milling uses a finely focused beam of massive ions (usually Ga+) to locally erode the surface of a

material through atomic sputtering. Nanoscale holes with diameters on the order of 10’s of nanometers are defined with regular cross sectional geometries in metals, semiconductors, and insulating materials. In order to improve the resolution of the pores with integrated annular electrodes, Jiang et al.(Jiang et al. 2010) systematically studied electron beam milling using a transmission electron microscope through 10 different metals including Al, Au, Cu, and Ni. In the case of gated nanopore devices, the final pore diameter is controlled by the thickness of the insulation layer that isolates the gate electrode from the fluid in the pore. The total thickness of the insulation layer needed to shrink a pore to the desired diameter depends on the resolution of the fabrication technique used to define the initial uninsulated nanopore. For example, shrinking a pore

20 nm radius to a 1 nm radius requires 19 nm of insulation compared to 9 nm of insulation needed to shrink a 10 nm pore to 1 nm. As a thicker insulation layer translates to higher device operating voltages for a given device geometry, better control over the diameter of the uninsulated nanopore increases the available parameter space for designed devices (i.e. gate insulation thickness and coupled final pore diameter).

Transmission electron microscopes have been used to define nanopores down to 1 nm diameters in Si3N4 (Heng et al. 2004; McNally et al. 2008), compared to 10 nm using a

FIB (Duan et al. 2013).

The dominating mechanism of TEM milling is surface sputtering of ions, leading to increase in the irregularity of the pore cross section as well as milling time as the atomic number of the gate material was increased (Jiang et al. 2010). The low milling

rate and irregularity of the pore cross sectional geometry made TEM milling a less attractive alternative to focused ion beam milling for heavier gate electrode materials such as Au, Al, Ti, Cu, and Ni. However, when lighter materials such carbon nanotubes were used TEM milling was able to define pores with diameters of 9-12 nm compared to

76 nm for pores milled with a FIB (Jiang et al. 2010).

Once the gate electrode is incorporated along a certain length of the nanopore, an insulation layer is applied to isolate the gate electrode from the fluid in the pore. Physical deposition methods such as PECVD (Kalman et al. 2009; Shin et al. 2012) or sputtering

(Shin et al. 2012) have been employed for the insulation layer but generally they are not able to fully coat the rough surface of the pore interior, allowing a higher gate leakage current compared to conformal methods (Shin et al. 2012). Atomic layer deposition provides a conformal insulation layer that allows the final nanopore diameter to be controlled within 1 nm (Nam et al. 2009; Jiang et al. 2010; Jiang et al. 2011; Paik et al.

2012). Each cycle in atomic layer deposition corresponds to a monolayer thick deposition from the reaction of the precursor gas molecule and water molecules on the surface of the substrate. The thickness of each layer approximately corresponds to the diameter of the precursor molecule. The process is self-limiting where the final thickness of the pore is limited by the size of the precursor molecule. Once the pore itself is smaller than the precursor molecule (~1-2 nm) the deposition stops as the precursor molecule can no longer penetrate into the pore. ALD can be time consuming compared to other methods depending on the thickness of the final oxide layer.

Shin et al.(Shin et al. 2012) used an anodization process to form an Al2O3 insulation layer on their aluminum gate electrode. A potential difference is applied between an electrolyte solution and the aluminum layer (anode, hence anodization) which causes the aluminum to oxidize. Through absorption of ions into the aluminum, the aluminum layer swells as the oxide forms. The oxide layer thickness and therefore the pore diameter depends on the maximum voltage used during the anodization process.

Longer dwell times at the maximum voltage can help reduce pinhole defects in the oxide layer. While the anodization process provides a conformal layer, the swelling of the aluminum layer as the oxide forms must be taken into account.

Joshi et al.(Joshi et al. 2010) used a thermally grown oxide to insulate a Si gate electrode. Thermally grown oxide is conformal in nature. Volume expansion and oxide growth rates are well characterized for oxidation of silicon allowing control over the final pore diameter.

Gated nanofluidic devices with circular or oval-shaped cross sections can also be fabricated using sacrificial layer etching (Vermesh et al. 2009). In this case the insulation layer which will serve as both the channel wall and the insulation layer for the gate electrode is applied to a sacrificial material. Karnik et al. (Karnik et al. 2005) coated a silicon nanowire with a 600 nm thick SiO2 layer. A Cr electrode was patterned on top of the SiO2 using UV lithography. The SiO2 was etched to gain access to the ends of the nanowires which were selectively etched to release nanopores. The fabricated nanopore geometry is controlled by the dimensions of the sacrificial silicon nanowires. A similar

technique was employed by Fan et al. (Fan et al. 2008) who used a co-block polymer template to fabricate a porous silica membrane. The organic polymer template was removed through a calcination process to release silica nanopores. A Cr/Au layer was sputtered over the nanopores and patterned to form gate electrodes along the length of the nanopores using UV lithography. Patterning the gate electrode along the length of the nanopores allows for more control over the placement of the gate electrode than in the fabrication protocols listed above, though dependence on gate electrode location was not investigated. Specific fabrication protocols used to fabricate gated nanopore devices by several studies referenced in this dissertation are summarized in Table 3.

Table 3: Select device dimensions, fabrication materials, and fabrication methods from previously reported gated nanopore devices. All of the devices listed here feature gate-all-around geometries except Karnik et al. (Karnik et al. 2005) and Fan et al.(Fan et al. 2008) who used sacrificial layer etching techniques to define nanopores and sputter deposition and lithography to define gate electrodes along the length on the outside of the nanopores. All device schematics are used or adapted (some labels removed) from the cited references. Device schematics reproduced with permission, as indicated in the footnotes. 1st Author Pore Length Nanopore Gate Gate Deposition Schematic Diameter Fabrication Dielectric 5 Fan (2008) < 7.9 nm 400 μm Dip-coating of solgel Cr/Au SiO2 Dip coating of precursor and solgel precursor calcination

6 Jiang (2010) 30 nm 100 nm FIB or TEM 10 types Al2O3 ALD

Jiang (2010) 20 nm 100 nm FIB Cr Al2O3 ALD Same as above

85 7 Kalman (2009) 5 – 12 nm 12 μm Pre-fab - Conical Au SiO2 PECVD

continued

5 Schematic reprinted by permission from Macmillan Publishers Ltd: Nature Materials Fan, R., S. Huh, R. Yan, J. Arnold and P. Yang (2008). Gated proton transport in aligned mesoporous silica films. Nature Materials 7: 303-307, copyright 2008

6 Schematic reproduced with permission from Jiang, Z., M. Mihovilovic, J. Chan and D. Stein (2010). Fabrication of nanopores with embedded annular electrodes and transverse carbon nanotube electrodes. J. Phys.: Condens. Matter 22: 454114, doi:10.1088/0953-8984/22/45/454114.

7 Springer and the original publisher Analytical Bioanalytical Chemistry, 394, 2009, 414, Control of Ionic Transport Through Gated Single Conical Nanopores, Kalman, E. B., O. Sudre, I. Vlassiouk and Z. S. Siwy, 1B, with kind permission from Springer Science and Business Media.

Table 3 continued 8 Ɨ Karnik (2005) 10 – 100 nm ~10 μm Sacrificial Etch of Cr SiO2 LPCVD Silicon Nanowires (Fan et al. 2003)

9 Lee (2015) 7.5 nm 20 μm E-beam / RIE AZO Al2O3 ALD Wet etching with BOE

10 Nam (2009) 1 – 2 nm 140 nm E-beam / RIE TiN TiO2 ALD

86 continued

8 Schematic reproduced with permission from Karnik, R., R. Fan, M. Yue, D. Li, P. Yang and A. Majumdar (2005). Electrostatic Control of Ions and Molecules in Nanofluidic Transistors. Nano Lett. 5(5): 943-948. Copyright 2005 American Chemical Society. 9 Schematic reproduced from Lee, S.-H., H. Lee, T. Jin, S. Park, B. J. Yoon, G. Y. Sung, K.-B. Kim and S. J. Kim (2015). Sub-10 nm transparent all- around-gated ambipolar ionic field effect transistor Nanoscale 7(3): 936-946. with permission of The Royal Society of Chemistry 10 Schematic reproduced with permission from Nam, S. W., M. J. Rooks, K. B. Kim and S. M. Rossnagel (2009). Ionic Field Effect Transistors with Sub-10 nm Multiple Nanopores. Nano Lett. 9(5): 2044-2048. Copyright 2009 American Chemical Society.

11 Petrossian, L., S. J. Wilk, P. Joshi, Sahar Hihath, S. M. Goodnick and T. J. Thornton (2010). Fabrication of Cylindrical Nanopores and Nanopore Arrays in Silicon-On-Insulator Substrates. J. Microelectromech. Syst. 16(6): 1419-1428. Copyright 2010 IEEE. Reprinted with permission from Joshi, P., A. Smolyanitsky, L. Petrossian, M. Goryll, M. Saraniti and T. J. Thornton (2010). Field effect modulation of ionic conductance of cylindrical silicon-on- insulator nanopore array. J. Appl. Phys. 107: 054701-054706. Copyright 2010 AIP Publishing LLC

Table 3 continued 12 Shin (2012) 20 nm 300 nm Pre-fab Al Al2O3 Anodization

13 Paik (2012) 160 – 220 80 – 140 FIB Au Al2O3 ALD nm nm

14 Vermesh ~25 nm 20 μm Silicon Nanowire ITO SiO2 LPCVD (2009) Templates (Melosh et al. 2003)

12 Schematic reproduced from Shin, S., B. S. Kim, J. Song, H. Lee and H. H. Cho (2012). A facile route for the fabrication of large-scale gate-all-around nanofluidic field-effect transistors with low leakage current. Lab Chip 12: 2568-2574 with permission of The Royal Society of Chemistry.

13 Schematic reproduced with permission from Paik, K.-H., Y. Liu, V. Tabard-Cossa, M. J. Waugh, D. E. Huber, J. Provine, R. T. Howe, R. W. Dutton and R. W. Davis (2012). Control of DNA Capture by Nanofluidic Transistors. ACS Nano 6(8): 6767-6775. Copyright 2012 American Chemical Society.

14 Schematic reproduced with permission from Vermesh, U., J. W. Choi, O. Vermesh, R. Fan, J. Nagarah and J. R. Heath (2009). Fast Nonlinear Ion Transport via Field-Induced Hydrodynamic Slip in Sub-20-nm Hydrophilic Nanofluidic Transistors. Nano Lett. 9(4): 1315-1319. Copyright 2009 American Chemical Society. 87

2.4.2 Gated Nanochannel Devices

Gated nanochannel devices feature a slit-like nanochannel or a nanochannel with a rectangular cross section. The gate electrode is patterned on one wall of the device over a select region of the length of the channel in contrast to the gate-all-around configuration for most gated nanopore devices (Figure 7). While the gate-all-around configuration is expected to be more efficient at controlling ionic transport for a given gate potential (Lee et al. 2015), the planar configuration is better suited for integration of multiple electrodes or studying dependence of flow gating on electrode position along the channel length

(Guan et al. 2011; Fuest et al. 2015). Additionally planar channels typically have optical access to the nanochannel itself, allowing larger parameter spaces for certain fluorescence studies.

Most gated nanochannel devices are fabricated using glass (fused silica (Karnik et al. 2005) or Pyrex (Matovic et al. 2012)) and/or silicon (Oh et al. 2008; Maleki et al.

2009; Oh et al. 2009; Oh et al. 2009; Veenhuis et al. 2009; Guan et al. 2011; Matovic et al. 2012) with a thermally grown oxide (Oh et al. 2008; Maleki et al. 2009; Oh et al.

2009; Oh et al. 2009; Guan et al. 2011) or an LPCVD Si3N4 insulation layer (Veenhuis et al. 2009) to prevent stray current paths during device testing. Channels are generally defined through lithography in combination with reactive ion etching (Karnik et al. 2005;

Oh et al. 2008; Oh et al. 2009; Oh et al. 2009; Veenhuis et al. 2009; Matovic et al. 2012) or through a direct writing processes such as focused ion beam milling (Maleki et al.

2009).

Gate electrodes are fabricated from metals such as Pt (Maleki et al. 2009), Cr

(Karnik et al. 2005), or doped (Oh et al. 2008; Oh et al. 2009; Oh et al. 2009) or undoped

(Veenhuis et al. 2009; Matovic et al. 2012) regions of the silicon wafer with a thermally grown oxide layer serving as the gate oxide. Bonding of two substrates to form sealed channels is performed through anodic bonding (Oh et al. 2008; Maleki et al. 2009; Oh et al. 2009; Oh et al. 2009; Veenhuis et al. 2009; Matovic et al. 2012) or techniques employing an interfacial adhesive layer (Karnik et al. 2005). As with all nanofluidic devices, channel collapse during bonding remains a challenge (Guan et al. 2011) where topography of the substrate introduced by the gate electrode creates an additional challenge for anodic and fusion bonding techniques (Maleki et al. 2009), which rely on the planarity of the two bonding surfaces to form leak-free seals (Mao et al. 2005).

Karnik et al. (Karnik et al. 2005) reported the first planar gated nanochannel device fabricated on a fused silica substrate. A sacrificial polysilicon layer was deposited on the fused silica substrate and patterned using UV lithography and reactive ion etching to form a template for the nanochannels. The sacrificial polysilicon layer was etched after device bonding, which helps avoid channel collapse during the bonding process.(Guan et al. 2011). A 600 nm thick layer of SiO2 was deposited over the polysilicon using low pressure chemical vapor deposition (LPCVD). A Cr layer was deposited over the SiO2 and patterned to form gate electrodes with a second SiO2 layer deposited over the gate electrodes. The SiO2 was selectively etched to gain access to the polysilicon.

Microchannels that would later serve as fluidic reservoirs were etched on a second fused silica wafer using UV lithography and wet etching with HF. The two fused silica wafers, one with microchannels and the other with polysilicon embedded in SiO2 and patterned gate electrodes were bonded using PDMS stamp and stick bonding (Satyanarayana et al.

2005), a technique that uses a thin interfacial layer of PDMS as an adhesive layer to bond

the two substrates and seal the reservoirs. The polysilicon was etched using a Xenon diflouride plasma to open the nanofluidic channels.

A similar sacrificial layer based fabrication procedure was employed by Guan et al. who patterned a Cr sacrificial layer on a 4 inch silicon wafer with a thermally grown oxide. PECVD was used to deposit 50 nm of SiO2 over the Cr sacrificial layer which was rapidly annealed to improve the quality of the oxide. Gate electrodes were defined on top of the SiO2 using a double lift off process. The reservoirs with support pillars were etched using DRIE (deep reactive ion etching) and bonded to a PDMS stamp. Cr wet etchant was pumped into the device to remove the Cr sacrificial layer. An example of a sacrificial layer process adapted to include gate electrodes is shown in Figure 17.

Pattern Sacrificial Layer Deposit Capping Layer Deposit and Pattern Electrode

Access Sacrificial Layer

Etch Sacrificial Layer

Substrate

Sacrificial Layer Capping Layer Gate Electrode

Figure 17: A sacrificial layer process (Figure 15) adapted to include gate electrodes. After patterning the sacrificial layer, an insulating or capping layer is applied. A metal layer is deposited on the capping layer and patterned to form a gate electrode. Another lithography and etch step is performed to gain access to sacrificial layer. The sacrificial layer is selectively etched to release nanofluidic channels.

In contrast, most other studies (Oh et al. 2008; Maleki et al. 2009; Oh et al. 2009;

Oh et al. 2009; Veenhuis et al. 2009; Matovic et al. 2012) used anodic bonding after the channel fabrication and gate electrode deposition and insulation to seal the nanochannels.

Veenhuis et al. (Veenhuis et al. 2009) developed a fabrication procedure similar to the one used by Schasfoort et al. (Schasfoort et al. 1999) to form the first planar gated microfluidic device. An oxide layer was thermally grown on a Si wafer. Nanofluidic channels were patterned using UV lithography and reactive ion etching to define nanotrenches in the SiO2. An insulating Si3N4 layer was deposited over the channels using low pressure chemical vapor deposition (LPCVD). The nanotreches defined on the

Si substrate were then bonded to a Pyrex cover via anodic bonding to form sealed channels. The gate electrodes and fluidic reservoirs were added after device bonding by using UV lithography, etching, and lift-off techniques on the backside of the Si wafer.

The channel depth reported by Veenhuis et al. was on the order of 100’s of nanometers.

Matovic et al.(Matovic et al. 2012) used a similar fabrication process to define nanochannels in a Pyrex wafer, also using UV lithography and reactive ion etching.

Fluidic reservoirs and channels were defined on the Pyrex wafer using UV lithography and wet etching with HF employing a Cr/Au etch mask. An SiO2 insulation layer was thermally grown on a Si wafer that would serve as a cover for the channels. The Si gate electrode and fluidic access ports were defined in the silicon wafer. The Si wafer with the gate electrode and fluidic access ports was bonded to the Pyrex wafer with defined channel network via anodic bonding to form sealed channels.

In several studies by Oh et al. (Oh et al. 2008; Oh et al. 2009; Oh et al. 2009) similar fabrication procedures were modified to include a wave-guide for interferometric

lithography, rather than UV lithography, to define the nanochannel pattern (Figure 18).

UV lithography and RIE were used to define patterns in thermally grown SiO2 on a silicon wafer. The patterned SiO2 served as a mask for selective boron doping of the wafer to form the gate electrode. The SiO2 layer was removed and an anti-reflective coating followed by photoresist were deposited. The nanochannel pattern was defined in the photoresist using interferometric lithography (IL). Cr was deposited and photoresist/Cr stacks were removed using lift-off in acetone. The Cr/anti-reflective coating (ARC) served as a hard mask and a CHF3–O2 plasma was used to etch nanochannels into the Si substrate. An oxide layer was thermally grown to insulate the channel from the Si substrate and to narrow the dimension of the channels defined by IL.

The Si substrate was bonded to a Pyrex cover with pre-drilled fluidic access ports via anodic bonding. Nanochannel width was on the order of 100 nm with the depth on the order of 100’s of nanometers.

Maleki et al. used focused ion beam milling to define the nanochannels, making their channels the only gated nanochannels which have both the depth and width less than

100 nm (Maleki et al. 2009). DRIE was used to define microfluidic reservoirs on a silicon wafer with a thermally grown oxide layer. Deposition and lift off processes were used to define Au/Cr contact pads. A Pt wire defined using FIB assisted deposition served as the gate electrode The nanochannel was then defined between the reservoirs, perpendicular to the Pt wire using FIB. The silicon wafer was anodically bonded to a glass wafer with pre-drilled fluidic access ports. Select dimensions and fabrication procedures of several gated nanochannel devices are summarized in Table 4.

Figure 18: A flow chart for the process developed by Oh et al. (Oh et al. 2008). A SiO2 mask (blue in b) is applied to a clean Si wafer (a) to allow selective doping of the Si substrate with boron (green). Panel (c) shows the boron doped region of the silicon substrate that will serve as the gate electrode. A photoresist and anti-reflective mask is applied to the Si (d) and patterned using interferometric lithography to create an evenly spaced array of parallel nanochannels (e). A Cr layer is applied (f) and a lift off process is used to form the negative image of the channels in Cr (g). The nanochannels are then etched into the Si substrate by reactive ion etching (h). The Cr etch mask is then removed and an oxide layer is thermally grown to insulate the gate electrode (green, boron doped Si) and the semiconducting Si substrate. Reproduced from Oh, Y.-J., T. C. Gamble, D. Leonhardt, C.-H. Chung, S. R. J. Brueck, C. F. Ivory, G. P. Lopez, D. N. Petsev and S. M. Han (2008). Monitoring FET flow control and wall adsorption of charged fluorescent dye molecules in nanochannels integrated into a multiple internal reflection infrared waveguide. Lab Chip 8: 251-258 with permission of The Royal Society of Chemistry.

Table 4: Select device dimensions, fabrication materials, and fabrication methods from previously reported gated nanofluidic devices. All of the devices listed here feature nanofluidic channels with a rectangular cross section.A The gate electrode formsB part16 nm Glass A of the length of the channel along one wall or in the case of Maleki et al., two walls. All device schematics are used from the cited PDMS A’ references. Device schematics reproduced with permission, as indicated in the footnotes. Glass Gold st PDMS 1 Author Depth Width Length Channel Fabrication Gate Gate Dielectric Deposition ChannelsSchematic Glass

15 Va A Fuest (2015) 16 nm 30 µm 5 mm UV lithography Au PDMS GlassSpun-Goldon C C Electrode D Nanochannel PDMS Sidewall A A’ Glass Substrate

PDMS Gate 16 nm

L1 L-L1 Inlet Glass Substrate Outlet µchannel Cross y μchannel μchannel L=5 mm Section x 16 Guan (2011) 8 nm 11 μm 116 μm Sacrificial Etch of Cr * SiO2 PECVD

Karnik 30 – 1 μm 120 μm Sacrificial Etch of poly Cr SiO2 LPCVD

9 17 4 (2005) 40 nm silicon

continued

15 More details provided in Chapters 3, 4, and 5. Schematic reproduced with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

17 Schematic reproduced with permission from Karnik, R., R. Fan, M. Yue, D. Li, P. Yang and A. Majumdar (2005). Electrostatic Control of Ions and Molecules in Nanofluidic Transistors. Nano Lett. 5(5): 943-948. Copyright 2005 American Chemical Society. 94

Table 4 continued

Matovic 155 nm 4 μm 10, 60, UV lithography and Si SiO2 Dry (2012)18 460 μm RIE oxidation

Maleki 20 nm 50 nm 2 μm Focused Ion Beam Pt wire SiO2 (2009)19 Milling

20 Oh (2008) 100 nm 400 – 16 mm Interferometric Doped Si SiO2 Thermal 500 nm Lithography and RIE Oxidation

95 Veenhuis 860 nm 5, 10, 12 mm RIE Si Si3N4 LPCVD

(2009)21 15,20, 100 μm

* Gate electrode is fabricated using a double lift-off though the gate material is no explicitly given

19 Schematic reprinted with permission from Maleki, T., S. Mohammadi and B. Ziaie (2009). A nanofluidic channel with embedded transverse electrodes. Nanotechnology 20: 105302 (1-6), doi: 10.1088/0957-4484/20/10/105302.

20 Reproduced from Oh, Y.-J., T. C. Gamble, D. Leonhardt, C.-H. Chung, S. R. J. Brueck, C. F. Ivory, G. P. Lopez, D. N. Petsev and S. M. Han (2008). Monitoring FET flow control and wall adsorption of charged fluorescent dye molecules in nanochannels integrated into a multiple internal reflection infrared waveguide. Lab Chip 8: 251-258 with permission of The Royal Society of Chemistry.

21 Schematic reproduced from Veenhuis, R. B. H., E. J. van der Wouden, J. W. van Nieuwkasteele, A. van den Berg and J. C. T. Eijkel (2009). Field-effect based attomole titrations in nanoconfinement. Lab Chip 9: 3472–3480 with permission of The Royal Society of Chemistry. 95

Chapter 3: Fabrication of a Gated Nanofluidic Device

Nanofluidic channels with embedded gate electrodes are attractive for a diverse range of applications because they allow active, tunable control over the surface charge at the wall-electrolyte interface (Jin et al. 2011; Guan et al. 2014; Fuest et al. 2015). The ability to modulate the surface charge in confined channels opens up exciting possibilities for electrostatic manipulation of charged species in a fluidic sample throughout the depth of the nanoscale channels (Karnik et al. 2005; Guan et al. 2011). However, before specific applications can be realized, reliable fabrication techniques that are versatile enough to incorporate various elements of device design need to be developed.

In recent years, several other reports have demonstrated the complexity and challenges in fabricating “gated” nanofluidic devices, or devices with electrodes embedded in the nanochannel wall (Mijatovic et al. 2005; Perry et al. 2006; Nam et al.

2009; Guan et al. 2014). This chapter reports on the development of fabrication procedures to produce micro- and nanofluidic networks with an array of individually addressable surface electrodes embedded in one wall of the nanochannels. As described in Section 2.3, gated nanofluidic devices are broadly classified into nanopore and nanochannel field effect devices. Fabrication protocols for nanopore field effect devices

(Section 2.4) typically involve milling or etching through a membrane stack of insulating and conducting layers, where the conducting layers form the gate electrodes. Since the

diameter of a milled pore increases with milling time, focused ion beam and other milling procedures place limitations on the thickness of the membrane stack for a desired nanoscale pore diameter. Etching based procedures are limited to materials which are compatible with dry etching techniques, limiting the choice of gate electrode materials.

Each electrode incorporated along the nanopore will add thickness to the membrane stack, where an additional insulation layer between metal electrode layers will be required to eliminate current paths between the conducting layers. Prevention of a conduction path through the membrane stack itself will place a lower limit on the insulator thickness, particularly considering the high contact area between layers (see

Figure 7). A nanochannel or planar configuration was therefore selected for the device design since a planar design more easily allows incorporation of multiple electrodes at desired spacing along the nanochannel length.

The device reported here consists of three layers. The bottom layer has the micro- and nanochannels, the intermediate layer is a dielectric material that isolates the gate electrodes from the fluid in the channels, and the top layer or cover which has the patterned array of electrodes and forms the 4th wall or roof of the nanochannels. The electrodes have an engineered size and spacing along the length of the nanochannel allowing investigation of the effect of the gate electrode location on the modulation of electrokinetic transport caused by the embedded electrode, an effect that has received limited attention in previous reports. In this dissertation results are reported with only one electrode active at a given time. However, the individually addressable electrodes further open up the possibility of using multiple electrodes at engineered locations with

independently applied potentials (i.e. individually addressable) to systematically alter the surface charge distribution along the channel length as well as the possibility of using multiple electrodes with time lagged signals, adding to versatility of the design.

As with previously reported gated nanofluidic device designs (Section 2.4), general fabrication techniques detailed in Section 2.3 were implemented or adapted to create a multi-step fabrication procedure for the gated nanofluidic device, where the available techniques were primarily determined by the choice of substrate materials

(bottom and top layers). Of the substrate materials that have well developed fabrication techniques (Section 2.3), glass substrates were selected for both the bottom layer with the micro- and nanochannel network and the top layer with the patterned electrode array, primarily due to the transparency and electrical insulation properties of glass. At least one transparent substrate was desired to allow optical access for inspection of microchannels post-bonding and to allow fluorescence based studies. While thermal growth of oxides for silicon is a well characterized process, using a second glass substrate eliminated the need to grow an oxide layer to prevent stray current paths through the substrate. A detailed description of the process developed to fabricate the device as well as relevant design considerations for each step are presented next. Characterization of the fabricated device was performed after each step in the fabrication process to confirm production of desired device features as well as to confirm functionality of the device.

3.1 Device Design

Figure 19 shows a schematic representation of the gated nanofluidic device with embedded electrodes. The channel network design consisted of two microchannels which served as fluidic reservoirs for a bank of nanofluidic channels etched in borosilicate glass.

A BB 16 nm Glass A

PDMS

Glass SubstrateGlass PDMS Gate insulation Gold 16 nm PDMS Channels μ channel Glass Substrate μ channel Glass y reservoir reservoir Va x C A Figure 19: (A) The schematic shows an exploded view of the gated nanofluidic device design. The fluidic network consisted of two 8 μm deep x 50 μm wide x 3.2 cm long microchannels connected by a bankGlass of Substrate three 16 nm deep x 30 μm wide x 5 mm long nanofluidic channels etched into borosilicate glass. An array of asymmetrically spaced, PDMS Gate individually addressable gold gate16 nmelectrodes (25 nm high x 25 μm wide) were patterned on a second glass substrate (cover). LThe1 coverL-L1 with the patterned gate electrodes was bonded to the substrate Inletwith theGlass channel Substrate networkOutlet using an intermediate PDMS layer y μ channel μ channel L=5 mm (red). The PDMS layerx isolated the gate electrodes from the fluid in the nanochannels. (B) The side view schematic shows the potential difference applied along the nanochannel length (axial potential, 푉푎). The direction of net fluid flow in the un-gated case (no potential applied to the embedded gate electrode) is marked by the red arrow. The gate electrode is used for active, tunable control over ionic transport through the nanofluidic channels, with changes in ionic transport characterized by changes in measured current. A full description of the experimental setup is provided below. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

The nominal dimensions of the microfluidic channels were 8 μm deep x 50 μm wide x

3.2 cm long. The microchannel length was chosen so that many parallel nanochannels could be added between the microfluidic channels to increase the total throughput and 99

therefore the magnitude of the current signal. Since the current through nanofluidic devices is typically on the order of pA to nA, several parallel nanochannels are often needed to ensure a reasonable current signal compared to the measurement noise. The depth and width of the microchannels were chosen to ensure that the volume of the microchannels was much greater than the volume of the nanochannels, so that the microchannel could be approximated as infinite reservoirs. The aspect ratio of the microchannels was chosen to ensure ease of bonding while maintaining a reasonable etching time for the microfluidic channels (8 minutes for ~ 8 μm depth).

The nanofluidic channels were nominally 16 nm deep x 30 μm wide x 5 mm long.

The low aspect ratio (Pinti et al. 2013) of the nanofluidic channels (depth << width) enables nanoscale effects similar to biological systems while providing high throughput and benefits of 1-D theoretical analysis (Prakash et al. 2008; Huo et al. 2011). The walls of the nanochannel are negatively charged, therefore, the nanochannels are expected to be cation selective under conditions of overlapped electric double layers. The length of the nanochannels allows the electric field to be approximated as 퐸푥 = 푉푎/퐿 where 퐸푥 is the axial electric field, 푉푎 is the potential difference in the axial direction, and 퐿 is the length of the nanochannel (Figure 19B) (Vlassiouk et al. 2008). The length of the nanochannel also allows incorporation of multiple electrodes at desired and/or designed spacing along the length of the nanochannels.

The device design featured six individually addressable gate electrodes spaced asymmetrically along the channel length (Figure 19A). The electrodes are considered individually addressable because an independent potential can be applied to each

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electrode. Details on electrode placement and spacing presented in Section 3.3. The gold

(Au) gate electrodes (25 nm high x 25 μm wide) were patterned on a second glass substrate that acts as a cover for the etched channels (Figure 19). A second glass substrate was chosen for the cover primarily for the electrical insulation properties of glass. The nominal height of the electrodes was chosen on the same order as the depth of the nanofluidic channels since protruding features on bonding surfaces result in unbonded regions and leaking devices (Maleki et al. 2009). Polydimethyl siloxane (PDMS) was chosen as the dielectric layer used to isolate the gate electrodes from the electrolyte within the nanochannels and to provide a surface for bonding the two substrates (one with channel features etched in borosilicate glass and the cover with the isolated gate electrodes). A schematic showing the exploded view of the device is shown in Figure

19A.

A potential difference between the two microchannel reservoirs (axial potential,

Va), drives electrokinetic flow through the nanofluidic channels. The net fluid flow for the un-gated case (no voltage applied to the embedded electrode) is indicated by the red arrow in Figure 19B. The device features gate electrodes embedded in the roof of the nanofluidic channel for active, tunable control over ionic transport through the nanofluidic channels by applying a potential to one or more of the gate electrodes.

Changes in electrokinetic transport are characterized by changes in measured current.

3.2 Channel Network Fabrication

Borosilicate glass substrates (Fisher Scientific No. 2 Borosilicate Cover Slips

50 mm x 24 mm x 0.17 to 0.25 mm thick, 12-543D) were used for the fluidic network.

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The channel networks were patterned using UV lithography and wet etching techniques.

An overview of the fabrication procedures for the micro- and nanofluidic channel network is shown in Figure 20 (Pinti et al. 2013). Next, each of the critical steps in the fabrication of devices is discussed in detail with the complete fabrication parameters used to make devices listed in Appendix C.

1 2 3 4

5 6 7 8

9 10 11 12

Figure 20: Flow chart of the channel network fabrication procedures (Pinti et al. 2013). Organic contaminates were removed from the borosilicate substrate with a Piranha solution (4:1 sulfuric acid to hydrogen peroxide). A chrome adhesion layer, followed by an inert Au metal mask layer was deposited on the Piranha cleaned substrate. Shipley 1813 positive tone photoresist was spun onto the metal mask, then exposed and developed to form the microchannel pattern. The substrate was exposed to gold etchant followed by chromium etchant to transfer the microchannel pattern into the metal etch mask. The microchannel pattern was then transferred, or etched, into the substrate using a 4:1 solution of DI water to 49% HF. The photoresist was stripped and a second UV lithography process with a spin process adapted for the non-planar substrate was used to pattern the nanofluidic channels. The nanochannels were etched with 10:1 buffered oxide etch. After the nanochannel pattern was transferred into the substrate, the metal mask was removed. Each step in the fabrication process is discussed in detail below. Reprinted with permission from Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013). Fabrication of Centimeter Long, Ultra-Low Aspect Ratio Nanochannel Networks in Borosilicate Glass Substrates. J. Nanotechnol. Eng. Med.. 4(2): 020905. Copyright 2013 ASME.

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3.2.1 Substrate Cleaning

First, a standard solvent de-grease was used to remove large particles and some of the organic contaminants from the glass surface. Substrates were carefully dried with N2 before soaking in a Piranha solution (4:1 96 % Sulfuric Acid to 30% Hydrogen

Peroxide). Piranha is an oxidizing solution commonly used to remove organic contaminants (Williams et al. 1996). The RMS surface roughness of the borosilicate substrate was measured before and after Piranha cleaning with an Asylum MFP-3D atomic force microscope (Figure 21). The reduction in the RMS surface roughness from

0.316 nm before Piranha cleaning to 0.076 nm after cleaning was attributed to removal of contaminants during the Piranha cleaning process that had not been removed by the solvent degrease.

Before Piranha Clean After Piranha Clean

Figure 21: Surface roughness of the borosilicate substrates measured before and after Piranha cleaning using an Asylum MFP-3D AFM. The RMS surface roughness decreased from 0.316 nm before cleaning to 0.076 nm after cleaning. The reduction of surface roughness was attributed to removal of contaminates on the glass surface during the cleaning process. The AFM scan size was 10 μm x 10 μm.

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3.2.2 Metal Etching Mask

A 10 nm chromium layer followed by a 100 nm gold masking layer were evaporated onto the Piranha cleaned substrate using a CHA Solution System E-Gun

Evaporator. Photoresist masking layers are prone to cracking and delamination from the glass substrate during isotropic wet etching with HF. The Cr layer serves as an adhesion layer and the Au layer is inert in the HF solution. The metal mask thus prevented pattern deformation due to photoresist delamination during wet chemical etching of the microchannel features (Bu et al. 2004; Iliescu et al. 2005; Tay et al. 2006; Zhu et al.

2009) (step 6, Figure 20). In Figure 22 SEM images of microfluidic channels wet etched without a metal etch mask (photoresist only) and with a metal etch mask (photoresist, Au, and Cr layers) are shown. The depth of the microchannel and un-bonded microchannel profile were also measured with a profilometer (Figure 22C and D). The sidewall profile for the microchannel etched with photoresist only has a broad, sloped shape in contrast to the relatively more abrupt, straight sidewalls for the microchannel etched with the metal mask. The total depth of the microchannel etched without the metal mask was ~1.5 µm compared to ~8 µm for the channel etched with the metal mask. The difference in depth for the same exposure time (8 minutes) to HF indicates that the photoresist only mask fully delaminated after about ~1.5 µm of etching. Once the mask delaminated, the HF solution began uniformly etching both the substrate and the channel rather than increasing the depth of the channel relative to the substrate surface. The delamination occurred unevenly resulting in a poorly controlled, irregular microchannel width.

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No metal mask Metal mask

µ channel

µ channel µ channel

A B

0.5 0 0.0 -2 -0.5

-1.0 -4

Height (um) Height

Height (um) Height -1.5 -6

-2.0 -8 0 50 100 150 200 250 300 0 50 100 150 200 250 300 C Distance (um) Distance (um) D

Figure 22: Comparison of a microfluidic channel etched using only photoresist as the masking layer (left panel) to a microfluidic channel etched with a photoresist layer, an inert Au metal layer, and a Cr adhesion layer as an etch mask (right panel). Both samples were exposed to a 4:1 DI water to 49% HF etching solution for 8 minutes. (A) SEM images of a microchannel etched without using a metal etch mask. The inset shows the irregular shape of the sidewall profile. (B) SEM images of a microchannel etched with a Cr/Au metal etch mask. The sidewall profile has a clear “step” from the substrate surface to the bottom of the microchannel. The inset shows the curved sidewall profile expected from an isotropic etch. The metal mask was not removed before the image in the inset was taken. SEM imaging confirmed that after etching the metal mask was still intact. (C) A profilometer scan of the microchannel etched without the metal mask. (D) A profilometer scan of the microchannel etched with the metal mask. A clear step is observed for the channel etched with the metal mask, in contrast to the channel etched without. The microchannel etched with the metal mask was ~ 8 µm deep in contrast to the channel etched without the metal mask which was ~ 1.5 µm deep. The difference in depth for the same exposure time to HF indicates that the mask fully delaminated after about ~1.5 µm of etching and the HF solution began uniformly etching the substrate and the channel rather than increasing the depth of the channel relative to the substrate surface.

105

Cr/Au masking layers have been shown to withstand up to 50 μm deep etches

(Iliescu et al. 2005; Tay et al. 2006). Beyond 50 μm, significant pinhole damage has been reported as the HF begins to penetrate through small defects in the metal masking layer that developed during the metal deposition. If the photoresist mask is not removed after patterning the metal mask, the hydrophobic nature of photoresist compared to the hydrophilic Cr/Au mask prevents penetration of HF into small defects in the metal mask thus reducing pinhole defects and increasing maximum etch depth to ~ 500 μm (Tay et al.

2006). In this work, the photoresist was not removed after patterning of the metal mask

(Figure 20, steps 5 and 6) and thus little pinhole damage was observed in etched samples.

The Au metal mask prevented the distortion of the sidewall profile caused by the photoresist delamination. The inset for the metal mask case (inset Figure 22B) was taken before the metal mask was removed, confirming that the metal mask was still intact after the HF etch. Characterization of the depth of the microchannel as a function of exposure time to the HF etchant can be found in Appendix B.

While the metal mask allowed deeper microchannels with more vertical sidewalls to be fabricated, notch defects were observed for both micro- and nanochannels due to residual stress in the Cr/Au masking layer. Tensile stress between 120 MPa (e-beam deposition) and 250-300 MPa (sputter deposition) has been measured for Cr/Au masking layers, with small defects in the masking layer acting as stress concentrators. As the isotropic etch progresses, gradients in stress develop near the edge of the masking layer causing mask breakage and notch defects (Iliescu et al. 2005). An SEM image of the notch defects present on the sidewall of an etched nanochannel is shown in Figure 23. The metal

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mask was removed before the image was taken. An SEM image that shows the notch defects in the metal mask is given in Appendix B.

200 nm

10 μm

Figure 23: An SEM image of the micro- and nanochannel interface of a 55 nm deep nanofluidic channel. The inset shows a zoomed in view of the nanochannel sidewall. The zoomed in image was taken at the location denoted by the red dashed box. Semi-circular “notch” defects in the nanochannel sidewall were caused by stress gradients at the edge of the Cr/Au metal mask. Stress gradients at the mask edges cause the mask to break as the isotropic etch progresses.

3.2.3 UV lithography

The channel network design required production of features with two different length scales on a single substrate (i.e. microchannels and nanochannels). The microfluidic channels were first patterned using UV lithography, with pattern transfer to the substrate achieved through wet etching with 4:1 DI water to 49% HF (Figure 20, step 6).

Photolithography begins with spin coating of a photo active polymer which is then exposed to UV light in the desired pattern. A photolithography mask with designed chromium and glass regions is placed between the substrate and the UV light source allowing selective

107

exposure of the photoresist (see Figure 11). For positive tone photoresists, such as Shipley

1813 used in this work, the UV light breaks the bonds of the photoresist in the exposed areas, reducing the molecular weight of the polymer. The exposed photoresist selectively dissolves in a chemical developer solution (MF-319 for Shipley S1813) leaving an unprotected region of the underlying metal mask in the desired pattern (Figure 20, step 4).

Regions where the metal mask was unprotected were chemically etched using a potassium iodide based solution for the gold layer (Transene Gold Etchant Type TFA) and an HCl based etchant for the chromium layer (Cyantek Cr-7S Chrome Etchant). After etching the metal mask, the glass substrate was left exposed in the desired pattern. The pattern was transferred to the glass substrate using a 4:1 solution of DI water to 49% HF with an etch rate of approximately 1 μm/min. Microchannels with depths of ~8 μm were etched for

8 minutes (Figure 22). The remainder of the substrate was protected from the etchant by the photoresist and, if the photoresist delaminated, by the inert gold layer.

Once the etching was completed the photoresist masking layer was removed by rinsing and sonicating in N-Methylpyrrolidone (NMP) for 7 minutes followed by rinsing with methanol and isopropyl alcohol (IPA). The substrate was thoroughly dried with N2 and then exposed to an oxygen plasma to remove any remaining photoresist. A second UV lithography and wet etching sequence was used for patterning the nanofluidic channels

(Figure 20, steps 8-11). Once the nanochannels were patterned, the metal etching mask was removed using Au and Cr etchants followed by soaking in an Aqua Regia (3:1 HCl to Nitric

Acid Solution) bath for 55 minutes which removed any remnants of the metal mask layers.

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Patterning of non-planar substrates (such as patterning nanochannels on the glass substrate with microchannels reported here) has been a challenge due to the 2-D nature of photolithography (Leong et al. 2005). Non-planarity of the substrate leads to uneven coating in the initial spin step and ultimately to exposed regions of glass in undesired areas.

Scanning electron microscope (SEM) images of an exposed “ridge” on the edge of the microchannel after spin coating with photoresist are shown in Figure 24.

A B

Figure 24: SEM images of an un-even layer of photo active polymer (photoresist). The photoresist was spun onto the substrate containing two previously fabricated microchannels. The “bright” regions represent uncoated glass on the edge of the microchannel that will be etched upon exposure to 10:1 buffered oxide etchant. (A) The full width of the microchannel is shown as well as an uncoated “ridge” that connects the nanochannels near their entrances. Note that an earlier design has 100 µm wide microchannels. All device testing data reported in this dissertation is for 50 µm wide microchannels. (B) A higher magnification of the area marked by the box in A. The top portion of the microchannel wall remains uncoated with photoresist. After etching, this will result in an undesired ~4 μm wide edge channel that created a perpendicular fluidic path connecting adjacent nanochannels. Fluid can flow between nanochannels on the path indicated by the red arrow. The dashed red line indicates the desired edge of the photoresist, which would ensure the microchannel was the only path between nanochannels.

The exposed ridges that formed during the nanochannel lithography step were transferred to the substrate during wet etching with 10:1 buffered oxide etchant (Figure 109

25) and subsequently adjacent nanochannels were connected by a ~ 4 μm wide “edge channel” which had the same depth as the nanochannels. Following substrate etching and device bonding, fluid would be able to flow between the nanochannels along the path indicated by the red arrows in Figure 24B and Figure 25. The dashed red line in Figure

24B indicates the desired edge of the photoresist, which would make the microchannel the only path between the nanochannels.

Figure 25: SEM image of two parallel nanofluidic channels connected by an etched ridge or “edge channel”. The edge channel runs parallel to the microfluidic channel and resulted from undesired exposed regions of the non-planar substrate following the nanochannel lithography step. The nanochannels shown in this image are 227 ± 6 nm deep. As the ridge is a defect that occurred during the nanochannel lithography step, the edge channel is the same depth as the nanochannels (Pinti et al. 2013). Fluid can flow between adjacent nanochannels along the path indicated by the red arrows. Reprinted with permission from Pinti, M, and S. Prakash (2011). A Two-Step Wet Etch Process for the Facile Fabrication of Hybrid Micro-Nanofluidic Devices. 2011 ASME International Mechanical Engineering Congress and Exposition, Denver, Colorado. Copyright 2011 ASME.

To eliminate defect formation, new fabrication techniques for non-planar fabrication have been developed by other groups (Jackman et al. 1995; Leong et al. 2005;

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Yeom et al. 2009). For example, detachment lithography uses a polymer stamp coated with a layer of photoresist which is brought into contact with the non-planar substrate and cured under heat and pressure. The polymer stamp is removed through a rapid peeling process and the photoresist is transferred to the substrate (Yeom et al. 2009). While methods such as detachment lithography can be used to create complex three dimensional structures, for the process reported here, a solution to the observed defect formation at the micro- and nanochannel interface that could be more easily incorporated into existing fabrication procedures was developed. The spin coating of the photoresist was modified by adding a third spin step and reducing the spin acceleration by 1.5 orders of magnitude compared to the microchannel spin recipe. The modified spin recipe produced a film that fully covered the pre-patterned substrate allowing production of the desired design and easy integration into existing process steps. A representative SEM image of 227 nm deep nanofluidic channels etched without the edge channel is shown in Figure 26. Detailed description of all process parameters, including spin recipes, is given in the Appendix C. After the nanochannel pattern was successfully defined using photolithography, the nanochannel pattern was transferred to the borosilicate substrate using 10:1 buffered oxide etchant

(BOE). The depth of the nanochannel prior to bonding depends on the exposure time to the wet etchant. Figure 27 shows the measured depth of nanofluidic channels as a function of time exposed to 10:1 BOE. Buffered oxide etchant is an HF solution that contains NH4F.

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Nanochannels

Gold PDMS Va ChannelsA Microchannel C Glass Va Figure 26: SEMA image of the micro- nanochannel interface in a properly fabricated C device. The ridge and subsequent edge channel produced after wet etching was Glass Substrate eliminated by adding a third spin step to the typical two-step photoresist spin recipe and reducing the spin acceleration by 1.5 orders of magnitude compared to standard recipes. PDMS Gate Reprinted with permission from Fuest, M., C. Boone, A.T. Conlisk, and S. Prakash; Glass16 nm Substrate Cation Dependent Transport in a Field Effect Nanofluidic Device. Technical Digest of the 18th International Conference on Solid-State Sensors, Actuators and Microsystems L1 L-L1 PDMS Gate Transducers 2015, Anchorage, Alaska, 6/21-25/2015 Transducers Research Foundation, Inlet Glass Substrate Outlet 16 nm y μchannel Clevelandμchannel (2015). Copyright 2015 IEEE. L=5L1 mm L-L1 x D Inlet Glass Substrate Outlet y μchannel μchannel L=5 mm Since the etch rate depends on the amount of free fluoride ions, adding ammonium x fluoride to HF stabilizes the amount of free fluoride ions and the solution pH, resulting in

a more controlled, constant etch rate compared to HF (Madou 1997). Depth measurements

for nanofluidic channels were performed using an Asylum MFP – 3D AFM. An example

of an AFM scan of a nanochannel etched for 20 seconds in 10:1 BOE is shown in Figure

28. The un-bonded nanochannel was 16 ± 1 nm in height and 31 ± 1 μm wide.

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250

200

150

100

Depth (nm)Depth 50

0 0 50 100 150 200 250 300 Etch Time (s)

Figure 27: An etch plot showing the depth of the un-bonded nanofluidic channel as a function of time exposed to 10:1 buffered oxide etchant. Depths ranged from 16 ± 1 nm for a 20 second etch time to 227 ± 6 nm for a 300 second etch time. The nanochannel depth was measured with an Asylum MFP-3D AFM. Reprinted with permission from Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013). Fabrication of Centimeter Long, Ultra-Low Aspect Ratio Nanochannel Networks in Borosilicate Glass Substrates. J. Nanotechnol. Eng. Med.. 4(2): 020905. Copyright 2013 ASME.

A B 31 μm

) 15 10 16 nm 5

Height (nm Height 0

0 10 20 30 40 Width (μm)

Figure 28: (A) An AFM line scan of an un-bonded nanochannel after 20 second exposure to 10:1 buffered oxide etchant. The depth was 16 ± 1 nm and the width was 31 ± 1 μm. Reprinted with permission from Pinti, M, and S. Prakash (2013 Fabrication of Hybrid Micro-Nanofluidic Devices with Centimeter Long Ultra-Low Aspect Ratio Nanochannels. 2013 Proceedings of the 2013 ASME International Mechanical Engineering Congress and Exposition, San Diego, California. Copyright 2013 ASME. (B) A 3-D image of the 16 nm deep x 31 μm wide un-bonded nanochannel. The AFM scan area was 40 μm x 40 μm.

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3.3 Embedded Electrode Array

The second glass substrate that served as the cover to the etched fluidic networks was a microscope slide (Fisherbrand Microscope Slide, 1 mm thick, 12-550C) custom cut to 54 mm x 54 mm at the glass shop in the Department of Chemistry at OSU. The glass cover was manually scrubbed using a cleanroom wipe with a 1% Alconox/DI water solution to remove visible contaminants from the glass cutting process. The cover was then cleaned with a standard solvent degrease as described earlier, carefully dried, and placed in a Piranha bath for 10 minutes. The glass covers were then rinsed with DI water and dried with N2.

A 7 nm thick Cr adhesion layer followed by an 18 nm thick Au metal layer was evaporated using a CHA Solution System E-Gun Evaporator for a total nominal electrode thickness of 25 nm. An AFM scan showing the measured electrode height is given in

Appendix B. The metal layers were patterned using standard UV lithography and wet- etched using Transene Gold Etchant Type TFA and Cyantek Corporation CR-7S Chrome

Etchant for the Au and Cr layers respectively to form the array of six individually addressable electrodes (Figure 29).

The electrodes were each 25 µm wide. The spacing between the six electrodes shown in Figure 29A was, from left to right, 30 µm, 30 µm, 60 µm, 30 µm, and 90 µm.

Once the electrode array had been defined on the glass cover, fluidic access ports were drilled in the cover using a drill press with a 3/32” (2.4 mm) diameter diamond core drill bit.

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B 100 µm A 100 µm

20 μm 10 μm

C D

Figure 29: A schematic representation of the glass cover with the patterned Au/Cr electrode array is shown in the center of the image. Insets show actual images of respective positions of the electrodes. (A) A micrograph image of the center of the electrode array showing the asymmetric placement of the six individually addressable electrodes. The image was taken using a 10x objective. (B) The micrograph image, taken using a 4x objective, shows curves in the electrodes needed to make the connections between the portion of the electrode over the nanochannels and the electrical contact pad. (C) An SEM image of the connection between an electrode and an electrical contact pad. The contact pads were used to make connections between the gate voltage power supply and the electrodes. (D) An SEM image of a bend in one of the electrodes.

The Au gate electrodes were coated with polydimethyl siloxane (PDMS) layer to insulate them from the fluid in the nanochannels post-bonding. The PDMS layer also served as a bonding surface to seal the glass cover with gold electrodes to the glass substrate with the etched fluidic network. The polydimethyl siloxane layer was formed by first

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mixing a 10:1 ratio by mass of Sylgard 184 elastomer base to Sylgard 184 elastomer curing agent. The liquid polymer was de-gased under vacuum and pre-cured for 1 hour and 20 minutes. The glass cover with patterned electrodes and drilled fluidic access ports was treated with oxygen plasma for 3 minutes at 200 W prior to spinning the pre-cured liquid

PDMS. Copper tape was used to seal the back side of the fluidic access ports during spin coating. Liquid polymer was injected into the fluidic access ports and spun at 300 rpm for

5 seconds. The glass cover was then fully coated with liquid PDMS and spun at 1000 rpm for 60 seconds.

The efficiency of the electrokinetic transport control from the gate electrodes in the final device decreases with the thickness of the dielectric layer, making the ideal case a thin continuous film of PDMS. The final thickness of a spin-coated polymer film depends on a balance of centrifugal forces and viscous forces. These forces are not constant with time or position during the spin process due to mass loss and significant changes in viscosity (maximum theoretical variation of 6 orders of magnitude (Bornside et al. 1989)) due to solvent losses from evaporation and convection during the spin process. Previous modeling reports have indicated that the final thickness of the polymer film decreases with maximum spin speed (휔) until 휔 ≈ 4000 rpm. Above a maximum spin speed of 4000 rpm the final polymer film thickness remains approximately constant

(Bornside et al. 1989). Initial spin recipes, thus, had a maximum speed of 5000 rpm for

60 seconds. Spun-on PDMS layers had discontinuities which caused leaking channels post-bonding. Figure 30A shows a representative image of a device with discontinuities in the PDMS. Each location near the fluidic channels where a patch of PDMS was

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missing resulted in a leak in the fluidic network. Maximum spin speeds in subsequent tests were reduced, with most consistent continuous coverage observed for a maximum spin speed of 1000 rpm (Figure 30B).

100 µm A B

Figure 30: (A) A bonded device with a discontinuous PDMS film. The regions of missing PDMS near the fluidic channels caused leaking. (B) Reducing the maximum spin speed of the liquid PDMS from 5000 rpm (device in A) to 1000 rpm (device in B) resulted in a continuous polymer film and a leak-free bond.

The final thickness of the PDMS film is determined by i.) the mass fraction of solvent in the liquid PDMS, which determines viscosity, ii.) the initial thickness of the

PDMS, iii.) the surface energy of the cover, and iv.) the spin recipe (i.e. number of steps and speed, acceleration, and time for each step). While full experimental characterization of film thickness as a function of the above parameters is beyond the scope of this work, process control is an essential component of reliable device fabrication. A full description of process parameters used here including PDMS mix, degas/pre-cure, and oxygen plasma treatment of covers before spinning, and spin recipe is given in Appendix C. The thickness of the PDMS layer for bonded devices was measured from device cross section images

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(Section 3.5). After spin-coating, the PDMS insulation layer was cured on a 70° C hot plate for at least 12 hours. In order to seal the 16 nm deep channels with glass-PDMS bonding procedures, the PDMS layer must be well-cured before bonding. Partially or inadequately cured PDMS collapsed into both micro- and nanofluidic channels, sealing them off and preventing or obstructing flow (Figure 31).

µ channel

PDMS

100 μm

Figure 31: A micrograph image of PDMS partially collapsed into the microfluidic channel. Partial PDMS collapse can prevent or obstruct flow. Fully curing the spun-on PDMS layer prior to bonding prevented partial PDMS collapse. To prevent collapse the PDMS layer was cured on a hot plate for at least 12 hours at 70°C. The image was taken using a 4x objective.

3.4 Device Bonding

The glass cover with the gold electrodes embedded in fully cured PDMS was bonded to the borosilicate substrate by glass-PDMS oxygen plasma bonding. The plasma was set to 60 W for 30 seconds with an oxygen flow rate of 50.0 sccm (chamber pressure

~ 285 mtorr). The PDMS surface is comprised of repeated units of –O – Si(CH3)2. The oxygen plasma oxidizes CH3 groups on the surface of the PDMS layer and silanol groups 118

(Si-OH) develop on the PDMS surface which form Si-O-Si covalent bonds (Garbassi et al.

1994; Qin et al. 2010) with Si-OH on the surface of the glass. A schematic representation of the expected surface chemistry of PDMS after oxygen plasma treatment is shown in

Figure 32.

Figure 32: A schematic representation of the bonding mechanism of oxygen plasma treated polydimethyl siloxane with a glass substrate (Sun et al. 2007 ). PDMS generally has surface methyl groups (– Si(CH3)2). Exposure to oxygen plasma oxidizes the PDMS surface resulting in surface silanol groups (SiOH) (Hillborg et al. 2000; Sun et al. 2007 ; Qin et al. 2010). The surface silanol groups on the oxidized PDMS surface and the silanol groups on the glass surface have a condensation reaction when placed in contact forming Si-O-Si covalent bonds between the two surfaces. Reproduced from Sun, Y. and J. A. Rogers (2007). Structural forms of single crystal semiconductor nanoribbons for high performance stretchable electronics. J. Mater. Chem. 17: 832–840 with permission of The Royal Society of Chemistry.

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Plasma power should be set above ~20 W to ensure adequate oxidation of CH3

(Bhattacharya et al. 2005). Ion bombardment energy increases with plasma power, causing damage to the PDMS structure and substantial loss of surface silanol density which decreases bond strength (Bhattacharya et al. 2005; Sun et al. 2007 ). Here 60W was chosen to keep the power as low as possible while ensuring that the plasma was stable (i.e., not “flashing”). The time was chosen to ensure adequate oxidation but to prevent PDMS surface cracking at long exposure times (> 60 s). PDMS cracking has been observed previously (Hillborg et al. 1999; Bhattacharya et al. 2005) and is attributed to chemical transformations on the PDMS surface known as surface chain scission reactions (Kim et al. 2001), though the effect is not fully understand

(Bhattacharya et al. 2005). The oxygen flow rate was set at the instrument maximum.

Bond strength is inversely proportional to contact angle since increased surface silanol groups render a surface hydrophilic (Hillborg et al. 1999). The contact angle of the plasma treated surfaces reduces with increased chamber pressure/oxygen flow rate.

Bhattacharya et al. reported that increasing the chamber pressure from 30 mtorr to

1000 mtorr reduced the contact of angle of the plasma treated PDMS from 19.2° to 2.5° and subsequently increased the bond strength of the PDMS-glass bond from 24 to 74 psi, where the bond strength was characterized in terms of the pressure where the interfacial bond began to separate (Bhattacharya et al. 2005). Plasma treatment decays with time

(Kim et al. 2001) thus bonding must be performed immediately after treatment, within approximately 1 minute of plasma treatment. The two plasma treated slides (electrode

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cover with PDMS layer and the glass substrate with channel features) were visually

aligned, mated by hand and rolled to finish the bond with a polyvinyl tube.

The formation of bonded leak-free nanochannel was verified through cross

sectional SEM images, micrograph images, fluorescence imaging, and current

measurements of the bonded devices. Figure 33 shows a cross section image of a 227 nm

channel (A) and a 16 nm channel (B). The PDMS thickness is estimated at 2 μm for the

227 nm channel and 0.5 μm for the 16 nm channel.

AA B 16 nm Glass

PDMS

Glass

Gold PDMS Channels Glass Va Figure 33: (A) A crossC section SEM image of a 227 nm deep Ax 31 μm wide nanofluidic channel. The PDMS layer here was measured to be ~2 μm thick. The inset shows a zoomed in view of the area marked by the white box. Reprinted with permission from Pinti, M., T. Kambham, B. Wang, and S. Prakash (2013). Fabrication of Centimeter Long, Ultra-Low Aspect Ratio NanochannelGlass Substrate Networks in Borosilicate Glass Substrates. J. Nanotechnol. Eng. Med.. 4(2): 020905. Copyright 2013 ASME. (B) A cross section SEM image of a 16 nm deep x 31 μmPDMS wide nanofluidicGate channel. The PDMS layer here was measured to be ~0.5 μm thick.16 Note nm that the entire channel width cannot be visualized in one frame. The cross sectionL1 SEM Limages-L1 confirm that the nanofluidic Inlet Outlet channels are bonded and open forGlass flow. Substrate Reprinted with permission from Fuest, M., C. y μchannel μchannel Boone, K. K. Rangharajan, A. T. ConliskL=5 mm and S. Prakash (2015). A Three-State x Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

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It must be noted that previous reports with sub-30 nm deep nanochannels have discussed significant challenges in obtaining accurate measurements of interfacial regions using SEMs from cross-section images (Duan et al. 2012). Due to the aspect ratio of the

16 nm channel, the entire cross section cannot by viewed in a single frame.

Images were also taken of the bonded nanofluidic channel using a Nikon HQ2

Cool Snap camera mounted on a Ti-U microscope. The micrograph images (Figure 34) show the interfacial region between the nanochannel filled with KCl electrolyte solution and an unfilled region where gas/vapor was present. The time elapsed images show the channel filling with KCl, shrinking the gas/vapor region providing further evidence that the channels are bonded and open for flow.

Figure 34: Time elapsed micrograph images of the interface of the KCl electrolyte and unfilled gas/vapor region of the 22 nm deep nanofluidic channels. The KCl electrolyte solution filled the channel with time, providing further evidence that the channel was bonded and open for flow. The images were taken using a 10x objective. Reprinted with permission from Pinti, M, and S. Prakash (2013). Fabrication of Hybrid Micro- Nanofluidic Devices with Centimeter Long Ultra-Low Aspect Ratio Nanochannels. 2013 Proceedings of the 2013 ASME International Mechanical Engineering Congress and Exposition, San Diego, California. Copyright 2013 ASME.

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One of the main limitations in the bonding process occurs from the spacing of the device features. The features must be a minimum distance apart in order for a bond to form. Bonding between the fluidic reservoirs ensuring the nanofluidic channels provided the only path for transport of fluid from microchannel reservoir to microchannel reservoir was critical for accurate experimental measurements. The presence of the drilled fluidic access ports creates non-planarity in the PDMS layer during the PDMS spin step. The distance between the drilled holes was increased from 1 cm in the initial channel design to 1.5 cm.

In addition to the spacing between the fluidic reservoirs, the spacing between the nanofluidic channels determines whether the bonding will be successful. The initial channel network design had a spacing of 50 μm between nanochannels resulting in no bonded, leak-free devices. Successful device bonding has been observed for spacing of

150 µm or larger (Figure 35), though it should be noted spacings between 50 and 150 µm were not tested. A full parametric study to determine the minimum distance necessary between nanofluidic channels to form a bond was not performed due to time constraints and the main focus of the project being on engineering nanofluidic devices that demonstrate new physical results in ion manipulation through these nanochannels.

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A B

100 μm

Figure 35: Micrograph images taken of bonded devices with different spacings between the nanochannels. The white arrows denote the spacing between two adjacent nanochannels. The nanochannels were 50 μm apart in A resulting in leaking devices. The channel spacing was increased to 200 μm in B resulting in properly bonded devices. The images were taken using a 10x objective.

Proper bonding between reservoirs was confirmed by measuring the resistances of the micro- and nanofluidic channels. The micro- and nanochannel resistances are given in

Table 5 for the representative case of a device filled with 1 mM KCl. The corresponding resistance paths are labeled on the device schematic in Figure 36. A four wire resistance measurement was used to estimate the resistance of the nanofluidic channels. Various two wire resistance measurements were performed in order to confirm device symmetry, or that expected symmetric paths have resistances with the same order of magnitude.

Properly bonded devices had a resistance on the order of 10’s of GΩ for four point and two point resistance measurements of the nanochannels. The microchannel resistances were on the order of 10’s of MΩ compared to GΩ for nanochannels. The microchannels were considered as equipotential for subsequent analysis with the entire potential drop

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occurring across the nanofluidic channels. In contrast, devices with leaks between the reservoirs had a “nanochannel” resistance on the order of 10’s of MΩ to kΩ.

Table 5: Resistance measurements across various paths of a micro- nanofluidic device filled with 1 mM KCl. Microchannel resistances were nearly 3 orders of magnitude lower than nanochannel resistances. Microchannels were therefore considered equipotential for subsequent analysis with the entire potential drop occurring across the nanofluidic channels. Two wire resistance measurements across various paths confirm channel network symmetry post fabrication. The corresponding paths are labeled in the schematic of the channel network in Figure 36.

2 Wire Measurements Path Resistance

1-2 Nanochannel 20 GΩ 1-4 Nanochannel 21 GΩ 2-3 Nanochannel 16 GΩ 3-4 Nanochannel 17 GΩ 1-3 Microchannel 22 MΩ 2-4 Microchannel 23 MΩ 4 Wire Measurements

Nanochannels 45 GΩ

1 2

3 4

Figure 36: Paths used for resistance measurements. For example, a two wire resistance measurement from 1-3 measures the resistance of the left microchannel.

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Proper device bonding was further confirmed through fluorescence imaging.

Figure 37 shows a bonded device with 57 nm deep nanofluidic channels. The nanochannels were filled with a 100 μM Rhodamine B fluorescent dye. No visible leaks were observed adding further evidence to support micrograph images, SEM images, and resistances measurements that indicate the devices were properly bonded.

Nanochannels

Figure 37: A fluorescence image of three 57 nm nanofluidic channels and one 8 µm deep microchannel filled with 100 μM Rhodamine B fluorescent dye. No visible leaks were observed adding further evidence to support micrograph images, SEM images, and resistances measurements that indicate the devices were properly bonded. The image was taken using a 10x objective.

Table 6 summarizes the aspect ratio (h/w) of successfully bonded nanofluidic channels. The aspect ratio reported here represents the lowest previously reported in the literature for nanofluidic channels that incorporate polymers in fabrication (Pinti et al.

2013). The ultra-low aspect ratio is desired for increased volumetric flow rate (which

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scales with channel width) while maintaining the nanoscale geometry for capturing functionality similar to biological systems.

Table 6: The table shows the time exposed to 10:1 buffered oxide etchant, the measured depth of the un-bonded nanochannel and the aspect ratio of the nanofluidic channel after bonding. The aspect ratio of 0.0005 is the lowest previously reported in literature that incorporates polymers in fabrication

Etch time (sec) Channel Depth (nm) Aspect Ratio

20 16 0.0005 30 22 0.0008 60 44 0.0015 90 57 0.0019 120 76 0.0025 300 227 0.0075

3.5 Device Characterization

The experimental set-up used for device testing is shown in Figure 38A. Two voltage sources (Keithley 3390 function generator in DC mode or Keithley 6517a electrometer) were used to apply an axial potential difference along the length of the nanochannel and to apply a gate potential to the embedded electrode. The current through the nanofluidic channels was monitored using a Keithley 6485 picoammeter. Gold wires

(99.9% pure Alfa Aesar) were inserted into the fluidic reservoirs to connect the axial voltage source and the picoammeter to the microchannel reservoirs. The device was placed in an Earth grounded Faraday cage to minimize electrical noise from the environment during current measurements.

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A B

Voltage Voltage Source Source Picoammeter

퐼 C Faraday Cage

Figure 38: Schematic representation of the experimental set-up for current measurements. Red is used to denote connections to the axial voltage source, purple is used to denote connections to the picoammeter, and green is used to denote connections to the gate voltage source. The color scheme was preserved in all three panels. (A) A schematic of the instruments used for current measurements and the connections between instruments. All potentials were applied with respect to the same ground for a common reference (black connections). Gold wires were used to connect the axial voltage source and picoammeter to the fluid in the microchannel reservoirs. The measurements were conducted in an Earth grounded Faraday cage to minimize electrical noise. (B) An exploded view schematic of the micro- and nanofluidic device with labeled connections to axial voltage source, gate voltage source, and picoammeter. (C) Nanochannel side view schematic generated from slicing (B) along the red dashed line. Connections to instruments are labeled.

For reference, the exploded view schematic is shown in Figure 38B with the locations of the axial power supply (red arrows), picoammeter (purple arrows), and gate power supply (green arrows) connections labeled on the schematic. Cutting the device along the red dashed line in Figure 38B would expose the side-view of the assembled device shown in Figure 38C. The connections are again labeled on the side-view

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schematic preserving the color scheme in all three panels with red indicating axial potential, purple the picoammeter, and green the gate potential connections respectively.

Current measurements were first taken with the gate electrode disconnected.

Figure 39 shows an I-V curve for 20 mM KCl with an applied axial potential ranging from 0 V to 400 V. In the axial potential range from 0 V to ~150 V the measured current was a linear function of axial voltage as expected from Ohm’s law where the bank of nanofluidic channels are modeled as circuit resistors. The measured channel resistance from the inverse slope of the I-V curve was 13.5 GΩ, on the same order expected for

16 nm deep, 30 μm wide, 5 mm long nanochannels. Note that the resistance is expected to be lower than the four wire resistance measurement in Table 5 because a higher concentration of KCl was used. The linear behavior of the I-V curve further confirmed nanochannels were open for flow and that the device was not leaking. At applied axial potentials ranging from 150 V to 240 V the measured current was constant with applied voltage corresponding to the “limiting regime”. As discussed in the previous chapter, nanofluidic channels are counter ion selective, meaning they preferentially transport ions with the opposite charge to the native charge on the nanochannel walls. Under the influence of an electric field cations migrate towards the cathode and anions towards the anode. Since the nanofluidic channels reported here have a negative surface charge they are expected to preferentially transport cations over anions. The imbalance of flux at the micro- and nanochannel interface is attributed to a phenomenon known as concentration polarization (Pu et al. 2004; Kim et al. 2010; Kim et al. 2010). The three distinct current regimes characteristic of concentration polarization (Ohmic, Limiting, and Overlimiting)

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are labeled in Figure 39. Above an applied axial potential of 240 V the measured current began to increase again corresponding to the overlimiting regime. For all subsequent experiments the applied axial potential was limited to Va ≤ 15 V, ensuring that non-linear

I-V behavior due to interfacial concentration polarization does not have a significant effect on the experiment.

16 Limiting 12

Overlimiting Ohmic 8

Current (nA) Current 4

0 0 100 200 300 400 Axial Voltage (V)

Figure 39: Measured current as a function of applied axial potential for 16 nm deep nanofluidic channels. The measured current has a linear dependence on applied axial potential in the range 0 V to 150 V. The limiting regime where measured current is constant with applied potential occurs for axial potentials ranging from 150 V to 240 V and the overlimiting regime begins at an applied axial potential of 240 V. This curve shows expected concentration polarization behavior for these devices. Subsequent tests are performed with an axial potential 푉푎 ≤ 15 V to ensure that effects of concentration polarization do not have a significant effect on the data.

Full characterization of the current-voltage behavior was investigated as a function of KCl concentration for a nanochannel etched with BOE for 20 seconds. The measured depth of the nanochannel before bonding was 16 nm (Figure 28). KCl is often used as the

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working fluid for characterization of ionic transport through nanofluidic channels due to similar ionic mobility’s for potassium and chloride ions (7.62 and 7.92x10-8 m2V-1s-1 respectively). The nanofluidic device was first operated with the gate electrode disconnected. The experimentally measured nanochannel conductance, G, given by the ratio of the measured current to applied axial potential (I/Va), follows a linear trend for high concentrations (≥ ~ 1 mM) as expected from bulk fluid conductance (Figure 40).

At low concentrations (≤ ~ 1 mM) conductance has nearly a constant value (Figure

40) indicating the surface charge governed regime (Stein et al. 2004; Karnik et al. 2005;

Schoch et al. 2005; Nam et al. 2009). To maintain electroneutrality, the net charge in the nanochannel volume must be equal and opposite the total charge on the nanochannel walls.

The number of charge carriers in the nanofluidic channel, and therefore, the conductance is determined by the surface charge at low concentration. The critical concentration where the transition between the bulk transport and surface charge governed transport occurs was

~1 mM in agreement with trends reported previously (see Figure 6) (Stein et al. 2004;

Karnik et al. 2005; Guan et al. 2011).

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10-8 Experimental Data (S) PNP Simulation Bulk Conductance 10-9

10-10

Conductance 10-11

-12 Intrinsic Intrinsic 10 10-5 10-4 10-3 10-2 10-1 KCl Concentration (M)

Figure 40: Nanochannel conductance for the un-gated case is shown as a function of KCl concentration. Conductance was independent of concentration at “low” concentration and follows a linear trend at “high” concentrations in agreement with previous reports (Stein et al. 2004; Karnik et al. 2005; Schoch et al. 2005) The transition between these two regimes occurs near the critical concentration of ~ 1 mM, with general agreement in published reports that the low concentration regime (푐푏푢푙푘< 1 mM) is the surface charge governed transport regime for nanofluidic channels. The dashed blue line is the conductance calculated from the analytical equation for the bulk conductance of KCl through 18 nm deep x 30 µm wide x 5mm long channels (퐺푏푢푙푘, Equation 33). The experimentally measured conductance agrees with a 2-D Poisson-Nernst-Planck model for a 16 nm deep nanochannel, confirming successful device operation according to established theory of ionic transport in nanofluidic channels.

The experimentally measured conductance is plotted alongside the conductance predicted from a Poisson-Nernst-Planck (PNP) model for ionic transport of KCl. A schematic of the micro- and nanofluidic system modeled using COMSOL Multiphysics is shown in Figure 41.

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푉푎 = 푉 푉푎 = 0푉 푐𝑖 = 푐푏푢푙푘 푐𝑖 = 푐푏푢푙푘

ℎ = 1 푛푚 ℎ 푒푠 = 2 0 푛푚 Inlet Outlet µ channel 퐿 = 푚푚 µ channel 𝜎 = −2 푚퐶/푚2 푦 푥 퐿 푒푠 = 100 푛푚

Figure 41: A schematic of the micro- nanofluidic system modeled with COMSOL multiphysics. Due to the low aspect ratio of the nanochannel (width >> height) the system can be modeled in two dimensions (Conlisk 2013). The inlet and outlet reservoirs, which correspond to microchannels in the fabricated device, were 100 nm long and 250 nm tall. The size of the channel in the model was 16 nm deep x 5 mm long to match the dimensions of the fabricated device. The KCl concentration in the inlet and outlet reservoirs was set to the bulk electrolyte concentration (ranging from 0.01 mM to 100 mM). Modeling the reservoirs accounts for the difference in concentration of species in the bulk electrolyte and in the nanochannel. The inlet microchannel was set to 5V while the outlet microchannel was grounded. The location where the concentration and potential boundary conditions were imposed is indicated with the red arrow in the schematic. A surface charge density of -2 mC/m2, consistent with previously reported values for glass at pH 7 (Guan et al. 2011; Jin et al. 2011), was imposed on all surfaces marked with the dark grey line (reservoirs and nanochannel).

Due to the low aspect ratio of the nanochannel (width >> height) the system can be modeled in two dimensions (Conlisk 2013). The size of the channel in the model was

16 nm deep x 5 mm long to match the dimensions of the fabricated device. The current was measured according to

푚=2 푧 푤퐹 퐿 ℎ 퐼 = 𝑖 ∫ ∫ ∑ 푁 푑푦푑푥 ( (30) 퐿 𝑖 0 0 𝑖 where 퐼 is the current, 푧𝑖 is the valence of species 𝑖, 푤 is the channel width, 퐹 is

Faraday’s constant, 퐿 is the channel length, ℎ is the channel height, and 푁𝑖 is the flux of the two charged species in the channel (K+ and Cl-). Here the flux was integrated across 133

all cross sections along the nanochannel length and then divided by the total length of the channel to obtain the average flux. The flux was calculated using the Poisson equation

(Equation 2-8) for the potential combined with the steady-state Nernst-Planck equation for mass transport (Equation 2-12). No flux was allowed through the walls of the channel.

The concentration in the reservoirs was set to the bulk electrolyte concentration, ranging between 0.01 mM and 100 mM. Modeling the reservoirs accounts for the difference in concentration of species in the bulk electrolyte and in the nanochannel. The size of the reservoirs was selected to ensure that the potential was constant in the reservoirs and that effects of reservoir surface charge was minimal, i.e. cation and anion concentration is equal to bulk concentration in the reservoir, except near the charged walls. A constant surface charge boundary condition was used for the potential at each of the charged walls according to

푑휙 𝜎 = −휀 푒 푑푦

푑휙 (31) = −휀 푒 푑푥

= −2 푚퐶/푚2

{3-32} which is the electroneutrality condition (see discussion in Chapter 5, Equation 60). Here

𝜎 is the surface charge density, 휀푒 is the permittivity of the electrolyte, and 휙 is the potential in the channel. The magnitude of the surface charge is consistent with previous reports for glass at pH 7 (Guan et al. 2011; Jin et al. 2011). The inlet microchannel

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reservoir was set to a potential of 5 V while the outlet microchannel potential was grounded (0 V). The continuity equation and the steady-state Navier-Stokes equation for an incompressible fluid with no slip (velocity equal zero) boundary conditions were used for the velocity (Equations 2-10 and 2-11). The predicted conductance was obtained by dividing the calculated current by the applied axial potential (5 V).

The conductance from the 2-D PNP model agrees with the measured experimental conductance. This further confirms successful fabrication of nanofluidic channels with the dimensions 16 nm deep x 30 µm wide x 5 mm long since the experimental data agrees with well-established theory for ion transport through nanofluidic channels with those dimensions. The full 2-D PNP model can be compared to analytical approximations used to estimate the surface charge density from the experimentally measured conductance

(Nam et al. 2009; Guan et al. 2011; Guan et al. 2014). The total intrinsic nanochannel conductance (퐺푎 = 퐼/푉푎) can be written as the summation of the surface charge governed

(SCG) and the bulk conductance

2푤휇 휎 퐹푤ℎ 퐺 = 퐺 + 퐺 = + + ∑푚 휇 푧 2푐 푏푢푙푘 (33) 푎 푆퐶퐺 푏푢푙푘 퐿 퐿 𝑖=1 𝑖 𝑖 𝑖

푏푢푙푘 where 휇+is the cation mobility, 휇𝑖 is the mobility of species 𝑖, and 푐𝑖 is the bulk electrolyte concentration. The dominate term in Equation 33 will depend on the bulk electrolyte concentration. The surface charge density here was estimated to be -2.7 mC/m2 from the conductance of 0.01 mM KCl. The analytical approximations

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over predicts the surface charge density fit to the data from the 2D PNP model which had a surface charge density of -2 mC/m2.

Similarly, the height of the bonded nanofluidic channels was estimated from the conductance data in the bulk conductance or high concentration range (퐺푏푢푙푘). The estimated height from conductance data in the high concentration range (푐푏푢푙푘 ≥ 10 mM) is 18 nm, where the bulk conductance for three 18 nm deep, 30 μm wide, 5 mm long nanochannels is plotted in Figure 40 (dashed blue line). The estimated depth is in reasonable agreement with the 2D PNP model (estimated height of 16 nm) and atomic force microscopy measurements that showed the nanochannel depth before bonding was

16 nm ± 1 nm (Figure 28) (Pinti et al. 2013), however, the analytical calculation for the height over predicts the height compared to the 2D PNP model.

3.6 Chapter Summary

Fabrication procedures for a micro- and nanofluidic device with individually addressable electrodes embedded in one wall of the nanochannel were developed. The micro- and nanochannel network was fabricated on a glass substrate due to the electrical insulation properties, optical clarity, and chemically inert nature of glass. UV lithography was implemented with a modified spin recipe to allow fabrication of nanochannels on a non-planar substrate that already contained etched microfluidic channels. A second glass substrate was used for the electrode cover. A spun on PDMS layer isolated the electrodes from the fluid in the nanochannel and provided a surface to bond the electrode cover to the substrate with the channel network via oxygen plasma bonding. Successful device fabrication was confirmed through optical micrograph images, SEM images, AFM

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measurements, fluorescence images, and electrical characterization of fabricated devices.

Measured intrinsic nanochannel conductance for KCl was compared to Poisson-Nernst-

Planck model for ion transport to further verify device functionality. The individually addressable electrodes can be placed at desired location and spacing opening up the possibility of using multiple electrodes at engineered locations to systematically alter the surface charge distribution along the channel length as well as the possibility of using multiple electrodes with time and space dependent signals, adding to versatility of the device. The effect of the gate electrode on ionic transport, quantified by changes in the measured current, is reported in Chapters 4 and 5.

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Chapter 4: Current Switching in a Gated Nanofluidic Device22

4.1 Gated Nanofluidic Devices for Fluidic Logic Circuits

Gated nanofluidic devices, geometrically analogous to semiconductor field effect transistors, feature a nanofluidic channel with a “gate” electrode embedded in the nanochannel wall for systematic manipulation of the surface potential at the dielectric- electrolyte interface (Guan et al. 2014; Prakash et al. 2014). The gate electrode is isolated from the aqueous electrolyte in the channel by a dielectric layer. An axial or streamwise potential applied between the inlet and outlet of the nanochannel drives streamwise transport of ions through the nanofluidic channel (Kuo et al. 2003; King et al. 2009; Pinti et al. 2013). An independently controlled applied voltage to the gate electrode allows active, tunable control over the local surface potential in the nanofluidic channel. Taking advantage of the nanoscale geometry, the local change in potential penetrates through the nanoscale depth of the channel (Liu et al. 2010) permitting active and reconfigurable control (Guan et al. 2011) over the concentration of charge carriers, or net space charge density, in the fluid volume (Karnik et al. 2005; Jin et al. 2011). Other methods for controlling the surface charge density in nanofluidic channels have been proposed, including chemical surface modification, and altering the pH of the electrolyte solution,

22 This chapter have been adapted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365– 2371. Copyright 2015 American Chemical Society. 138

among other methods detailed in Chapter 2. The main advantage of gated nanofluidic devices is that they allow reconfigurable changes to the surface charge post fabrication by altering the potential applied to the gate electrode (Karnik et al. 2005; Guan et al. 2011;

Hu et al. 2012; Guan et al. 2014). This active control over the concentration of ionic species modulates electrokinetic flows as measured by changes in current through the nanofluidic architecture (nanopore or nanochannel) (Karnik et al. 2005; Nam et al. 2009;

Guan et al. 2011; Jiang et al. 2011; Fiori et al. 2013; Pardon et al. 2013). An increase in current indicates a higher concentration of charge carriers flowing through the nanochannel and a decrease in current indicates a lower concentration of charge carriers flowing through the nanochannel (Karnik et al. 2005; Guan et al. 2011).

Gated nanofluidic devices, or flow-FETs, have been proposed as the basis for ionic circuits (Karnik et al. 2005; Mishra et al. 2014), with the goal of performing detailed logic functions similar to solid-state circuits for controlled transport of ionic species in small volumes (nL or less) of fluid. Many technological demonstrations have shown manipulation of ions and biomolecules at femtoliter volumes (Karnik et al. 2005) for biosensing (Huo et al. 2011; Prakash et al. 2012), sample concentration (Kim et al.

2010), molecular sorting (Ai et al. 2010), and separations (Kim et al. 2010; O’Hern et al.

2014) moving towards the still elusive goal of performing controlled ion transport functions similar to biological systems (Siwy et al. 2002; Gouaux et al. 2005;

Sparreboom et al. 2009; Guan et al. 2011). Most advances in development of ionic circuit elements till date have focused on ionic diodes and current rectifiers (Daiguji et al. 2005;

Vlassiouk et al. 2008; Kovarik et al. 2009; Vlassiouk et al. 2009; Cheng et al. 2010; Jin

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et al. 2011; Picallo et al. 2013; Bocquet et al. 2014). Nearly all nanofluidic diodes operate in a fixed rectification regime with no changes possible to rectifying properties post device fabrication. A recent demonstration of tunable, reconfigurable rectification with a gated nanofluidic device demonstrates the advantage of using flow-FET devices for building elements of ionic circuitry (Guan et al. 2011). In contrast to diodes that permit flow of current and, therefore, ions in a preferential direction based on axial potential direction, current switching, or the ability to switch the current “on” and “off” arising from gate control for fixed axial potential has not yet been reported. Switching or ideal flow gating is a key advance required for ionic circuits in moving towards fluidic logic control as well as specific applications such as artificial ion channels (Huo et al.

2011; Duan et al. 2013 ).

This chapter reports on the implementation of a gated nanofluidic device with

16 nm deep channels as a current switch controlled by systematically manipulating the potential applied to the gate electrode. All measured current states were referenced with respect to the un-gated case i.e., the case where only an axial potential was applied but no gate potential was applied. The device reported in this paper is in an asymmetric configuration (Figure 42), with details discussed later. A positive current increasing with applied gate voltage (forward state) and a negative measured current (reverse state) for a fixed axial voltage were observed in addition to a device state where the measured current was nearly zero (off state) during the gating of the nanofluidic device. Therefore, the purpose of this chapter is to demonstrate the operation of a gated nanofluidic switch controlled by a gate electrode across a broad range of experimental parameters.

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4.2 Experimental Design

In recent years, several other reports have demonstrated the complexity and challenges in fabricating gated nanochannels with insulated gate electrodes (Karnik et al.

2005; Nam et al. 2009; Joshi et al. 2010; Jiang et al. 2011; Shin et al. 2012). In this dissertation, an alternate fabrication sequence (Pinti et al. 2013) was developed for gated nanofluidic devices that relies on photolithography, wet etching, and oxygen plasma bonding techniques (Mijatovic et al. 2005; Perry et al. 2006; Duan et al. 2012) to yield a sealed nanofluidic device with details presented in Chapter 3. The nanofluidic device consisted of two microfluidic channels as fluidic reservoirs for a bank of three 16 nm deep x 30 μm wide x 5 mm long nanofluidic channels etched in borosilicate glass (Figure

42). The low aspect ratio (Pinti et al. 2013) of the nanofluidic channels (depth << width) enables nanoscale effects similar to biological systems while providing high throughput and benefits of 1-D theoretical analysis (Prakash et al. 2008; Huo et al. 2011). Gold (Au) gate electrodes (20 nm high x 25 μm wide) were patterned on a second glass substrate that acts as a cover for the etched channels (Figure 42A). The Au gate electrodes were asymmetrically placed along the length of the nanofluidic channel to allow investigation of the effect of electrode location on the field effect control, or current modulation. A polydimethyl siloxane (PDMS) layer spun over the Au electrodes isolated the gate electrodes from the electrolyte within the nanochannels and provided a surface for bonding the two substrates (one with channel features etched in borosilicate glass and the

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A B 16 nm Glass A PDMS A’ Glass

Gold PDMS Channels Glass

Va A Glass Gold C C Electrode D Nanochannel PDMS Sidewall A A’ Glass Substrate

PDMS Gate 16 nm

L1 L-L1 Inlet Glass Substrate Outlet µchannel Cross y μchannel μchannel L=5 mm Section x

Figure 42: (A) An exploded view schematic of the fabricated gated nanofluidic device. The fluidic network consisted of two 10 μm deep x 50 μm wide x 3.2 cm long microchannels connected by a bank of three 16 nm deep x 30 μm wide x 5 mm long nanochannels wet-etched into borosilicate glass. Gold gate electrodes (20 nm high x 25 μm wide) were patterned on a second glass substrate (cover) and bonded to the substrate with the channel network using an intermediate PDMS layer. The PDMS layer isolated the gate electrodes from the fluid in the nanochannels. (B) A scanning electron microscope (SEM) image of the bonded nanochannel cross section. The complete nanochannel width of 30 μm does not permit imaging the entire cross section in one frame. From the SEM image, the PDMS dielectric layer was ~ 500 nm thick. (C) An exploded side view of the device. The red dash-dot line in Figure 42A indicates the cut- line (A-A’) used to generate the side view schematic. (D) The assembled side view schematic shows the experimental set-up with the applied axial (Va) and gate (Vg) potentials. Only one electrode is shown as only one electrode was active at a given time. The direction of fluid flow in the un-gated case (Vg = 0 V) is marked by the red arrow. The axial and gate potentials are referenced to the same ground. The location of a given electrode is the relative distance of the center of the electrode from the nanochannel inlet as indicated in the schematic by L1. The light green dashed line indicates the region where the gate electrode is expected to alter the surface charge density, as described below. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

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cover with the isolated gate electrodes). Detailed fabrication procedures for the channel networks and device bonding were reported in Chapter 3.

A schematic showing the exploded view of the fabricated device is shown in

Figure 42A. A scanning electron microscope (SEM) image of the nanochannel cross section is shown in Figure 42B, showing the PDMS dielectric layer was ~ 500 nm thick.

The exploded side view schematic (Figure 42C) shows the glass cover with asymmetrically spaced Au gate electrodes isolated from the fluid by a PDMS dielectric layer. The cut-line along A-A’ was used to generate the side view schematic and is indicated by the red dash-dot line on the full device schematic (Figure 42A). The device featured six individually addressable gate electrodes with each electrode location given by the relative distance from the nanochannel inlet to the center of the gate electrode. In this chapter, only one of the six electrodes was active at a given time and the results are described in the sections to follow.

4.2.1 Electrode Location

The gated nanofluidic field effect device has 6 individually addressable electrodes grouped towards center of the nanofluidic channels (along the length). The micrograph image taken with a Nikon Ti-U microscope (Figure 43) with a HSQ2 Cool Snap camera shows the bank of electrodes. The locations of the three nanochannels (16 nm deep x

30 μm x 5 mm long) are marked with dashed white lines. Each electrode is labeled with its relative location along the length of the nanofluidic channel as measured from the center of each 25 μm wide electrode. The device can also be rotated 180°, which would change the relative position of each electrode from (푥퐿) to (퐿 – 푥퐿).

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Figure 43: A micrograph image of the 6 individually addressable electrodes. The electrodes are labeled with their relative location along the nanochannel length 퐿 = 5 mm. The location of the nanofluidic channels is marked with white dashed lines. The device can also be rotated 180°, changing the relative locations from 푥퐿 to (퐿 − 푥퐿). Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

In line with previous reports (Karnik et al. 2005; Kalman et al. 2009), electrolyte solutions of KCl in DI (de-ionized) water at concentrations varied between 0.1 mM to

100 mM at pH 7 ± 0.2 were used as the working fluid. A potential difference between the two microchannel reservoirs (axial potential, Va), drives flow through the nanofluidic channels as shown schematically in Figure 42D. The net direction of fluid flow for the un-gated case (gate voltage, Vg = 0 V), indicated by the red arrow in Figure 42D, is in the same direction as the net transport of K+ ions (Conlisk 2013). Since the electrical resistance of the microchannel was significantly lower than the nanochannels (order of

MΩ for the microchannels compared to GΩ for the nanochannels, as measured for

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channels filled with 1 mM KCl, Chapter 3, Table 5), each microchannel was considered essentially equipotential for subsequent analysis. A Keithley 6517a electrometer was used to apply a potential difference between the two microchannel reservoirs (axial potential, Va). The axial potential was varied from 1 to 5 V. A second power supply (Data

Precision, Model # 8200) was used to apply the gate potential to the embedded gate electrode, where all potentials were applied with respect to the same ground for a common reference (Figure 38). Current through the nanofluidic channels was monitored using a Keithley 6485 picoammeter. Each data point for measured current is the average of 10 current measurements with error bars representing one standard deviation in the mean. In order to minimize external electrical interference, all measurements were conducted in an earth grounded Faraday cage. Leakage current through the PDMS dielectric layer was also measured to confirm adequate electrical isolation of the gate electrodes in accordance with previous reports for gated nanochannels (Nam et al. 2009;

Joshi et al. 2010; Guan et al. 2011; Shin et al. 2012).

4.2.2 Gate Leakage Current

Gate leakage current through the PDMS dielectric layer was measured separately for each KCl concentration by setting a potential difference between the microchannel reservoirs and the gate electrode (grounded) as in previous reports (Nam et al. 2009; Oh et al. 2009; Shin et al. 2012) to ensure adequate isolation of the gate electrode. Leakage current from the gate electrode, through the PDMS dielectric, into the nanochannel changes the pH of the electrolyte solution in the channel with equations and detailed discussion given in Chapter 2. Applying a potential to the gate electrode is known to

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induce a local change in surface charge density at the dielectric/electrolyte interface. The location where the surface charge density is expected to be altered by the gate electrode is indicated by the light green dashed line in Figure 42E. The extent to which the effect of the gate electrode extends beyond the width of the electrode itself remains an open question. A shift in the electrolyte pH would alter the surface charge density of the entire channel in addition to the local change induced by the gate electrode. The point of zero charge of silica is pH 2 with the magnitude of the surface charge increasing with pH

(𝜎 ≈ 0 at pH 2, 𝜎 ≈ -2 mC/m2 at pH 7 for silica). The gate leakage current is measured and a threshold limit is set to ensure that i.) the pH of the electrolyte can be approximated as constant for all values of 푉푔, and therefore changes in surface charge density are only local changes caused by the gate electrode, and ii.) the system can be analyzed in terms of

+ - + - - + the simplified case of transport of K and Cl rather than K , Cl , OH , and H3O . The dependence of electrolyte transport on solution pH will be investigated in detail for the ungated and gated case in Chapter 5. A threshold of gate leakage current/axial current in the un-gated case (Ileakage/Iun-gated) of 1 is set for all measurements based on a previous report (Guan et al. 2011), ensuring the axial current exceeds the leakage current, and thus, limiting the range of gate voltages used in this study to ± 2 V for 1 mM and ± 3 V for 0.1, 10 and 100 mM. Gate leakage current for 1 mM KCl is shown in Figure 44 referenced to axial current for Va = 3V. The gate leakage current/axial current for

1 mM KCl exceeds the threshold of 1 for the point Va = 1 V and Vg = 3 V. We, therefore, limited our parameter space for 1 mM KCl to Vg = ± 2 V.

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1 mM KCl, V = 3 V a 1

0.5

/I 0

-0.5

-1 -3 -2 -1 0 1 2 3 Voltage (V)

Figure 44: A representative image showing gate leakage current measurement for 1 mM KCl referenced to the axial current for Va = 3 V. The axial voltage range of 1-5 V and gate sweeps from -2 to +2 V were used in all reported data for 1 mM KCl to meet the threshold for gate leakage current at Va = 1 V, as described above. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

4.3 Current Switching

The gated nanofluidic device was first operated with Vg = 0 V, also referred to as the un-gated case. The measured nanochannel conductance is shown in Figure 40.

Nanochannel conductance, Ga, given by the ratio of the measured current to applied axial potential (I/Va), follows a linear trend for high concentrations (≥ ~ 1 mM) as expected from bulk fluid conductance (Stein et al. 2004; Karnik et al. 2005; Nam et al. 2009; Guan et al. 2011; Guan et al. 2014). At low concentrations (≤ ~ 1 mM) conductance has nearly a constant value (Figure 40) indicating the surface charge governed regime (Stein et al.

2004; Karnik et al. 2005; Schoch et al. 2005; Nam et al. 2009). To maintain electroneutrality, the net charge in the nanochannel volume must be equal and opposite to

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the total charge on the nanochannel walls. The number of charge carriers in the nanofluidic channel, and therefore, the conductance is determined by the surface charge at low concentration. The critical concentration where the transition between the bulk transport and surface charge governed transport occurs was ~1 mM in agreement with trends reported previously (Stein et al. 2004; Karnik et al. 2005; Guan et al. 2011).

Applying a gate voltage causes a change or modulation of measured current through the nanofluidic device with respect to the un-gated case (Vg = 0 V). As a representative case, current through the nanochannels as function of the gate voltage for

1 mM KCl solution at an axial potential of 3 V is reported in Figure 45. The gate electrode was positioned at 0.57 L, where L is the total length of the nanochannel (Figure

42D).

As the gate voltage was increased from 0 V to 2 V, current through the nanochannel increased from 0.106 nA to 0.220 nA. As the gate voltage was swept from

0 V to -2 V the measured current decreased until the current was switched off i.e., no measurable current was recorded at Vg = -1.4 V with Va still at 3 V. Changing the gate voltage from -1.4 V to -2 V reversed the polarity of the measured current with a current of -0.026 nA for Va = 3 V and Vg = -2 V. Therefore, the device has three states of operation with respect to the un-gated case; a forward current, an off or zero current case, and a reverse current state for a fixed axial potential.

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A 0.25 1 mM 0.20

0.15 Forward 0.10

0.05 Off

Current (nA) Current 0.00 Reverse -0.05 -2 -1 0 1 2 Gate Voltage (V)

Figure 45: The plot shows the measured current as a function of gate voltage with the overall trend showing evidence for operation of a nanofluidic field effect device as a 3-state ionic current switch. A current of 0.106 nA was measured through the nanofluidic channels for Va = 3 V, Vg = 0 V. For Vg = 0 V to – 2 V, the measured current decreased from 0.106 nA to -0.026 nA with no measureable current at Vg = -1.4 V. Here +2 V applied to the gate electrode results in 0.220 nA of current. From the un-gated conductance for 1 mM KCl (Figure 40), achieving the same current, i.e., 0.220 nA purely from Va requires Va = 7.0 V. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

To our knowledge, this device presents the first demonstration of current switching in a nanofluidic field effect configuration, with tunable control over both the magnitude and direction of current. Figure 46 shows repeatable on-off operation of the nanofluidic field effect switch. For fixed axial potential, the gate voltage can be tuned to modulate the current to the desired value. For example, in Figure 46 the applied voltages for 0.1 mM KCl were cycled from Va= 3 V, Vg = 0 V producing 0.024 ± 0.002 nA of current to Va = 3 V, Vg = -3 V to switch off the current. While, the details on concentration dependence of measured current modulation with Vg are discussed later, it

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is worth noting here that in the surface charged governed regime (typically with electrolyte concentration ≤ 1 mM for the un-gated case) controlling the gate potential allows switching of the current.

0.25 B 0.1 mM 0.20 0.15 0.10

0.05 On

Current (nA) Current 0.00 Off -0.05 0 20 40 60 80 Time (s)

Figure 46: Current switching for 0.1 mM KCl indicating the gate voltage can be tuned to produce the desired current. The current is 0.024 ± 0.002 nA for Va = 3 V, Vg = 0 V and switched off for Va = 3 V, Vg = -3 V. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

Using previously reported analytical models to explain the observed data trends for electrokinetically driven flow (Pu et al. 2004; Nam et al. 2009; Guan et al. 2011), the components of the current due to electromigration of K+ and Cl- are given by

+ 퐼퐾+ = 푧𝑖퐹(푧𝑖휇퐾+ 퐴[퐾 ]퐸) and (34)

− 퐼퐶푙− = 푧𝑖퐹(푧𝑖휇퐶푙−퐴[퐶푙 ]퐸) (35)

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where, 퐼𝑖 is the current due to a species i, 휇𝑖 is the ionic mobility of species i, A is the cross section area of the nanochannel, [𝑖] is the concentration of species i in the nanochannel, and 퐸 is the electric field (Pu et al. 2004; Guan et al. 2011). The 5 mm long nanochannels (compared to 30 μm width and 16 nm depth) are sufficiently long such that the electric field in the un-gated case can be approximated as 퐸 = 푉푎/퐿, as reported previously for nearly 1-D nanochannels (Vlassiouk et al. 2008). The ionic mobility, μi is given by 퐷𝑖퐹⁄푅푇 where 퐷𝑖 is the diffusion coefficient of species i, 퐹 is Faraday’s constant, 푅 is the universal gas constant, and 푇 is the temperature (Conlisk 2013). Note, that the term in parenthesis in the equations above is the flux of the ions under the influence of an electric field (Pu et al. 2004). Applying the previously reported assumption, 휇퐾+ ≈ 휇퐶푙− (Guan et al. 2011), the total current due to the summation of the cationic and anionic contributions is given by,

+ − 퐼푡표푡푎푙 = 퐹휇퐾+ 퐴([퐾 ] + [퐶푙 ])퐸. (36)

Consequently, any change in current for a finite gate potential compared to the un-gated case will be caused by a change in the ionic concentration and/or a change in the electric field within the nanofluidic channel (Equation 3). Since, the gate electrode is known to induce a local change in the effective surface charge on the channel wall (Jin et al. 2011; Singh et al. 2011; Singh et al. 2012), to maintain overall electroneutrality of the system the relative concentration of potassium and chloride within the nanofluidic channel must change (Karnik et al. 2005; Guan et al. 2011; Jin et al. 2011). Karnik et al.

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(Karnik et al. 2005) experimentally verified this relative change in concentration of ionic species through fluorescence measurements. The consequence of this change in relative species concentration is the modulation of the current due to increased or decreased availability of charge carriers (Karnik et al. 2005; Jin et al. 2011). In addition to the change in the total number of charge carriers in the channel, it is likely with the gate voltage turned on, the local electric field modulation also causes a change in the local concentration, which will influence the flow of current. Further investigation of the nature of concentration profiles is needed (Rutkowska et al. 2013), though past experimental work has also implied influence of concentration gradients on current profiles (Guan et al. 2011; Singh et al. 2011), which can include the possibility of negative current.

The change in concentration is often analyzed in terms of the charge stored by the gate electrode/dielectric/electrolyte capacitor (Horiuchi et al. 2006; Guan et al. 2011;

Guan et al. 2014), approximating the flow-FET as an equivalent electric circuit for analysis of data trends (Guan et al. 2011; Guan et al. 2014). In these previous reports, the electric field through the nanochannel is considered to be the same in the un-gated and gated cases. While change in the species concentration will result in current modulation and is required to maintain overall electroneutrality, given the sign of each term in

Equation 3, reversal of the current from positive to negative, as observed in Figure 45, requires a change in the direction of the electric field. The determination of the exact mechanism for this expected reversal of electric field within the nanochannel will likely require detailed numerical models as discussed below, and is beyond the scope of this

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work. A hypothesis based on discussion of relevant literature and further device characterization is presented next.

Detailed numerical models have shown that the potential of the gate electrode can penetrate through the entire depth of the nanochannel (Liu et al. 2010; Liu et al. 2010).

The gate electrode de-screening model presented by Liu et al. (Liu et al. 2010) suggests that ionic flux driven by the axial potential through the nanochannel along with high electric fields (on the same order as the thermal voltage) prevent the formation of an electric double layer (EDL) in the electrolyte region immediately below the gate electrode, leaving the gate electrode partially “de-screened.” The result is a local region in the nanochannel with a potential proportional to the gate electrode that penetrates throughout the depth of the nanochannel. The partial de-screening of the gate electrode is one proposed explanation for why experimentally observed current modulation exceeds predictions of capacitive or electric double layer based models (Liu et al. 2010; Yusko et al. 2010). Additional numerical reports on two dimensional analysis of gated nanofluidic channels have also shown that the electric field in the nanochannel is significantly more complicated by applying a potential to the gate electrode (Jin et al. 2011; Singh et al.

2011; Singh et al. 2012) than is captured by analytical models. The electric field throughout the nanofluidic-architecture is a function of both applied axial and gate potentials as well as gate electrode location, which alters the impact of the field effect on the measured current (Ai et al. 2011; Singh et al. 2012). However, many challenges remain in numerically quantifying the effect of transverse electrostatics from the gate

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electrode on streamwise transport of ions and fluid for real nanofluidic field effect devices (Liu et al. 2010; Liu et al. 2010).

In the present case, we hypothesize that the electrolyte region directly below the gate electrode is at some potential αVg. The variable α is an empirical parameter that accounts for potential change from the gated dielectric-electrolyte interface through the depth of the nanofluidic channel to the other physical wall of the device (see Figure 47 for a visual representation). It is likely that α depends on a variety of factors including dielectric material (Karnik et al. 2005), dielectric thickness (Guan et al. 2011; Singh et al.

2012), gate electrode length (Jin et al. 2011; Singh et al. 2011; Singh et al. 2012), gate electrode position (Jin et al. 2011; Singh et al. 2011), and electrolyte concentration (Liu et al. 2010). As α  0, the system approaches the previously reported capacitor model where the gate electrode modulates the ionic concentration in the channel but the electric fields in the gated and un-gated cases are the same. Therefore, the change in potential within the nanochannel in the region below the gate electrode alters the electric field in the nanochannel and enables the switching behavior observed in Figure 45 and Figure 46.

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Figure 47: A visual representation of the change in potential induced by the gate electrode. Inlet and outlet channels are labeled with respect to un-gated flow and are designated in this way for reference. The gate potential is referenced to the outlet/grounded microchannel. Application of a gate voltage changes the potential in the nanochannel, and necessarily the electric field, where the potential in the nanochannel below the gate will be proportional to the gate voltage (훼푉푔). The location dependent potential profile will be significantly complicated compared to the un-gated case. The proportionality factor, 훼, will depend on a variety of factors dielectric material (Karnik et al. 2005), dielectric thickness (Guan et al. 2011; Singh et al. 2012), gate electrode location (Jin et al. 2011; Singh et al. 2011; Singh et al. 2012), gate electrode position (Jin et al. 2011; Singh et al. 2011), and electrolyte concentration (Liu et al. 2010). Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365– 2371. Copyright 2015 American Chemical Society.

4.4 Axial and Gate Potential Dependence

In order to further test the hypothesis that a change in electric field induced by the gate electrode is responsible for the observed 3-state current switch, Va, Vg, and L1 (center of gate electrode as measured from nanochannel inlet) were varied systematically and the subsequent effect on the measured current through the nanofluidic channels is reported.

Figure 48 shows measured current at three values of axial potential (Va). For the representative case, KCl concentration was 1 mM and the gate electrode was located at

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0.57 L. Interestingly, for all three values of Va, the slope in Figure 48, dI/dVg, remained constant with a value of 0.060 ± 0.003 nA/V.

The slope represents the change in current caused by the applied gate potential. For the axial potential range reported here (1-5 V) the measured current (in the axial or x-direction) can be approximated as the sum of the contributions due to Va and Vg respectively,

+ − + − 푉푎 훼푉푔 퐼 = 휇퐴퐹([퐾푔푎푡푒푑] + [퐶푙푔푎푡푒푑])퐸 = 휇퐴퐹([퐾푔푎푡푒푑] + [퐶푙푔푎푡푒푑]) ( + ) (37) 퐿 퐿−퐿1

+ − where, [퐾푔푎푡푒푑] and [퐶푙푔푎푡푒푑] are the concentration of potassium and chloride ions in the channel in the gated case. Upon application of a gate voltage, the concentration of species in the nanochannel will change to maintain overall electroneutrality (Jin et al. 2011;

Singh et al. 2011). It is expected that the change in concentration required to satisfy electroneutrality will depend on the magnitude and polarity of the gate voltage (Nam et

푉 al. 2009; Jin et al. 2011). The term 푎 is the electric field in the nanochannel in the 퐿

훼푉 un-gated case (Vlassiouk et al. 2008) and the term 푔 is the contribution to the electric 퐿−퐿1 field from the gate electrode where L-L1 is the distance from the gate electrode to the grounded microchannel. Note that for Vg = 0 V Equation 37 becomes the un-gated case with [i]=[iun-gated]. As 훼 → 0 and Vg ≠ 0, Equation 37 approaches the capacitor model used in previous reports (Guan et al. 2011; Guan et al. 2014) with the same electric field in the gated and un-gated cases.

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0.3 5 V 3 V 1 V 0.2

0.1

0.0

Current (nA) Current

-0.1

-2 -1 0 1 2 Gate Voltage (V)

Figure 48: A representative plot showing current modulation in a nanochannel filled with 1 mM KCl as a function of gate voltage for three test axial potentials. In all three cases the slope, 푑퐼/푑푉푔, remained constant with a value of 0.060 ± 0.003 nA/V. It is worth noting that in the same device for a given electrolyte concentration, the measured current can be switched off for different combinations of Va and Vg. In addition, current reversal was also be obtained by systematically tuning Vg with respect to Va. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

As all real dielectric materials in nanofluidic field effect devices permit a finite gate leakage current (Horiuchi et al. 2006; Fan et al. 2008; Nam et al. 2009; Oh et al.

2009; Joshi et al. 2010; Guan et al. 2011; Shin et al. 2012; Rutkowska et al. 2013), in addition to the capacitive coupling of the gate electrode and the nanofluidic channel, a finite gate leakage current was also measured through the PDMS dielectric layer. One implication of the finite leakage current is that the insulating or isolation PDMS layer forms an equivalent RC circuit between the surface electrode and the fluid, as detailed in

Chapter 2.

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Figure 49 shows the measured gate leakage current (GLC) plotted alongside the data presented in Figure 48. The value of the gate leakage current is lower than the measured axial current, particularly for the forward current state. The slope, or the change in current per unit gate voltage, for the gate leakage current data is significantly lower than the slope of the axial current, indicating the modulation of measured current is not dominated by gate leakage current. The finite gate leakage current, though small, may contribute to the change in electric field (Rutkowska et al. 2013), likely enhancing the effect of the gate electrode relative to the ideal dielectric case.

0.3 5 V 3 V 1 V 0.2 GLC 0.1

Current (nA) Current 0.0

-0.1

-2 -1 0 1 2 Gate Voltage (V)

Figure 49: A representative plot showing gate leakage current (GLC) for 1 mM KCl plotted alongside the data shown in Figure 48. The measured axial current is higher than the measured gate leakage current, particularly in the forward current state. Finite gate leakage current may contribute to the change in the electric field, likely enhancing the effect of the gate electrode relative to the ideal dielectric case. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

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From Equation 37, the contribution to the electric field from the gate electrode has either an additive or subtractive effect when compared to the un-gated axial field, as all potentials are applied with respect to the same reference. Application of a gate voltage will either enhance the effect of the axial voltage or reduce the effect, with the possibility

푉 of reversal in the electric field based on the relative magnitude and polarity of 푎 with 퐿

훼푉푔 respect to . For example, in the case of a positive axial potential (i.e. Va = +3 V) the 퐿−퐿1 contribution to the electric field from the gate electrode will be in the same direction as the axial field for a positive gate voltage (+Vg) leading to an increase in electric field and, therefore, forward current (Figure 50). In the case of a positive axial potential (i.e.

Va = +3 V) and a negative gate voltage (-Vg), the contribution due to the gate electrode will be opposite to the axial field leading to a decrease in electric field and, therefore, current.

When the sign of the axial potential is reversed (i.e. Va = -3 V) the relative impact of the gate potential will also be reversed, that is, a (+Vg) decreases the magnitude of the field while a negative gate potential (-Vg) increases the magnitude of the field. This leads to a decrease in current (i.e. smaller value of negative current, Figure 50) for Va = -3 V and Vg > 0 and an increase in current for Va= -3 V and Vg < 0 (i.e. larger value of negative current). In Figure 50, zero current was measured at Va = +3 V, Vg = -1.4 V, and

Va = -3 V and Vg = +1.8 V, consistent with modeling results of Ai et al. (Ai et al. 2011) that showed changes to the electric field induced by the gate electrode dramatically decreased ionic current when Va and Vg were of opposite sign. In further support of the

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proposed hypothesis, current modulation in the nanofluidic field effect switch follows the expected dependence on relative axial and gate potential.

0.2 3 V -3 V 0.1

0.0

-0.1

Current (nA)

-0.2

-2 -1 0 1 2 Gate Voltage (V)

Figure 50: A representative plot which demonstrates that the current modulation depends on the additive or subtractive effect of the electric field induced by the gate electrode with respect to the axial field. The gate electrode was located at 0.57 L. For Va = +3 V a negative gate voltage (-Vg) decreases the magnitude of the current while for Va = -3 V the same negative gate voltage (-Vg) increases the magnitude of the current. Here, current was switched off for Va = +3 V with Vg = -1.4 V, and Va = -3 V with Vg = +1.8 V, consistent with modeling results that showed changes to the electric field induced by the gate electrode dramatically decrease ionic current when Va and Vg were of opposite sign. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

4.5 Gate Location

Considering the effect of changing the gate location, as L1 is increased from the center of the channel (0.50 L) towards the grounded microchannel (L), the contribution of

훼푉 the gate electrode to the electric field, 푔 , is expected to increase. This means that for a 퐿−퐿1 given axial potential (Va) the change in current induced by the gate electrode will increase 160

as L1 increases. Figure 51 shows measured current at fixed axial voltage for a gate voltage sweep from -2 to +2 V for three representative electrode locations of 0.43 L,

0.48 L, and 0.57 L. The current modulation, quantified by the slope dI/dVg, was

0.003 nA/V, 0.014 nA/V, and 0.060 nA/V for 0.43 L, 0.48 L, and 0.57 L respectively.

The increased current modulation with L1 indicates increased contribution to the electric

훼푉 field by the gate electrode, or increase in 푔 as expected. Of the three location (0.43 퐿, 퐿−퐿1

0.48 퐿 and 0.57 퐿) reported, locations 0.43 퐿 and 0.57 퐿 correspond to the same physical electrode (Figure 43), indicating that the change in 푑퐼/푑푉푔 observed for various electrode locations is not caused by variation in electrode fabrication.

0.43 L 0.48 L 0.57 L 0.25 0.25 0.25 0.20 dI/dVg=0.003 nA/V 0.20 0.014 nA/V 0.20 0.060 nA/V 0.15 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.05

Current (nA) Current

Current (nA) 0.00 Current (nA) 0.00 0.00 -0.05 -0.05 -0.05 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 Gate Voltage (V) Gate Voltage (V) Gate Voltage (V)

Figure 51: Current modulation increases as the relative distance of the gate electrode from the channel inlet, L1, increases, in agreement with the proposed hypothesis. The increase in modulation for the representative case of 1 mM KCl (Va = 3 V) is demonstrated by the increase in the slope as shown in the plots above going from the left to right panels. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

Analysis based on electromigration similar to previous reports (Pu et al. 2004;

Nam et al. 2009; Guan et al. 2011) allows qualitative prediction of observed data trends

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for various ranges of Va, Vg, and L1. However, such an analysis based on electromigration alone does not consider effects of local accumulation and depletion of ions and subsequent changes in species concentrations. Since, a concentration gradient in the nanochannel is needed to maintain steady-state current and flux balance for incompressible flow, detailed modeling or experimental determination of actual ion distributions and analysis of the effect of these gradients on the current in gated nanofluidic channels will be useful and is the subject of future work.

4.6 Electrolyte Concentration

The observed current modulation is expected to depend on bulk KCl concentration (Nam et al. 2009; Liu et al. 2010). Figure 52 shows a summary of gating the nanochannels for 0.1 mM to 100 mM KCl at pH 7 ± 0.2. Due to differences in conductance for various concentrations, the current in Figure 52 is reported as a dimensionless current, ΔI/I0 = (Igated – Iun-gated)/Iun-gated. The dimensionless number ΔI/I0 is the change in current due to the gate compared to the current in the un-gated case. The current off state (Igated = 0 nA) corresponds to a dimensionless number of -1. A dimensionless current of 0 indicates the un-gated case (Vg = 0 V, Igated = Iun-gated).

Since switching the current off requires ΔI/I0 = -1, as bulk concentration increases higher gate voltage is required to achieve the off current state. The change in current induced by the gate electrode (ΔI) is smaller relative to the un-gated current (smaller

ΔI/I0) as bulk KCl concentration increases. Decrease in current modulation with increasing bulk KCl concentration is attributed to enhanced screening of the gate electrode by the KCl solution at higher concentrations. At low concentration, a gate

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voltage of -1.4 V and -3 V was required to switch off the current for 1 mM KCl and

0.1 mM KCl respectively (demonstrated in Figure 45 and Figure 46). The lower current modulation for 0.1 mM KCl compared to 1 mM KCl is likely due to increased availability of charge carriers in the 1 mM case as with highly overlapped electric double layers for the 0.1 mM case, the co-ions are excluded from the nanochannels (Kemery et al. 1998; Guan et al. 2011).

1.5 0.1 mM 1.0 1 mM 10 mM 0.5 100 mM

0 0.0

I / I

 -0.5

-1.0

-1.5 -2 -1 0 1 2 Gate Voltage (V)

Figure 52: The plot shows dependence of current modulation on bulk KCl concentration for a representative axial potential of Va = 3 V. Error bars were smaller than the markers and are therefore not shown explicitly. Current modulation was observed to decrease as bulk KCl concentration increases likely due to enhanced screening of the gate electrode. Reprinted with permission from Fuest, M., C. Boone, K. K. Rangharajan, A. T. Conlisk and S. Prakash (2015). A Three-State Nanofluidic Field Effect Switch. Nano Lett. 15(4): 2365–2371. Copyright 2015 American Chemical Society.

4.7 Chapter Summary

A 3-state nanofluidic field effect current switch, with a forward current, an off or zero current, and a reverse current state has been demonstrated in this chapter. For a fixed

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streamwise potential, the electric field within the nanofluidic channel is altered by systematically controlling the potential applied to a gate electrode embedded in the nanochannel wall. The change in electric field was confirmed by systematically altering the applied potentials (푉푎 and 푉푔), as well as the electrode location, 퐿1. The dependence of current modulation, or the ability of the gate electrode to alter the current, was investigated as function of electrolyte concentration. The ability to switch the current state was observed for electrolyte concentration corresponding to the surface charge governed regime for ionic transport, while the effect of the gate electrode decreased as

푐푏푢푙푘 approached 100 mM. Development of a current switch represents a key addition to existing ionic circuit elements towards the development of fluidic logic circuits.

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Chapter 5: Cation Dependent Surface Charge Regulation in

Gated Nanofluidic Devices

5.1 The role of surface charge in ionic transport

Surface charge is a fundamental parameter that governs nanoscale fluid transport enabling numerous applications in energy conversion (van der Heyden et al. 2006; Wen et al. 2012; Prakash et al. 2014), fluid-analogs of solid-state electronics (Daiguji et al. 2005;

Karnik et al. 2005; Guan et al. 2011), and biosensing (Hou et al. 2011; Prakash et al. 2012).

Basic science studies over decades have evaluated the role of surface charge at solid/liquid interfaces since surface charge governs generation of local potentials and all electrostatic interactions (Prakash et al. 2009) including site-specific binding in a vast majority of the membrane proteins in biological entities such as ion channels and ion pumps (Hille 2001).

Ion channels and ion pumps regulate ion transport across cell membranes for essential physiological functions (Gadsby 2009). Divalent ions such as calcium and magnesium play a critical role in regulating the opening, selectivity, and conductance of both cation and anion ion channels with direct implications for numerous physiological processes such as neuronal excitability, epithelial fluid secretion, cancer cell proliferation, and blood pressure regulation (Bichet 2003; Li 2011; Ma 2012; Pardo 2014; Peters 2015). Several studies have evaluated the exact mechanisms of both high flux and low flux voltage gated potassium ion channels that are mediated and/or regulated by calcium ions (Xia 1988; Li 2011; Jensen 165

2012). In biological entities channel structure and conformation, sub-units with local binding sites, relative wetting or hydrophobicity characteristics, local electrostatic domains at the channel entrance and within the ion channels, and surface charge have been identified as important parameters governing ion flux, selectivity, and levels of ion conductance and rectification (Li 2011; Vargas 2012; Aguilella 2014; Tang 2014; Lorinczi

2015), which can guide attempts to mimic functionality of ion channels and ion pumps in artificial nanoscale devices. Experimental investigations in synthetic micro- and nanochannels have led to the development of theoretical models that show surface charge regulation as function of electrolyte composition (van der Heyden et al. 2006; Datta et al.

2009; Li et al. 2015) and pH (Datta et al. 2009; Martins et al. 2013). The effect of local variation of electrostatic properties in nanoscale conduits on transport of polyvalent electrolytes and electrolyte mixtures, which form the basis for most biological systems or practical applications, has not yet been reported. Therefore, the purpose of this chapter is to demonstrate that systematic changes in local electrostatic surface state significantly impact ion transport in nanochannels as function of cation type.

Electrodes embedded in the wall of nanofluidic channels act as active, tunable gates to systematically modify local surface potential and/or surface charge and consequently the local electrostatic state at the dielectric-fluid interface (Karnik et al. 2005; Guan et al.

2011). Geometrically analogous to semi-conductor field effect transistors, gated nanofluidic devices feature one or more gate electrodes embedded in the nanochannel wall, separated from the electrolyte in the channel by a dielectric layer. In contrast to microfluidics where the gate electrode controls only interfacial properties near the

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electrode, under conditions of interacting electric double layers in nanofluidic channels, the gate potential influences the electric field throughout the nanochannel depth (Karnik et al. 2005; Fuest et al. 2015), as demonstrated in Chapter 4. Nearly all reports to date have used monovalent symmetric electrolytes with the majority of experimental and modeling studies focusing on transport of KCl (Karnik et al. 2005; Fan et al. 2008; Kalman et al.

2009; Liu et al. 2010; Liu et al. 2010; Jin et al. 2011; Shin et al. 2012; Singh et al. 2012;

Pardon et al. 2013; Guan et al. 2014; Lee et al. 2015), with limited evaluation of HCl (Fan et al. 2008; Joshi et al. 2010) and glycine based buffer solutions (Jiang et al. 2011). In this chapter, transport of two monovalent (KCl, NaCl) and two divalent electrolytes (MgCl2,

CaCl2) through a gated nanofluidic device was investigated to determine how surface charge regulation influences transport across nanoscale conduits as function of ion type

Previous reports have shown that adding trace amounts (few µM) of divalent electrolytes to monovalent electrolyte solutions in synthetic microchannels significantly reduces the zeta (ζ) potential, or the potential at the interface between the classically immobile Stern and mobile diffuse layers of the electric double layer (see Section 2.1)

(Datta et al. 2009). The change in ζ potential is caused by enhanced ion-wall interaction for divalent cations compared to monovalent cations (Zheng et al. 2003; Datta et al. 2009).

Ion associations between polyvalent cations and dangling oxygen bonds on negatively charged surfaces such as silica, reduce or even reverse the polarity of the effective surface charge density (Qiao et al. 2004; Lorenz et al. 2007; He et al. 2009). Reversal of the effective surface charge leads to charge inversion, where the diffuse layer is primarily comprised of co-ions ions rather than counter ions as in the classical picture of the electric

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double layer (Grosberg et al. 2002; Qiao et al. 2004; van der Heyden et al. 2006; van der

Heyden et al. 2006; Lorenz et al. 2007; He et al. 2009; Li et al. 2015). Mean field theory based on the Poisson equation for the potential and a Boltzmann distribution of ions fails to predict charge inversion, since it is caused by the discrete nature of ions and water molecules which is not taken into account in mean field theory (Qiao et al. 2004; Lorenz et al. 2007). Charge inversion plays a critical role in biological systems directly influencing viral packing, DNA translocation, and nucleic acid folding (Grosberg et al. 2002; van der

Heyden et al. 2006; He et al. 2009; Li et al. 2015), further motivating investigation of charge inversion (van der Heyden et al. 2006; Li et al. 2015) and the importance of divalent ions within electrolyte mixtures (Boda et al. 2006).

Nanochannels with a negative surface charge density such as the devices here are cation selective under conditions of interacting electric double layers, therefore, the cation is varied across electrolyte solutions for a fixed anion (chloride). To our knowledge, this dissertation presents the first systematic comparison of electrolyte solutions in a gated nanofluidic device. The concentration dependent intrinsic nanochannel conductance

(un-gated) was first investigated to not only provide validation against existing reports, but also to demonstrate cation dependent surface charge regulation for two monovalent (NaCl and KCl) and two divalent (CaCl2 and MgCl2) electrolyte solutions. A site binding model for the surface charge density confirms ion adsorption must be considered to realistically model experimental data trends for intrinsic nanochannel conductance as a function of pH.

For the first time, the role of ion-adsorption in regulating the surface charge was

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investigated using the gate electrode to modulate the local surface state under various experimental conditions.

5.2 Methodology for Cation Dependence Study

Three nanofluidic channels with an array of embedded gate electrodes connected two microchannel reservoirs (Figure 53). The embedded gate electrodes allowed systematic evaluation of surface charge regulation by cation type. Details on device fabrication and device operation as a nanofluidic switch have been reported in Chapters 3 and 4 respectively.

Four individually addressable Au gate electrodes were embedded in the roof of the nanofluidic channels and separated from the electrolyte in the nanochannel by a polydimethyl siloxane (PDMS) dielectric layer. Only one gate electrode was used for this study. The micro- and nanofluidic network was patterned on a glass substrate using UV lithography and wet etching techniques. Individually addressable Au gate electrodes were patterned onto a second glass substrate. A PDMS dielectric layer was spun onto the glass cover containing the electrode array. The cover with embedded electrodes and the glass substrate with the patterned channel network were bonded via O2 plasma bonding to form sealed channels.

The device testing setup included two power supplies (Keithley 3390 function generators) used to supply independent axial (푉푎) and gate (푉푔) potentials. Current (퐼) through the nanochannels was monitored using a Keithley 6485 picoammeter. Devices were first tested with the gate electrodes floating at each respective concentration/pH/electrolyte composition in order to measure the intrinsic nanochannel

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conductance (퐺 = 퐼/푉푎). All electrical measurements were conducted in an earth-grounded Faraday cage. Dedicated devices for each type of electrolyte were used to avoid contamination, with the obvious exception of devices used for electrolyte mixtures.

Electrolyte solutions were prepared for concentrations ranging from 0.01 mM to 100 mM at pH 7 ± 0.2. Each device was initially tested with deionized water (10-7 M) to provide the same baseline for comparison between devices. Only devices with an initial DI conductance within 4.4 ± 0.5 pS were used for comparison of results across devices as a function of cation type. The gate was located at 퐿푔 = 0.43 ± 0.02 for all devices as dependence of device operation on gate location was discussed in Chapter 4.

After initial conductance measurements with deionized water, electrolyte concentrations were tested in ascending order of concentration. After the electrolyte concentration was increased, the device was thoroughly rinsed with the next highest concentration, similar to previously reported procedures (Duan et al. 2010). Monovalent electrolytes (KCl and NaCl) were tested at 6 concentrations including DI water and concentrations ranging from 0.01 mM to 100 mM in order of magnitude increments.

Divalent electrolytes (CaCl2 and MgCl2) were tested at those concentrations with the addition of 0.33 mM and 3.33 mM to match the ionic strength for KCl and NaCl at 1 mM and 10 mM respectively (see Table 7). Overall data trends were verified over multiple devices with data for each experimental condition comprising several data runs over multiple days.

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B A PDMS Glass Glass Channels Gate Electrode PDMS Channels Gold

Nanochannel

퐿푔 C 200 nm D 200 nm PDMS 200 nm PDMS NanochannelNanochannel Glass Glass

Open nanochannel Bonded interface A 2 B 2 Figure10 53: (A) Schematic showing the layers of the10 nanofluidic device. Two KCl CaCl2 NaCl microchannels (8 µm deep x 50 µm wide x 3 cm long) served MgCl as2 reservoirs to a bank of three nanochannels (16 nm deep x 30 µm wide x 2.5 mm long). The micro- and nanochannel network was fabricated on a borosilicate glass substrate with individually addressable101 gold (Au) gate electrodes patterned on10 the1 glass cover. A polydimethyl siloxane (PDMS) dielectric layer supported on the glass cover isolated the gate electrodes from the aqueous electrolytes in the nanochannels. (B) Side-view schematic of the nanochannel, showing the active gate electrode for the data reported. Electrical 0 0 connections (pS) Conductance nsic 10 are shown with yellow lines. An axial (pS) Conductance nsic 10 potential difference, 푉푎, was applied between the two microchannel reservoirs. An independently controlled gate potential, 푉푔,

Intri Intri applied to10 the-7 gate10-6 electrode10-5 10-4 modified10-3 10 -2the10 local-1 surface10 charge-7 10-6 density10-5 10 and-4 10the-3 local10-2 10-1 electric field at theConcentration dielectric/electrolyte (M) interface enabling fieldConcentration-effect control (M)over ionic transport through the nanochannel. Changes in ionic transport were quantified through a current (퐼) measurement with all potentials applied with respect to the same ground. The gate electrode was located at a distance 퐿푔 = 0.43 ± 0.02 퐿, where 퐿 is the total nanochannel length and 퐿푔 is the relative distance from the gate electrode to the grounded microchannel (Fuest et al. 2015). (C) Scanning electron microscope (SEM) image of an open nanochannel cross section. The slit-like channel cross section lies between the arrows. The dashed red lines denote the locations on the device where the SEMs were taken. The channel height was ~16 nm, as expected from previous reports on device fabrication and characterization (Pinti et al. 2013; Fuest et al. 2015). (D) SEM image of PDMS bonded to glass in regions where no channel is expected.

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Table 7. Debye Length as a function of electrolyte concentration for 1:1 (KCl and NaCl) and 2:1 (CaCl2 and MgCl2) electrolytes.

Electrolyte Concentration Ionic Strength Debye Length (mM) (mM) (nm) KCl / NaCl 0.01 mM 0.0100 96 CaCl2 / MgCl2 0.01 mM 0.0300 56 CaCl2 / MgCl2 0.033mM 0.1 30 KCl / NaCl 0.1 mM 0.1 30 CaCl2 / MgCl2 0.1 mM 0.3 18 CaCl2 / MgCl2 0.333 mM 1 9.5 KCl / NaCl 1 mM 1 9.5 CaCl2 / MgCl2 1 mM 3 5.5 CaCl2 / MgCl2 3.33 mM 10 3.0 KCl / NaCl 10 mM 10 3.0 CaCl2 / MgCl2 10 mM 30 1.8 CaCl2 / MgCl2 33.3 mM 100 0.96 KCl / NaCl 100 mM 100 0.96 CaCl2 / MgCl2 100 mM 300 0.55 CaCl2 / MgCl2 333 mM 1000 0.30

After initial conductance measurements with deionized water, electrolyte concentrations were tested in ascending order of concentration. Before the electrolyte concentration was increased, the device was thoroughly rinsed with the next highest concentration, similar to previously reported procedures (Duan et al. 2010). Monovalent electrolytes (KCl and NaCl) were tested at 6 concentrations including DI water and concentrations ranging from 0.01 mM to 100 mM in order of magnitude increments.

Divalent electrolytes (CaCl2 and MgCl2) were tested at those concentrations with the addition of 0.33 mM and 3.33 mM to match the ionic strength for KCl and NaCl at 1 mM and 10 mM respectively.

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5.3 Dependence of Nanochannel Conductance on Ion Type

A potential difference along the nanochannel length, or the axial potential, 푉푎, drives ionic transport through the nanofluidic channel. A separate and independently controlled potential applied to one gate electrode modified the local surface charge density at the dielectric-electrolyte interface and subsequently the local electric field in the nanochannel. The primary measurable metric for quantifying ionic transport is the measured current (퐼) given by

ℎ 푚 퐼 = 푤퐹 ∫ ∑ 푧𝑖 푁𝑖 푑푦 (38) 0 𝑖=1

Here 푤 is the width of the channel, 퐹 is Faraday’s constant, ℎ is the height of the nanochannel, 푚 is the number of species in the channel, 푧𝑖 is the valence of species 𝑖, and

푁𝑖 is the molar flux of each species. The electrical connections for the axial potential, gate potential, and picoammeter to the gated nanofluidic device are shown schematically in

Figure 53B.

The nanofluidic device was first operated with the gate electrode floating (푉푔 = 0 V) to measure the intrinsic nanochannel conductance (퐺푎 = 퐼/푉푎) as a function of cation type

(Figure 54). In agreement with previously reported trends for KCl (Stein et al. 2004; Karnik et al. 2005; Schoch et al. 2005) and anomalous transport of NaCl with respect to KCl (Duan et al. 2010), the two monovalent cations showed similar intrinsic conductance (퐺푎) within experimental uncertainty.

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B A PDMS Glass Glass Channels Gate Electrode PDMS Channels Gold

Nanochannel

퐿푔 C 200 nm D 200 nm PDMS 200 nm PDMS NanochannelNanochannel Glass Glass Open nanochannel Bonded interface

A 102 B 102

KCl CaCl2 NaCl MgCl2

101 101

0 0 nsic Conductance (pS) Conductance nsic 10 (pS) Conductance nsic 10

Intri Intri 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10-7 10-6 10-5 10-4 10-3 10-2 10-1 Concentration (M) Concentration (M)

Figure 54: (A) The intrinsic nanochannel conductance, measured with the gate electrode floating (푉푔 = 0 V) , was independent of concentration at low concentration for monovalent electrolytes KCl and NaCl indicating surface charge governed transport. The conductance depended linearly on concentration at high concentrations, in agreement with general previous trends reported (Stein et al. 2004; Karnik et al. 2005; Schoch et al. 2005; Duan et al. 2010). (B) The intrinsic nanochannel conductance for divalent electrolytes MgCl2 and CaCl2 shows surface charge governed behavior similar to monovalent electrolytes for (푐푏푢푙푘 < ~0.1 mM. The conductance decreased at 푐푏푢푙푘 ≈ ~1 mM for MgCl2 and 푐푏푢푙푘 ≈ ~3.33 mM for CaCl2. The decrease in conductance is likely due to adsorption of divalent cations to the negatively charged walls as described in the main text. The dashed lines are intended as eye-guides only.

The intrinsic conductance of both KCl and NaCl was independent of concentration at low concentrations (푐푏푢푙푘 < ~1 mM), indicating surface charge governed transport while the conductance had a linear dependence on concentration at high concentrations

(푐푏푢푙푘 > ~1 mM). To satisfy electroneutrality, the total space charge within the nanochannel volume must be equal and opposite to the total charge on the nanochannel walls, with the balance of cations and anions determined by the additional counter ions needed to balance the total surface charge. The number of charge carriers in the nanochannel is determined by the surface charge at low concentrations, corresponding to

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the plateau region in the conductance plot where conductance is independent of concentration (Figure 54A). At higher concentration the conductance is dominated by bulk transport behavior, which has a linear dependence on electrolyte concentration. As discussed in Chapter 2, the total intrinsic nanochannel conductance (퐺 = 퐼/푉푎) can be written as the summation of the surface charge governed (SCG) and the bulk conductance according to

푚 2푤푧 휇 |𝜎| 퐹푤ℎ 퐺 = 퐺 + 퐺 = 푐푎푡 + + ∑ 휇 푧 2푐 푏푢푙푘 (39) 푎 푆퐶퐺 푏푢푙푘 퐿 퐿 𝑖 𝑖 𝑖 𝑖=1

where 푤 is the channel width, 푧푐푎푡 is the valence of the cation, 휇+is the cation mobility, 𝜎 is the surface charge density (assumed to be negative), 퐿 is the channel length, 휇𝑖 is the

푏푢푙푘 mobility of species 𝑖, ℎ is the channel height, and 푐𝑖 is the bulk electrolyte concentration (Guan et al. 2014). The dominant term in Equation 39 will depend on the bulk electrolyte concentration (Guan et al. 2014). At the transition concentration, 푐푡, the bulk and SCG conductances are similar.

In contrast to the monovalent cations, cation dependent intrinsic conductance was

2+ 2+ observed for the divalent cations, Ca and Mg . 퐺푎 of CaCl2 and MgCl2 (Figure 54B) was independent of bulk concentration at 푐푏푢푙푘 ≤ ~ 0.1 mM, suggesting SCG transport.

Conductance of MgCl2 showed a marked decrease in conductance from 4.5 pS at

푐푏푢푙푘= 0.1 mM to 1.2 pS at 푐푏푢푙푘= 1 mM. CaCl2 conductance decreased from 4.0 pS for

푐푏푢푙푘 = 1 mM to 0.8 pS for 푐푏푢푙푘 = 3.33 mM showing a change in conductance per unit

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concentration of 1.39 S/mM for CaCl2 and 3.67 S/mM for MgCl2 before transitioning to linear concentration dependence in the bulk transport regime.

Since, 퐺푎 is proportional to 𝜎 for dilute electrolyte solutions (푐푏푢푙푘 ≤ ~ 1 mM)

(Stein et al. 2004; Karnik et al. 2005; Schoch et al. 2005; Duan et al. 2010; Guan et al.

2011; Guan et al. 2014), the decrease in 퐺푎 for divalent ions corresponds to ~ 3.75x reduction in 𝜎 for MgCl2 between 푐푏푢푙푘 = 0.1 mM and 푐푏푢푙푘 = 1 mM and ~ 5x reduction in 𝜎 for CaCl2 between 푐푏푢푙푘 = 1 mM and 푐푏푢푙푘 = 3.33 mM. Two distinct transition concentrations exist for intrinsic conductance of divalent cations: (i) reduction in 𝜎 due to cation adsorption (discussed below) with 푐푎 ≈ 0.1 mM for MgCl2 and 푐푎 ≈ 0.1 mM for

CaCl2 and (ii) transition to bulk transport behavior, 푐푡 ≈ 1 mM for MgCl2 and 푐푡 ≈ 10 mM for CaCl2.

Changes in the local surface charge density and electric field were induced by the gate electrode to modulate ionic transport and, therefore, the measured current (Karnik et al. 2005; Liu et al. 2010; Guan et al. 2011; Jin et al. 2011). The current was monitored at electrolyte concentrations between 0.01 and 100 mM for +3 V ≤ 푉푔≤ -3 V at a fixed axial potential (푉푎) (Fuest et al. 2015). A representative plot of measured current v. gate voltage as a function of cation type is shown in Figure 55 for 10 mM KCl, 10 mM NaCl, 3.33 mM

CaCl2, and 3.33 mM MgCl2. The ionic strength of the electrolyte solutions was matched to ensure consistent values of the Debye length or the characteristic screening length of the surface potential, across cases. The current has a linear dependence on gate voltage for a fixed axial potential 푉푎 = 3 V.

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50 KCl 45 NaCl CaCl 40 2 MgCl 35 2 30 25 20 15

Current (pA) Current 10 5 0 -3 -2 -1 0 1 2 3 Gate Voltage (V)

Figure 55: A representative plot of the measured current v. gate voltage as a function of cation type for 10 mM KCl, 10 mM NaCl, 3.33 mM CaCl2, and 3.33 mM MgCl2. The ionic strength of the electrolyte solutions was matched to ensure consistent values of the Debye length or the characteristic screening length of the surface potential, across cases. For all cases 푉푎 = 3 V.

Following previously reported analysis (Fan et al. 2008; Nam et al. 2009), the total current arises from the gated and intrinsic conductances (Fan et al. 2008; Nam et al. 2009;

Fuest et al. 2015), 퐺푔 and 퐺푎 respectively. Applying a potential to the gate electrode modifies the local surface charge and the local electric field within the nanochannel (Karnik et al. 2005; Liu et al. 2010; Ai et al. 2011; Guan et al. 2011; Fuest et al. 2015). Considering electrokinetic transport of an electrolyte solution, the current in the nanofluidic channel can be written as (Pu et al. 2004; Nam et al. 2009; Guan et al. 2011)

푚 2 푛푎푛표 퐼 = 푤ℎ퐹 ∑ 휇𝑖푧𝑖 푐𝑖 퐸 (40) 𝑖=1

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푛푎푛표 where 푧 is the valence, 휇 is the ionic mobility, 푐𝑖 is the concentration in the nanochannel, and 퐸 is the electric field. Note that Equation 39 is easily derived from

푛푎푛표 Equation 40 by considering that 푐𝑖 is determined by the bulk electrolyte concentration and the electroneutrality condition. The concentration of each species in the nanochannel,

푛푎푛표 푐𝑖 , is altered in response to the change in surface charge induced by the gate electrode

(Karnik et al. 2005; Fan et al. 2008; Jiang et al. 2011; Jin et al. 2011). The electric field, which can be approximated as 퐸 = 푉푎/퐿 in the ungated case for long channels (퐿 > ~ 1 µm)

(Vlassiouk et al. 2008), can be written to include the contribution from the gate electrode according to as in Chapter 4 (Fuest et al. 2015)

푉푎 훼푉푔 퐸 = + (41) 퐿 퐿푔

where 훼 is an empirical fitting parameter that accounts for the potential drop across the dielectric (Fuest et al. 2015) and 퐿푔 is the distance from the inlet microchannel to the gate electrode. Since the total current can be approximated as the superposition between the axial and gate contributions (Fan et al. 2008; Nam et al. 2009; Guan et al. 2011), Equation

40 is re-written as

푚 푉 퐼 = 푤ℎ퐹 ∑ 휇 푧 2푐 푢푛푔푎푡푒푑 푎 𝑖 𝑖 𝑖 퐿 𝑖=1 푚 푚 훼푉 (42) 2 푔푎푡푒푑 2 푢푛푔푎푡푒푑 푔 + 푤ℎ퐹 (∑ 휇𝑖푧𝑖 푐𝑖 − ∑ 휇𝑖푧𝑖 푐𝑖 ) 퐿푔 𝑖=1 𝑖=1

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or simply

퐼 = 퐺푎푉푎 + 퐺푔푉푔 (43)

where 퐺푎 is the intrinsic nanochannel conductance and 퐺푔 is the gated nanochannel conductance (Karnik et al. 2005; Fan et al. 2008; Nam et al. 2009). The gated nanochannel conductance was determined from linear regression of the 퐼 v. 푉푔 curve for a fixed 푉푎.

The dimensionless number, 퐺푔⁄퐺푎, compares the gated nanochannel conductance to the intrinsic nanochannel conductance. Figure 56A shows that the manipulation of the surface charge at the dielectric-liquid interface modulates the conductance for bulk concentrations corresponding to the surface charge governed regime (Figure 54A) with the level of modulation due to the gate electrode decreasing as 푐푏푢푙푘 approaches 100 mM. For the monovalent cations, the maximum value of 퐺푔⁄퐺푎 was observed at the transition concentration, 푐푡 ≈ 1 mM, consistent with previous reports for KCl and HCl (Fan et al.

2008; Nam et al. 2009), and data shown in Chapter 4 for KCl. Since the conductance ratio for NaCl follows a similar to trend to KCl the relative effect of the gate electrode was approximately equivalent for both monovalent ions tested.

In contrast to the monovalent ions, cation dependent behavior was observed for

2+ 2+ divalent Mg and Ca . For MgCl2, 퐺푔⁄퐺푎 at 푐푏푢푙푘 = 0.1 mM was 0.2 compared to ~ 0.8 for monovalent ions even though KCl, NaCl, and MgCl2 have comparable intrinsic nanochannel conductance at 0.1 mM. Starting at 0.1 mM, the effect of the gate began to increase with concentration for MgCl2, with the maximum value of 퐺푔⁄퐺푎 at 1 mM, which

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is the transition concentration to bulk transport behavior for MgCl2. Note that the ionic strength of MgCl2 which determines the Debye length, is 1/3 of the ionic strength for an equivalent concentration of KCl or NaCl (Table 7).

A 1.2 B 1.2

KCl MgCl2 NaCl CaCl 1.0 1.0 2 0.8 0.8

a 0.6 0.6

/ G

G G 0.4 0.4 0.2 0.2 0.0 0.0 10-4 10-3 10-2 10-1 10-4 10-3 10-2 10-1 Concentration (M) Concentration (M)

Figure 56: The conductance ratio as a function of cation type. The conductance ratio 퐺푔⁄퐺푎 is a non-dimensional parameter that compares the gated nanochannel conductance, 퐺푔, to the intrinsic nanochannel conductance, 퐺푎. For all measurements, the gate was located at 퐿푔= 0.43 ± 0.02 (Fuest et al. 2015). (A) The maximum conductance ratio was observed at the transition concentration for KCl and NaCl, in agreement with previous reports for KCl and HCl (Fan et al. 2008; Nam et al. 2009). (B) Local minimums of the conductance ratio for divalent ions correspond to the transition concentration where cation adsorption reduced the magnitude of 𝜎 (ca = 0.1 mM for MgCl2 and ca = 1 mM for CaCl2). Cation adsorption to the charged glass (and PDMS) walls regulates the surface charge density thus preventing the gate electrode from altering the surface charge density. The dashed lines are intended as eye-guides only.

2+ 2+ In a contrast to Mg , 퐺푔⁄퐺푎 for Ca decreased from 0.9 at 0.33 mM (which was transition from SCG) to ~0.3 at 1 mM. 퐺푔⁄퐺푎 also showed a local maxima at 3.33 mM for

CaCl2, which is the transition concentration to bulk transport behavior. Consequently, the

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gate electrode showed reduced modulation for divalent ions at the transition concentration where 𝜎 decreased (푐푎). We hypothesize that at the transition concentration, 푐푎, the gate potential induces ion associations which prevent the gate electrode from altering the effective surface charge density leading to a local minimum in the conductance ratio and regulation of the surface charge as a function of cation type.

5.4 Cation Dependent Transport of Electrolyte Mixtures

Most practical applications and real biological systems contain electrolyte solutions comprising multiple ionic species. However, systematic study of gated nanochannel conductance for even simple electrolyte mixtures has not yet been explored. KCl and CaCl2 were selected for comparison given the broader set of knowledge existing for these two electrolytes and the vital role of calcium ions in many biological systems with nanoscale critical length scales (Xia 1988; Li 2011; Jensen 2012). Electrolyte mixtures of KCl and

CaCl2 were evaluated at pH = 7 ± 0.2 at a fixed ionic strength to ensure a consistent Debye length across experiments. The relative composition of the electrolyte solution was altered from 0% CaCl2 (i.e., 1 mM KCl) to 100 % CaCl2 (0.33 mM CaCl2). The electrolyte compositions and corresponding concentrations of each electrolyte are summarized in

Table 8.

The intrinsic nanochannel conductance as a function of the percentage of CaCl2 in the bulk electrolyte solution is shown in Figure 57A. As CaCl2 percentage was increased from 0 to 25% the conductance decreased from ~ 2.8 pS to 1.4 pS. Further increasing the

CaCl2 percentage from 25 to 50% caused the conductance to decrease further but only from

1.4 pS to 1.2 pS. Further increasing the CaCl2 percentage from 25 to 50% caused the

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conductance to decrease from 1.4 pS to 1.2 pS, with no change beyond 50% CaCl2.

2+ + Therefore, starting at 25% Ca in the solution, 퐺푎 was independent of K concentration.

Table 8: A summary of electrolyte compositions and the corresponding prepared concentrations. Electrolyte Composition Concentrations Electrolyte Ionic Strength 100% KCl 1 mM KCl 1 mM 75% KCl / 25% CaCl2 0.5 mM KCl; 0.167 mM 1 mM CaCl2 50% KCl / 50% CaCl2 0.25 mM KCl; 0.25 mM 1 mM CaCl2 25% KCl / 75% CaCl2 0.1 mM KCl; 0.3 mM 1 mM CaCl2 100% CaCl2 0.33 mM CaCl2 1 mM

With 0% CaCl2 case as the baseline, 퐺푎 was estimated as a function of electrolyte composition. The current through the nanochannel is given in Equation 40. The intrinsic nanochannel conductance for an electrolyte mixture prepared from KCl and CaCl2 is then given by

퐹푤ℎ 푛푎푛표 푛푎푛표 푛푎푛표 퐺 = (휇 + 푐 + + 4휇 2+푐 2+ + 휇 − 푐 − ) (44) 푎 퐿 퐾 퐾 퐶푎 퐶푎 퐶푙 퐶푙

푛푎푛표 where 푐𝑖 is the concentration of a species 𝑖 in the nanochannel and is related to the surface

푛푎푛표 charge density in the SCG by 퐹ℎ푧𝑖푐𝑖 = 𝜎. Consistent with previous reports for single electrolytes (Stein et al. 2004; Schoch et al. 2005; Duan et al. 2010), a constant surface charge density was assumed for all electrolyte compositions. Consequently, to maintain system electroneutrality, the space charge density, 𝜌휀, within the nanochannel volume must also remain constant across electrolyte compositions (Equation 45). 182

A 3.2 B 1.2 Measured Estimated 2.8 1.0 0.8

2.4 0



2.0 / 0.6

EC  0.4 1.6 0.2 1.2

Intrinsic Conductance (pS) Conductance Intrinsic 0.0 0 25 50 75 100 0 25 50 75 100 Composition (% CaCl ) Composition (% CaCl ) 2 2

Figure 57: (A) The measured intrinsic nanochannel conductance as a function of electrolyte composition for a fixed ionic strength of 1 mM. The estimated values are based on the intrinsic nanochannel conductance of 1 mM KCl assuming a constant surface charge density and that the ratio cations in the bulk is preserved in the nanochannel (Equations 44 to 48). The constant surface charge assumption fails to predict experimentally measured conductance (B) The deduced surface charge density ratio as a function of electrolyte composition calculated using the measured intrinsic nanochannel conductance at each electrolyte composition and Equations 46, 47, and 49. The surface charge density for each electrolyte composition (𝜎퐸퐶) is shown relative to the surface charge density for the 0% CaCl2, or 1 mM KCl, case (𝜎0). The surface charge density decreases with the introduction of Ca2+ and remained constant with K+ concentration for % CaCl2 ≥ ~25%.

Using 0% CaCl2 (or, 100% KCl) as the baseline case, since 𝜌휀 is constant the total concentration of all ionic species within the nanochannel is expressed in terms of the space charge density in the 0% CaCl2 (100% KCl) case as

푛푎푛표 푛푎푛표 푛푎푛표 100 푐퐾+ + 2푐퐶푎2+ + 푐퐶푙− = 푐퐾+ (45)

100 where 푐퐾+ is the concentration in the nanochannel for the 100% KCl (0% CaCl2 case). It is further assumed that the relative concentration of cations in the nanochannel is equal to 183

the relative concentration of cations in the bulk (Martins et al. 2013), as there is no way to currently measure the actual concentration within the nanochannels, or

푛푎푛표 2+ 푛푎푛표 푐퐶푎2+ = 푝푟표퐶푎 푐푡표푡푎푙 (46)

푛푎푛표 + 푛푎푛표 푐퐾+ = 푝푟표퐾 푐푡표푡푎푙 (47)

2+ 푏푢푙푘 푏푢푙푘 + 푏푢푙푘 푏푢푙푘 where 푝푟표퐶푎 = 푐퐶푎2+/푐푡표푡푎푙 and 푝푟표퐾 = 푐퐾+ /푐푡표푡푎푙. Given that 휇퐶푎2+ = 0.434 휇퐾+ and neglecting the concentration of chloride ions due to permselectivity for interacting electric double layers, the conductance at a given electrolyte composition (퐺퐸퐶) can be written in terms of the conductance in the 100% KCl case (퐺100% 퐾퐶푙) from Equations

44 and 45 to 47 as

2+ + 퐺퐸퐶 1.73 푝푟표퐶푎 + 푝푟표퐾 = ( 2+ + ) (48) 퐺100% 퐾퐶푙 2푝푟표퐶푎 + 푝푟표퐾

where 푝푟표퐶푎2+and 푝푟표퐾+ are the proportions of Ca2+ and K+ in the bulk solution respectively (i.e. 0.25 and 0.75 for 25% CaCl2 and 75% KCl).

The measured and estimated values of the intrinsic nanochannel conductance as a function of electrolyte composition are shown in Figure 57B (with values listed in Table

9). The difference between the measured and predicted estimated values shows that the constant space charge density and, therefore, constant surface charge assumption fails for

퐺푎 in KCl/CaCl2 mixtures. Alternately, there could be a non-zero chloride conductance in the nanochannel that is not accounted for in the estimated value. However, using 25% 184

CaCl2 as an example, the difference between the predicted and measured values is 1.2 pS, with measured and estimated values of 1.4 pS and 2.6 pS respectively. Considering that

휇퐶푙− = 1.04휇퐾+ and the measured conductance for the 100% KCl case is 2.75 pS, the disagreement between the measured and estimated values cannot be attributed to the neglected chloride conductance alone. Additionally, it cannot simply be the ratio of charge carriers within the nanochannel which has changed since the estimated value of the 100 %

CaCl2 conductance was also significantly higher than the measured 100% CaCl2 conductance. The difference between the predicted 100% KCl and 100% CaCl2 cases was

14% while the difference between the measured values was 85%.

Table 9: Measured and estimated values for the conductance as a function of electrolyte composition. Conductance values are given as a ratio of the conductance at a given electrolyte composition over the conductance of the 0% CaCl2 (i.e. 100% KCl case). Predicted values of the conductance are calculated using Equation 48 under the assumptions that the proportion of the cations in the nanochannel is equal to the relative proportion of cation concentration in the bulk and that the surface charge is constant across cases. The conductance values calculated from Equation 48 failed to predict the measured conductance indicating the constant surface charge assumption is invalid.

Electrolyte Composition GEC /G100%KCl estimated GEC /G100%KCl measured 100% KCl 1 1 75% KCl / 25% CaCl2 0.95 0.49 50% KCl / 50% CaCl2 0.91 0.42 25% KCl / 75% CaCl2 0.89 0.40 100% CaCl2 0.87 0.41

Since the constant surface charge assumption failed to predict the measured conductance for electrolyte mixtures, the measured conductance was used to calculate the value of the effective surface charge density. The assumption that the relative concentration 185

of cations in the nanochannel is equal to the relative concentration of cations in the bulk

(Martins et al. 2013) (Equations 46 and 47) was retained. From Equation 39, 46, 47, 49 and the electroneutrality condition the relative surface charge density at a given electrolyte composition is given by

퐺 퐸퐶 (2푝푟표퐶푎2+ + 푝푟표퐾+) 𝜎퐸퐶 퐺100% 퐾퐶푙 (49) = 2+ + 𝜎0 1.73 푝푟표퐶푎 + 푝푟표퐾

where 𝜎퐸퐶 is the surface charge density for a given electrolyte composition and 𝜎0 is the surface charge density for the 0% CaCl2 (100% KCl) case.

The calculated surface charge density ratio is shown in Figure 57B. The calculated surface charge density dropped to ~ ½ its value when moving from 0 % CaCl2 to 25 %

CaCl2. As the relative concentration was increased beyond 25 % CaCl2 the predicted surface charge density was approximately constant with a maximum percent difference of

13%. The decrease in surface charge density caused by introduction of Ca2+, which does not further decrease with additional Ca2+, suggests affinity of Ca2+ for the charged wall compared to K+ ions through experimentally deduced surface charge density.

Consequently, addition of divalent ions can be used to regulate the effective surface charge density and thereby directly affect the nanochannel conductance.

Figure 58A shows the gated nanochannel conductance as a function of electrolyte composition at pH 7. Similar to the trends in Figure 57A, Ca2+ reduced 𝜎 and suppressed

퐺푔 (Figure 58A). The highest 퐺푔 was observed at 0% CaCl2 with approximately equivalent gated conductance for electrolyte compositions greater than 25% CaCl2. 186

A B 1.4 0.7 1.2 0.6 1.0 0.5

0.8 a 0.4

/ G 0.6 g 0.3

G 0.4 0.2 0.2 0.1

Gated Conductance (pS) Conductance Gated 0.0 0.0 0 25 50 75 100 0 25 50 75 100 Composition (% CaCl ) Composition (% CaCl ) 2 2

Figure 58: The gated conductance and conductance ratio (퐺푔/퐺푎) as a function of electrolyte composition at a fixed ionic strength of 1 mM. (A) The gated nanochannel conductance decreased as % CaCl2 was increased from 0% to 25%, consistent with the trend for intrinsic conductance as a function of electrolyte composition. Similar to the decrease in intrinsic conductance, decrease in gated conductance was attributed to Ca2+ adsorption. The drop in gated conductance between 0% CaCl2 (1 mM KCl) and 25% CaCl2 was only 43% compared to 68% for the intrinsic nanochannel conductance. (B) The conductance ratio (퐺푔/퐺푎) showed that gate modulation decreased with % CaCl2 greater than 25%, with an approximately constant value of 퐺푔/퐺푎 beyond 25% CaCl2, suggesting that with surface charge regulated by ion adsorption, the gate is limited in modulating the dielectric/fluid potential.

The decrease in 퐺푔 between 0% CaCl2 and 25% CaCl2 was 43% compared to 68% for 퐺푎. Considering 퐺푔/ 퐺푎 (Figure 58B) and the above observations about the ability of the gate to modulate conductance, we hypothesize that the effect of the gate electrode is reduced at electrolyte compositions greater than 25% CaCl2 because the gate is unable to manipulate the surface potential with adsorbed ions. Therefore, the presence of divalent cations in solution leads to surface charge regulation due to ion adsorption. In order to evaluate the surface charge regulation hypothesis, the comprehensive, and at times 187

unexpected experimental results here are placed in context of known site binding models

(Dove et al. 2005; Sverjensky 2006; Datta et al. 2009).

5.5 Surface Charge Regulation

Numerous past reports systematically manipulate the surface charge density by altering pH of the electrolyte solution, which affects the dissociation of the surface silanol groups in silica nanochannels and thus the effective surface charge density (Behrens et al.

2001; Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011; Martins et al. 2013). While tuning the potential applied to the embedded gate electrode is known to create local variation in the surface charge density, altering the pH of the electrolyte globally modifies the nanochannel surface charge density. A site binding model (SBM) (Dove et al. 2005;

Sverjensky 2006; Datta et al. 2009) was implemented for each electrolyte solution (1:1 and

2:1 electrolytes) to calculated the surface charge density as function of pH. Two cases were considered for calculating 𝜎, (i) only deprotonation of surface silanol groups, and (ii) deprotonation and cation adsorption to deprotonated surface sites.

5.5.1 Site Binding Model

The modified and improved site binding model in this work follows from the detailed models developed by Datta et al. (Dove et al. 2005; Sverjensky 2006; Datta et al.

2009). Here the Debye-Hückel linearization was not used (Datta et al. 2009); however, as the measurements are based on current and electrical properties, the Stern layer capacitance was added (Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011), to account for the fact that the surface potential, 휙푆 is different from the zeta potential, ζ i.e. 휙푆 ≠ 휁.

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The total surface charge density (𝜎) is given by the sum of the contributions from each type of ionizable surface group (Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011),

𝜎 = 푒(Γ+ − Γ−) (50)

where Γ+ is the total number density of positively charged surface sites, Γ− is the total number density of negatively charged surface sites, and 푒 is the elementary charge. For silica, negative surface sites arise from the deprotonation of surface silanol groups according to the reaction (Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011),

푆𝑖푂퐻 ⇌ 푆𝑖푂− + 퐻+ (51)

where the equilibrium constant for the deprotonation reaction (푝퐾1) can be written from the law of mass action as (Behrens et al. 2001; Datta et al. 2009)

− [퐻+] Γ푆푖푂 푆 = 10−푝퐾1 (푀표푙/푙) (52) Γ푆푖푂퐻

+ The surface proton concentration ([퐻 ]푆) was assumed to follow a Boltzmann distribution

(Behrens et al. 2001; Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011)

+ + −퐹휙푆 (53) [퐻 ]푆 = [퐻 ]퐵exp ( ⁄푅푇)

189

+ where 휙푆 is the surface potential and the bulk proton concentration ([퐻 ]퐵) is related to the solution pH by

+ −푝퐻 [퐻 ]퐵 = 10 (푀표푙/푙) (54)

For a monovalent symmetric electrolyte such as KCl, K+ adsorbs to the negatively charged surface sites according to (Datta et al. 2009)

푆𝑖푂퐻 + 퐾+ ⇌ 푆𝑖푂퐾 + 퐻+ (55)

Note, that monovalent cation adsorption to the charged silica wall leads to neutralization

+ of surface sites (Datta et al. 2009). The equilibrium constant for the adsorption of K (푝퐾푀) is given by

+ 푆𝑖푂퐾 [퐻 ]퐵Γ −푝퐾푀 (56) + 푆𝑖푂퐻 = 10 (푀표푙/푙) [퐾 ]퐵Γ

+ + + + where [퐻 ]퐵 and [퐾 ]퐵 are the bulk concentration of H and K respectively. The total number density of surface sites (Γ), including the density of neutral cites Γ푆𝑖푂퐻 and Γ푆𝑖푂퐾 is

− Γ = Γ푆𝑖푂퐻 + Γ푆𝑖푂퐾 + Γ푆𝑖푂 (57)

190

The surface charge densiiity arising from chemical reactions between the surface and the monovalent electrolyte is therefore

−푝퐾1+푝퐻 퐹휙푆 −푒Γ (10 exp (− ⁄푅푇)) 𝜎 = (58) −푋−푝퐾 +푝퐻 −푝퐾 +푝퐻 퐹휙푆 1 + 10 푀 + 10 1 exp (− ⁄푅푇)

for 10-X M KCl. Subsequently, the equation for the surface charge density arising from deprotonation (no ion adsorption) is given by

−푝퐾1+푝퐻 퐹휙푆 −푒Γ (10 exp ( ⁄푅푇)) 𝜎 = . (59) −푝퐾 +푝퐻 퐹휙푆 1 + 10 1 exp ( ⁄푅푇)

An independent solution for the surface charge as a function of surface potential was also obtained implementing the Poisson-Boltzmann description of the ion distribution near the charged wall (Datta et al. 2009; Jiang et al. 2010; Jiang et al. 2011). The electroneutrality condition requires that the total charge in the fluid volume must be equal and opposite the total surface charge, or (Conlisk 2013)

ℎ/2 ℎ/2 푑2휙 푑휙 (60) 𝜎 = ∫ 𝜌푒푑푦 = −휀푒 ∫ 2 푑푦 = −휀푒 0 0 푑푦 푑푦

where 휀푒 is the permittivity of the electrolyte. Given the ultra-low aspect ratio nanochannels (0.0005) here with near-infinite length (2.5 mm) with respect to 16 nm 191

channel depth, the Poisson equation was written in a 1-D form with a Boltzmann distribution for the space charge density, and solved analytically for 𝜎.

푧 퐹휙 푧 퐹휙 2 −퐹(푐 exp (− 푐푎푡 ⁄ ) + 푐 exp (− 푎푛 ⁄ )) 푑 휙 −𝜌푒 푐푎푡 푅푇 푎푛 푅푇 (61) 2 = = 푑푦 휀푒 휀푒

푑휙 Equation 61 was solved analytically for and thus 𝜎. Here 푐 and 푐 are the 푑푦 푐푎푡 푎푛 concentrations of the cation and anion respectively and 푧푐푎푡 and 푧푎푛 are the valence of the cation and anion respectively. The equation for the surface charge for a symmetric monovalent electrolyte is

푧퐹 𝜎 = √8푅푇휀 퐼 푠𝑖푛ℎ ( 휁) (62) 푒 푆 2푅푇

which is the well-known Grahame equation for a monovalent symmetric electrolyte. The zeta potential (휁) is related to the surface potential (휙푆) by (Behrens et al. 2001)

𝜎푆 + 퐶푆푡푒 푛휁 휙푆 = . (63) 퐶푆푡푒 푛

2 where, the Stern layer capacitance, 퐶푆푡푒 푛 was 2.9 F/m (Behrens et al. 2001; Jiang et al.

2010; Jiang et al. 2011). Equations 58 and 62 (ion adsorption case) and Equations 59 and

192

62 (no adsorption case) were solved self-consistently for σ and ζ for a 1:1 electrolyte as a function of pH. Here the ionic strength, Is is given by

1 퐼 = ∑ 푧 2푐 . (64) 푆 2 𝑖 𝑖

Similarly, site binding reactions for divalent cations such as Ca2+ are given by

(Pierre et al. 1990; Dove et al. 2005; Sverjensky 2006; Datta et al. 2009)

푆𝑖푂퐻 + 퐶푎2+ + 푂퐻− ⟺ 푆𝑖푂퐶푎(푂퐻) + 퐻+ (65)

푆𝑖푂퐻 + 퐶푎2+ ⟺ 푆𝑖푂퐶푎+ + 퐻+ (66)

with corresponding equilibrium constants

+ 푆𝑖푂퐶푎(푂퐻) [퐻 ]퐵Γ −푝퐾퐷1 (67) 2+ − 푆𝑖푂퐻 = 10 (푀표푙/푙) [퐶푎 ]퐵[푂퐻 ]퐵Γ

+ 푆𝑖푂퐶푎2+ [퐻 ]퐵Γ = 10−푝퐾퐷2 (푀표푙/푙) (68) 2+ 퐹휙푆 푆𝑖푂퐻 [퐶푎 ]퐵푒푥푝 (− ⁄푅푇) Γ

Equation 65 represents a neutralization of a surface site by a Ca2+ and an OH- ion while

Equation 66 is an adsorption reaction of a Ca2+ ion to a negatively charged site that allows the possibility of local reversal of the surface charge density from negative to positive.

However, it is worth noting that as yet there is not a consensus for the dominant mechanism of adsorption of divalent ions (here Ca2+) (Pierre et al. 1990; Dove et al. 2005; Datta et al. 193

2009), with possible changes in ion adsorption behavior with solution pH (Dove et al.

2005; Datta et al. 2009). Consequently, both adsorption mechanisms were considered in this work.

Similarly, the total number density of surface sites (Γ) for a 2:1 electrolyte,

+ including the neutral cites Γ푆𝑖푂퐻 and Γ푆𝑖푂퐶푎(푂퐻) and the positive Γ푆𝑖푂퐶푎 is

+ − Γ = Γ푆𝑖푂퐻 + Γ푆𝑖푂퐶푎(푂퐻) + Γ푆𝑖푂퐶푎 + Γ푆𝑖푂 . (69)

The surface charge density arising from chemical reactions between the surface and a 2:1 electrolyte solution such as CaCl2 is

𝜎 = −퐹휙 퐹휙 푒Γ(10−푝퐾퐷2+푝퐻[퐶푎2+] 푒푥 푝( 푆⁄ )−10−푝퐾1+푝퐻푒푥푝( 푆⁄ )) 퐵 푅푇 푅푇 (70) . −푝퐾 +푝퐻 2+ −퐹휙푆 −푝퐾 −14 2+ −푝퐾 +푝퐻 퐹휙푆 1+10 퐷2 [퐶푎 ]퐵푒푥 푝( ⁄푅푇)+10 퐷1 [퐶푎 ]퐵+10 1 푒푥푝( ⁄푅푇)

Subsequently, without ion adsorption the surface charge density is given by

Equation 59. The Poisson Equation with a Boltzmann distribution for the space charge density was also solved for a 2:1 electrolyte to obtain an independent solution for the surface charge density as a function of ζ given by,

𝜎 = −√2퐼푆푅푇휀푒√exp (−2퐹휁/푅푇) + exp (퐹휁/푅푇) − 3. (71)

194

Equations 70 and 71 (ion adsorption case) and Equations 59 and 71 (no adsorption case) were solved self-consistently similar to the monovalent cation cases for the surface charge density and ζ for a 2:1 electrolyte as a function of pH (Conlisk 2013). The ion adsorption reactions and their corresponding equilibrium constants are summarized in Table 10.

Table 10: Summary of the adsorption reactions between a negatively charged surface and cations in the electrolyte solution for a 1:1 and a 2:1 electrolyte. The corresponding equilibrium constants for each reaction are listed in terms of the bulk species concentrations. Electrolyte Adsorption Reaction Equilibrium Constant + + + 푆𝑖푂퐾 1:1 푆𝑖푂퐻 + 퐾 ⇌ 푆𝑖푂퐾 + 퐻 [퐻 ]퐵Γ = 10−푝퐾푀 + 푆𝑖푂퐻 [퐾 ]퐵Γ

2+ − + 푆𝑖푂퐶푎(푂퐻) 2:1 푆𝑖푂퐻 + 퐶푎 + 푂퐻 [퐻 ]퐵Γ = 10−푝퐾퐷1 ⟺ 푆𝑖푂퐶푎(푂퐻) 2+ − 푆𝑖푂퐻 + [퐶푎 ]퐵[푂퐻 ]퐵Γ + 퐻

2:1 푆𝑖푂퐻 + 퐶푎2+ ⟺ 푆𝑖푂퐶푎+ + 푆𝑖푂퐶푎2+ [퐻 ]퐵Γ + 퐻+ 2+ 퐹휙푆 푆𝑖푂퐻 [퐶푎 ]퐵푒푥푝 (− ⁄푅푇) Γ = 10−푝퐾퐷2

Figure 59A shows the SBM values for 𝜎 for a 1:1 electrolyte without (black line) and with (colored lines) adsorption of cations. 푝퐾1 and 푝퐾푀 are the equilibrium constants for the deprotonation and adsorption reactions respectively. As expected, at pH values near the isoelectric point for silica (pH 2 – 4), 𝜎 was not affected by ion adsorption. As the pH increased neutralization of surface sites via cation adsorption reduced the magnitude of 𝜎,

+ with the extent of K adsorption determined by 푝퐾푀. For a given 푝퐾1 = 8.5, the surface charge density with adsorption deviates from the pure deprotonation case at 푝퐻 ≈ 6 for 195

푝퐾푀 = 3.5 and at 푝퐻 ≈ 7 for 푝퐾푀 = 5.5. For all cases reported in this Chapter 푝퐾1 = 8.5, consistent with previously reported values for silica (Behrens et al. 2001; Jiang et al. 2010;

Jiang et al. 2011). The surface charge density of PDMS was assumed to be the same as the surface charge density of glass (Kirby et al. 2004), as discussed in Chapter 2.

A B 0.000 0.00 -0.005 -0.01

)

2 2 -0.02 -0.010

C/m

( -0.03

(

pK = 8.5 pK = 3.5 pK = 8.5 pK = 2.5 pK = 6

 1 D1 D2 -0.015 1 M  pK = 8.5 pK = 2.5 pK = 6.5 pK1 = 8.5 pKM = 4.5 -0.04 1 D1 D2 pK = 8.5 pK = 5.5 pK = 8.5 pK = 2.5 pK = 7 -0.020 1 M 1 D1 D2 pK = 8.5 pK1 = 8.5 -0.05 1 -0.025 -0.06 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 pH pH

Figure 59: The surface charge density calculated from the SBM for a 1:1 and a 2:1 electrolyte solution (A) The predicted surface charge density for a 1:1 electrolyte using KCl as representative case. The case of only surface site deprotonation (black line) is compared to a site binding model that accounts for neutralization of surface sites via + adsorption of K ions (green, red, blue curves). For a given 푝퐾1, ion adsorption becomes significant at more basic pH as 푝퐾푀 increases. (B) The predicted surface charge density for a 2:1 electrolyte using CaCl2 as a representative case. Site binding reactions between Ca2+ either neutralize a surface site or reverse the polarity of an individual surface site. The black curve considered only surface site deprotonation while the pink, green, and 2+ blue curves consider both adsorption mechanisms of Ca . For a given 푝퐾1 = 8.5, 푝퐾퐷1 = 2.5, ion adsorption becomes significant at more basic pH as 푝퐾퐷2 increases. Note, equilibrium constants for most surface reactions are unknown and were therefore used as fit parameters to experimental data (Sverjensky 2006; Datta et al. 2009).

Figure 59B shows the SBM values of 𝜎 for a 2:1 electrolyte without (black line) and with adsorption (colored lines) of divalent cations. 푝퐾퐷1 and 푝퐾퐷2 are the equilibrium 196

constants of divalent cation adsorption that result in neutralization of a surface site

(Equation 65) or reversal of the polarity of an individual surface site (Equation 66) respectively. The surface charge density with adsorption deviates from the pure deprotonation reaction at 푝퐻 ≈ 6 for 푝퐾퐷1 = 8.5 and 푝퐾퐷2 = 6 and for 푝퐻 ≈ 7.5 for

푝퐾1 = 8.5 and 푝퐾퐷2 = 7. For all cases with ion adsorption shown in Figure 59B (colored lines) 푝퐾퐷1 = 2.5. The 푝퐾퐷2 values reported in Figure 59B did not yield a net positive charge density, as the total surface charge density will be either negative or positive for a fixed 푝퐾퐷2. The SBM, therefore, does not predict charge inversion for a fixed 푝퐾퐷2 (van der Heyden et al. 2006; Li et al. 2015).

5.4.2 Effect of Surface Charge Regulation on Nanochannel Conductance

The SBM was used to estimate 퐺푎 as a function of pH (Figure 60A). Since experimentally measured 푝퐾 values for most ion adsorption reactions are unknown, the

푝퐾 values were used as fit parameters to experimental conductance (Sverjensky 2006;

-8 2 -8 2 Datta et al. 2009). In Equation 39, 휇퐾+ =7.62 x 10 m /Vs and 휇퐶푎2+ =3.08x10 m /Vs

+ 2+ were used for the ionic mobility of K and Ca respectively (Conlisk 2013) and 퐺푏푢푙푘 was fit from the experimental data to account for finite measured conductance at the isoelectric point for silica (pH ≈ 2) (Behrens et al. 2001). Here, 𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 consistent with previous reports (Kirby et al. 2004). Additionally, a parametric numerical study incorporating 𝜎푃퐷푀푆 ≠ 𝜎푔푙푎푠푠 performed with COMSOL did not show significant influence of top-bottom wall surface charge heterogeneity on 퐺푎 (see below).

197

A B 20 KCl 5 1 mM KCl pK1=8.5 pKM = 4.5 0.33 mM CaCl2 CaCl 16 2 4 pK1=8.5 pKD1 = 2.5 pKD2 = 5.8 12 3

8 2

4 1

Gated Conductance (pS) Conductance Gated

Intrinsic Conductance (pS) Conductance Intrinsic 0 0 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 pH pH

Figure 60: Use of solution pH to modify surface charge density and the effect on intrinsic and gated nanochannel conductance. (A) Intrinsic nanochannel conductance as a function of pH for 1 mM KCl and 0.33 mM CaCl2 with equivalent ionic strength for both solutions. Since conductance is proportional to the surface charge density, Equation 39 was used to calculate the intrinsic conductance using the calculated surface charge density from the site binding model (SBM). Equilibrium constants used as fit parameters for the model are listed in the legend (Sverjensky 2006; Datta et al. 2009). The site binding model accurately described the conductance behavior of the nanochannel for 1 mM KCl and 0.33 mM CaCl2 at pH ≥ 6. Below pH 6 the experimental conductance of CaCl2 filled channel increased as pH decreased to 2. The site bonding model combined 2+ with Equation 39 for 퐺푎 considering only conductance of Ca failed to predict the observed increase in conductance for CaCl2 at pH = 2. However, a numerical model with + 4 ionic species that includes mobility of H captured the increase in 퐺푎 for CaCl2 as discussed below. The model with 4 ionic species yields incorrect theoretical prediction for the anomalous transport of KCl, which does not show an increase in conductance at highly acidic pH (pH = 2). (B) Gated conductance as a function of pH for 1 mM KCl and 0.33 mM CaCl2. A local maximum for the gate conductance was observed at pH = 8. The gated conductance increased between pH 4 and pH 2 for CaCl2 in agreement with observed trends for intrinsic nanochannel conductance as a function of pH. The dashed lines are intended as eye-guides only.

For a representative 1 mM KCl, the SBM determined 퐺푎 matched experimental 퐺푎

+ at all pH for 푝퐾푀 = 4.5, 퐺푎 indicating that adsorption of K affects the magnitude of 𝜎 at pH ≥ ~ 6. For 0.33 mM CaCl2, the SBM determined 퐺푎 matched experimental 퐺푎 at pH ≥

2+ 6 with 푝퐾퐷1 = 2.5 and 푝퐾퐷2 = 5.8, indicating that Ca adsorption has a significant effect 198

on the magnitude of 𝜎 above pH > ~6. Therefore, the site binding model confirms our hypothesis that ion adsorption regulates the surface charge density as a function of cation type.

The SBM with Equation 39 for the conductance, however, was unable to capture the predicted intrinsic nanochannel conductance at low pH (pH 2 and pH 4) for CaCl2 when only conductance of the Ca2+ ion was considered. The parametric numerical study

(discussed below) with ionic mobility of all 4 ionic species included (K+, Cl-, H+, and OH-

2+ - + - for KCl and Ca , Cl , H , and OH for CaCl2) correctly predicts the increase in 퐺푎 at pH 2

2+ + for Ca but fails to capture the constant 퐺푎 for K at pH ≤ ~6. The increase in the computed conductance from the 4 species numerical model from pH 4 to pH 2 is due to the higher concentration of H+ ions and the significantly higher mobility of H+ compared to K+ and

2+ + Ca (휇퐻+ ≈ 휇퐾+ (Duan et al. 2010)). Experimentally, increase in conductance due to H

+ ions was observed for CaCl2 but not for KCl. This anomalous result for K can also be inferred from the relative conductance of 10 mM HCl compared to 10 mM KCl reported by Duan et al. (Duan et al. 2010).

As now expected, gated conductance of the divalent cation (Figure 60B), Ca2+ as a

+ function of pH showed significantly different behavior than the monovalent K ion. 퐺푎 for

K+ between pH 8 – pH 10 was nearly independent of pH, with a similar trend for Ca2+ filled

+ nanochannels. However, 퐺푔 for K filled channels increased from pH 6 to pH 8, before sharply decreasing at pH 10. Interestingly, as pH was increased from pH 6 to pH 10, the

2+ + 퐶푎퐶푙2 퐾퐶푙 Ca followed similar trends as K with the 퐺푔 < 퐺푔 at pH 8, further suggesting that

Ca2+ limits modulation of the potential at the dielectric/fluid interface by the gate electrode.

199

2+ Ca filled nanochannels showed the highest measured 퐺푔 at pH 2, in-line with 퐺푎 trends,

+ which likely indicate increased concentration of H in the diffuse layer for CaCl2 at pH 2.

By contrast, 퐺푔 (and 퐺푎) remain nearly unchanged between pH 2 – pH 6 for KCl.

5.5.3 COMSOL Model

An additional model implementing 2-D Poisson-Nernst-Planck (PNP) model for ionic transport was performed using COMSOL Multiphysics. Models were performed for

1 mM KCl and for 0.33 mM CaCl2 as a function of pH. A schematic of the micro- and nanofluidic system modeled using COMSOL is shown in Figure 41.

Due to the ultra-low aspect ratios of the nanochannels (width >> height) considered here the system was modeled in two dimensions (Conlisk 2013). The size of the channel in the model was 16 nm deep x 2.5 mm long to match the dimensions of the fabricated device. The current was calculated according to

푚=4 푧 푤퐹 퐿 ℎ 퐼 = 𝑖 ∫ ∫ ∑ 푁⃗⃗⃗ 푑푦푑푥 퐿 푖 (72) 0 0 𝑖 . {3-73} where 퐼 is the current, 푧𝑖 is the valence of species 𝑖, 푤 is the channel width, 퐹 is Faraday’s constant, 퐿 is the channel length, ℎ is the channel height, and 푁𝑖 is the flux of the two charged species in the channel. The current measured in COMSOL was multiplied by a factor of 3 to account for multiple nanofluidic channels in the fabricated device.

200

푉푎 = 푉 푉푎 = 0푉 푐𝑖 = 푐푏푢푙푘 푐𝑖 = 푐푏푢푙푘

ℎ = 1 푛푚 ℎ 푒푠 = 2 0 푛푚 Inlet Outlet µ channel 퐿 = 2. 푚푚 µ channel 푦 푥 퐿 푒푠 = 00 푛푚

Figure 61: A schematic of the micro- nanofluidic system modeled with COMSOL multiphysics. Due to the low aspect ratio of the nanochannel (width >> height) the system can be modeled in two dimensions (Conlisk 2013). The inlet and outlet reservoirs, which correspond to the near-infinite reservoirs represented by the microchannels in the fabricated device, were 500 nm long and 250 nm tall. The size of the channel in the model was 16 nm deep x 2.5 mm long to match the dimensions of the fabricated device. The concentration in the inlet and outlet reservoirs was set to the bulk electrolyte concentration with all four species considered (that is K+, Cl-, OH-, and H+ for KCl and 2+ - - + Ca , Cl , OH , and H for CaCl2) for ionic transport. Inlet microchannel was set to 5V while the outlet microchannel was grounded to match the experimental case for 푉푎 = 5V. The location where the concentration and potential boundary conditions were imposed is indicated with the red arrow in the schematic. The surface charge density for each pH was imposed on all surfaces marked with the dark grey line (reservoirs and nanochannel) with the magnitude set according to the site binding model (SBM) as discussed below.

Here the total flux of ions (K+, Cl-, OH-, and H+ for KCl and Ca2+, Cl-, OH-, and H+ for CaCl2) was integrated across all cross sections along the nanochannel length and then divided by the total length of the channel to obtain the average flux. The flux was calculated using the Poisson equation for the potential (휙) according to

𝜌푒 ∇ ∙ (휀푅∇휙) = − . (74) 휀0

where 휀푅 is the relative permittivity of the electrolyte solution, 휀0 is the permittivity of free space, and 𝜌푒 is the space charge is given by 201

푚

𝜌푒 = 퐹 ∑ 푧𝑖푐𝑖. (75) 𝑖=1

The Poisson equation was combined with the steady-state Nernst-Planck equation for mass transport

휕푐 𝑖 = −∇ ∙ 푁⃗⃗⃗ = 0 (76) 휕푡 푖

where the flux of a species 𝑖 is given by

푁⃗⃗⃗ 푖 = −퐷𝑖∇푐𝑖 − 휇𝑖푧𝑖퐹푐𝑖∇휙 + 푐𝑖푢⃗ . (77)

Here, 퐷𝑖 is the coefficient of diffusion, ∇푐𝑖 is the concentration gradient, 휇𝑖 is the ionic mobility, 푧𝑖 is the valence, 푐𝑖 is the concentration of each species i in the nanochannel, and

퐹 is Faraday’s constant, ∇휙 is the electric field, and 푢⃗ is the velocity of the fluid flow. The ionic mobility is given by Einstein’s relation, 휇𝑖 = 퐷𝑖퐹/푅푇, where 푅 is the universal gas constant, and 푇 is the temperature.

The inlet microchannel reservoir was set to a potential of 5 V while the outlet microchannel potential was grounded (0 V) to match the 푉푎 = 5V case. Details of the nanochannels being operated under both 푉푎 = 3V and 푉푎 = 5V have been reported previously (Fuest et al. 2015) and the 5V case was chosen here as a representative example.

The continuity equation and the steady-state Navier-Stokes equation for an incompressible fluid were used for the velocity given by

2 −∇푝 + 휂∇ 푢⃗ − 𝜌푒∇휙 = 0 (78) 202

∇ ∙ 푢⃗ = 0 (79)

where 휂 is the fluid viscosity and ∇푝 is the pressure gradient.

The size of the reservoirs was selected to ensure that the potential was constant in the reservoirs and that effects of reservoir surface charge was minimal i.e., cation and anion concentration is equal to bulk concentration in the reservoir, except near the charged walls

(Jin et al. 2011). The walls were impermeable to flow with no velocity slip. The concentration in the reservoirs was set to the bulk electrolyte concentration, which was

1 mM for KCl and 0.33 mM CaCl2 respectively. All 4 ions were considered in the model

+ - - + 2+ - - + (that is K , Cl , OH , and H for KCl and Ca , Cl , OH , and H for CaCl2). The concentration of H+ in the reservoir was set to 10-pH and the concentration of OH- to 10-(14- pH). A constant surface charge boundary condition was used for the potential at each of the charged walls according to (Jin et al. 2011)

푑휙 𝜎 = −휀푒 푑푦 (80) 푑휙 = −휀 . 푒 푑푥

Here, 𝜎 is the surface charge density, 휀푒 is the permittivity of the electrolyte, and 휙 is the potential in the channel. The predicted conductance was obtained by dividing the calculated current by the applied axial potential (5 V).

203

The magnitude of the surface charge density was set using the site binding model.

Three different cases were numerically compared as a function of pH for a 1 mM KCl electrolyte to determine if there is any significant effect due to possible inhomogeneous surface charge density between the glass and PDMS charged walls. The values of the surface charge density input into COMSOL Multiphysics for each of the three cases for

1 mM KCl are listed in Table 11.

Table 11: Values of the surface charge density as a function of pH used in COMSOL simulations for 1 mM KCl. The values indicated by the “*” were calculated from the site binding model described above for (푝퐾1 = 8.5 and 푝퐾푀 = 4.5). The surface charge density predicted by the site binding model is given by 𝜎푆퐵. KCl Case 1: Homogenous Case 2: Case 3 : 흈푷푫푴푺 = 흈 풍 풔풔 Inhomogenous Inhomogenous = 흈푺푩푴 흈푷푫푴푺 = ퟎ. ퟐퟓ흈 풍 풔풔 흈푷푫푴푺 = ퟎ. ퟐퟓ흈 풍 풔풔 흈 풍 풔풔 = 흈푺푩푴 (흈푷푫푴푺 + 흈 풍 풔풔)/ퟐ = 흈푺푩푴 pH Suface Suface Suface Suface Suface Suface Charge Charge Charge Charge Charge Charge Density Density Density Density Density Density (C/m2) (C/m2) (C/m2) (C/m2) (C/m2) (C/m2) Silica* PDMS* Silica* PDMS Silica PDMS 2 0 0 0 0 0 0 4 0 0 0 0 0 0 6 -0.0004 -0.0004 -0.0004 -0.0001 -0.00064 -0.00016 7 -0.0016 -0.0016 -0.0016 -0.0004 -0.00256 -0.00064 8 -0.0028 -0.0028 -0.0028 -0.0007 -0.00448 -0.00112 10 -0.0032 -0.0032 -0.0032 -0.0008 -0.00512 -0.00128 * Values predicted from the site binding model (SBM) used for fits in Figure 60.

In Case 1 (𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠where the magnitude of 𝜎 for each pH was set using the site binding model, that is (𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 = 𝜎푆퐵푀). In Case 2 (𝜎푃퐷푀푆 = 0.2 𝜎푔푙푎푠푠)

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where the magnitude of 𝜎푆𝑖푙𝑖푐푎 for each pH was set using the site binding model (𝜎푔푙푎푠푠 =

𝜎푆퐵푀). In Case 3 (𝜎푃퐷푀푆 = 0.2 𝜎푔푙푎푠푠) and the average value of the surface charge density was set by the site binding model, that is, (𝜎푃퐷푀푆 + 𝜎푔푙푎푠푠)/2 = 𝜎푆퐵푀. For CaCl2, only the homogenous case was considered (𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 = 𝜎푆퐵푀) as discussed below. The values of the surface charge density are listed in Table 12.

Table 12: Values of the surface charge density as a function of pH used in COMSOL simulations for 0.33 mM CaCl2. Only the homogenous case was considered for CaCl2 where 𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 = 𝜎푆퐵 and 𝜎푆퐵 is the surface charge density predicted by the site binding model for (푝퐾1 = 8.5, 푝퐾퐷1 = 2.5, and 푝퐾퐷2 = 5.8).

CaCl2 Case 1: Homogenous 흈푷푫푴푺 = 흈 풍 풔풔 = 흈푺푩 pH Suface Suface Charge Charge Density Density (C/m2) (C/m2) Silica* PDMS* 2 0 0 4 0 0 6 -0.0002 -0.0002 7 -0.0014 -0.0014 8 -0.0027 -0.0027 10 -0.0031 -0.0031 * Values predicted from the site binding model used for fits in Figure 60.

The conductance for three 16 nm deep x 30 µm wide x 2.5 mm long nanochannels calculated using COMSOL Multiphysics is shown in Figure 62. The experimentally measured intrinsic conductance for KCl and CaCl2 is plotted against the predicted values from COMSOL. There are two important differences that should be noted between the

COMSOL model presented here and the analytical model presented above (fit in Figure

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60). First, the COMSOL model allows variation of the surface charge density on the top and bottom walls to determine if inhomogenous surface charge density arising from PDMS and glass significantly affect the measured conductance. The analytical model inherently assumes the surface charge density is the same on both walls (Kirby et al. 2004). Second, the COMSOL model was performed considering conductance contributions from 4 species

+ - - + 2+ - - + (that is K , Cl , OH , and H for KCl and Ca , Cl , OH , and H for CaCl2) while the

+ 2+ analytical model only considered K for KCl and Ca for CaCl2.

100

1 KCl Data CaCl2 Data

PDMS =Silica (KCl) PDMS =Silica (CaCl2)

PDMS =0.25 Silica

PDMS =0.25 Silica (Avg)

Intrinsic Conductance (pS) Conductance Intrinsic 0.1 2 3 4 5 6 7 8 9 10

Figure 62: The calculated conductance from COMSOL Multiphysics. The surface charge density used for each of the three cases for KCl are given in Table 11 while the surface charge density used for the CaCl2 case is given in Table 12. No difference was observed between the homogenous case (𝜎푃퐷푀푆 = 𝜎푆𝑖푙𝑖푐푎 = 𝜎푆퐵) and the case where the average surface charge density was preserved ((𝜎푃퐷푀푆 + 𝜎푆𝑖푙𝑖푐푎)/2 = 𝜎푆퐵).

First considering the COMSOL model for KCl, no difference was observed between the homogenous case 𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 = 𝜎푆퐵 and the case where the surface 206

charge density was assigned based on the average between the two walls ((𝜎푃퐷푀푆 +

𝜎푆𝑖푙𝑖푐푎)/2 = 𝜎푆퐵) despite four fold difference in the surface charge density between the top and bottom walls in the inhomogenous case (𝜎푃퐷푀푆 = 0.2 𝜎푔푙푎푠푠). The site binding model for the surface charge density, therefore, captures the average surface charge density of the nanochannel walls, even if there is a difference in magnitude between the silica and

PDMS surfaces. Since there was not a significant difference between the homogenous

(𝜎푃퐷푀푆 = 𝜎푔푙푎푠푠 = 𝜎푆퐵) and the inhomogenous case where (𝜎푃퐷푀푆 + 𝜎푔푙푎푠푠)/2 = 𝜎푆퐵 for KCl, only the homogenous surface charge density case was modeled for CaCl2.

Considering the homogenous cases, the COMSOL model predicts the overall trend in the conductance data for pH ≥ 6 for KCl, with an offset from the experimentally measured values. In the site binding model, the equilibrium constants were adjusted as in previous reports (Sverjensky 2006; Datta et al. 2009) to fit the experimental data. The fits for the equilibrium constants were set using the analytical model to relate the surface charge density to the conductance (Figure 60), which considered only conductance of K+. The same equilibrium constants fit to the analytical model were used to set the values of the surface charge density that were input into the four species numerical model solved using

COMSOL model. An offset between the numerical results that included all four species

(K+, Cl-, OH-, and H+) and the experimental data is therefore expected. A better fit could be obtained by adjusting the equilibrium constants for each reactions (Table 10) which physically corresponds to adjusting the proportion of negative, neutral, and in the case of

Ca2+, positively charged surface sites. Thus, exact numerical values of our calculated surface charge density will change; however, minor adjustments to estimate the unknown

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equilibrium constants to obtain a better fit between the numerical model and the experimental data will not alter the conclusion that cation adsorption affects the magnitude of the surface charge density as a function of pH.

The four species numerical model solved using COMSOL predicted the observed data trends for intrinsic nanochannel conductance of CaCl2 for all pH values with an offset between the experimentally measured and numerically calculated values as discussed for

KCl. The numerical model predicts that the conductance of KCl will increase at pH 4 and

+ further at pH 2 for both KCl and CaCl2 due to the higher concentration of H ions at acidic pH (10 mM for pH 2) and the significantly higher mobility of H+ compared to K+ and Ca2+

+ (휇퐻+ ≈ 휇퐾+(Duan et al. 2010)). Interestingly, increase in conductance due to H ions was not observed for KCl at pH 2. This anomalous result for K+ can also be inferred from the relative conductance of 10 mM HCl compared to 10 mM KCl reported by Duan et al.

[S16].

5.5.4 Site Binding Model with Electrode

Since the micro-nanochannel gated device has been considered analogous to solid- state electronic devices (Nam et al. 2009; Guan et al. 2011), the gate electrode/gate dielectric/electrolyte system was also modeled as two parallel plate capacitors in series, similar to procedures by Jiang and Stein (Schasfoort et al. 1999; Jiang et al. 2010; Jiang et al. 2011). A schematic of the system is shown in Figure 63.

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Electric Double Layer

( ) (ζ)

Cins CStern

+ -

- +

- + + - + + K K + + -

- K K+ - +

+ - +

+ +

+ -

+ + - - + + + - + +

Cl + - -

K+ -

+ + +

- - -

+ Stern Layer Stern - + + - + + Cl Layer Diffuse Cl

Gate Electrode Gate - + -

- + - Electrolyte Bulk + + + + +

PDMS Dielectric Layer PDMSDielectric -

+ + + +

K K -

+ + +

- + - - K + + - + + + - K -

+ + + +

- K -

+ + K+ Cation (Potassium Ion) + Water (H O) Molecule + - 2 Cl- Anion (Chloride Ion)

Figure 63: The micro-nanochannel gated device has been considered analogous to solid- state electronic devices, therefore, the gate electrode-dielectric-electrolyte interface was modeled in terms of capacitors in series, similar to a previous report by Jiang and Stein (Jiang et al. 2010).

One capacitor accounts for the charge stored across the gate dielectric and the second capacitor accounts for the charge stored by the Stern layer. The surface charge density can then be expressed as (Jiang et al. 2011)

𝜎 = 퐶푆푡푒 푛(휑푆 − 휁) − 퐶𝑖푛푠(푉푔 − 휑푆) (81)

2 where 퐶푆푡푒 푛 is the Stern layer capacitance (F/m ), 휁 is the zeta potential, and 퐶𝑖푛푠 is the capacitance of the dielectric layer (F/m2).

Accordingly, Equations 58, 59, and 70 were updated by substituting

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𝜎 + 퐶𝑖푛푠푉푔 + 퐶푆푡푒 푛휁 휑푆 = (82) 퐶𝑖푛푠 + 퐶푆푡푒 푛

And Equations 62 and 71 become

퐶𝑖푛푠 𝜎 = √8푅푇휀 퐼 푠𝑖푛ℎ(퐹휁⁄2푅푇) + 퐶 (휁 − 푉 ) (83) 퐶 푒 푆 𝑖푛푠 푔

And

퐶𝑖푛푠 𝜎 = ± √2퐼 푅푇휀 √exp (−2퐹휁/푅푇) + exp (퐹휁/푅푇) − 3 + 퐶 (휁 퐶 푆 푒 𝑖푛푠 (84) − 푉푔)

Please note that

퐶 𝜎 = 푖푛푠 √2퐼 푅푇휀 √exp (−2퐹휁/푅푇) + exp (퐹휁/푅푇) − 3 for 휁 > 0 and 퐶 푆 푒

퐶 𝜎 = − 푖푛푠 √2퐼 푅푇휀 √exp (−2퐹휁/푅푇) + exp (퐹휁/푅푇) − 3 for 휁 < 0. 퐶 푆 푒

The updated equations were then solved self-consistently for the chemical surface charge density and the zeta potential for both monovalent symmetric electrolytes and for a

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2:1 electrolyte. The value of the zeta potential was then used in Equations 62 for a 1:1 electrolyte and Equation 71 for a 2:1 electrolyte to determine 𝜎퐸퐷퐿, or the effective surface charge density at the slip plane, consistent with previously reported methods.

As discussed above, the surface charge density is proportional to the nanochannel conductance and therefore the ion transport through the nanochannels. The gate potential is an active, externally controllable method to regulate the surface charge density and thus the local potential at the dielectric-electrolyte interface enabling the field effect control over ion transport for applications such as ionic diodes and transistors (Karnik et al. 2005;

Nam et al. 2009; Guan et al. 2011). However, very little is known about the efficacy of the gate to modulate surface charge and therefore exert control over the nanofluidic transport in the presence of ion adsorption and subsequent cation type-driven surface charge regulation. The predicted effect of ion adsorption on the ability of the gate potential to modulate the surface charge as a function of gate voltage is shown for the monovalent case without and with monovalent ion adsorption and for the divalent case without and with divalent ion adsorption in Figure 64, for -3 V ≤ Vg ≤ +3 V. The same pK values used for the fits in Figure 60 were used (푝퐾1 = 8.5, 푝퐾푀 = 4.5, 푝퐾퐷1 = 2.5, 푝퐾퐷2 = 5.8).

The effect of the gate electrode can be quantified in terms of the change in surface charge density per volt applied to the electrode, or the slope of the σ v. 푉푔 plots shown in

Figure 64. The non-linearity σ v. 푉푔 plots is caused by surface buffering, consistent with results from Jiang et al. (Jiang et al. 2010). Surface buffering is a shift in the equilibrium deprotonation state of the surface and subsequently the point of zero charge. As the gate

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electrode changes the local effective surface charge state, the gate electrode tunes the point of zero charge to a higher pH compared to pH in the intrinsicModel case. with Gate Electrode

1:1 Without Adsorption 2:1 Without Adsorption

1:1 With Adsorption 2:1 With Adsorption

Figure 64: Predicted values of the surface charge at the dielectric-electrolyte interface from the gated nanochannel model with and without ion adsorption. The non-linearity in the surface charge density v. gate voltage plot is caused by surface buffering. Surface buffering is a shift in the equilibrium deprotonation state of the surface. The gate electrode is tuning the point of zero charge to a higher pH compared to pH in the ungated case, consistent with results from Jiang et al.(Jiang et al. 2010) A clear maximum change in the slope of the surface charged density v. gate voltage plot was observed for the pH 2 and 4 case. The case of surface site deprotonation with the possibility of monovalent ion adsorption. Surface buffering is not observed for pH 2 and pH 4.

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A clear maximum of the slope was observed for pH 2 across all cases Figure 64, consistent with results from Jiang et al. for monovalent electrolytes (Jiang et al. 2010). The overall effect of ion adsorption was to reduce the magnitude of the surface charge density in the 푉푔 = 0 V case and to reduce the magnitude of the slope. For example, for the divalent case without adsorption at pH 10 the gate electrode tunes the surface charge density from

2 2 ~-0.065 C/m to ~-0.042 C/m between 푉푔 = -3 V and 푉푔 =3 V. In contrast when ion adsorption was considered for the 2:1 case at pH = 10, the gate electrode tunes the surface

2 2 charge density from ~-0.004 C/m to ~-0.002 C/m between 푉푔 = -3 V and 푉푔 =3 V.

Despite clear differences between the case of pure deprotonation and the case with ion adsorption, the model does not fully predict experimental trends for gated conductance.

The main limitation of the gated model shown here is that the model does not account for changes in the bulk pH as a function of gate voltage. Experimental measurements in a gated nanofluidic device demonstrated that the gate electrode alters the deprotonation state of the nanochannel by adsorbing or releasing protons in response to the gate potential (Veenhuis et al. 2009). The bulk proton concentration and thus the solution pH changes as a function of gate voltage

5.6 Summary and Conclusions

This chapter presented for the first time surface charge regulation as a function of cation type for gated nanochannels, or channels where local change in the surface potential at the dielectric/fluid interface are induced by an embedded gate electrode. A broad parametric study with 16 nm deep nanochannels for a large range of evaluated electrolyte concentrations (10-7-10-1 M), widest reported pH range (pH 2-10), and electrolyte mixtures,

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demonstrated that systematic changes in local electrostatic surface state are impacted by ion adsorption, and the resulting nanoscale ion transport is strongly affected by cation type in a gated nanofluidic device. Several results were in agreement with previous reports, yet several unexpected observations were noted along with critical implications for nanofluidic transport. The intrinsic nanochannel conductance was measured as a function of cation type for pH 7 KCl, NaCl, CaCl2, and MgCl2. In agreement with previous reports, no significant difference was observed for the intrinsic nanochannel conductance of KCl compared to

NaCl inspite of 38% difference in ionic mobility of K+ and Na+. Conductance decreased for MgCl2 and CaCl2 at concentrations typically associated with surface charge governed transport for monovalent electrolytes (at 1 mM and 3.33 mM respectively), suggesting a decrease in the total surface charge density due to divalent cation adsorption to the negatively charged walls. Consequently, addition of divalent ions can be used to regulate the effective surface charge density and thereby directly affect the gated nanochannel conductance.

A modified and improved site binding model for the surface charge density confirmed that ion adsorption has a significant impact on the surface charge density at pH > 6 for KCl and CaCl2. Data from KCl and CaCl2 electrolyte mixtures clearly indicated that Ca2+ in the mixture is the dominating ion as determined by a decrease in surface charge density when CaCl2 was added (between 0% CaCl2 composition and 25% CaCl2 composition) and a surface charge density that was independent of KCl concentration for

% CaCl2 > 25%. Ion adsorption between the charged walls and the cations in the electrolyte

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regulate the surface charge density thus limiting the ability of the gate electrode to alter the net surface charge density and consequently modulate nanochannel conductance.

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Chapter 6: Summary, Conclusions, and Contributions

This dissertation has presented results on active electrokinetic transport control in a gated nanofluidic device. This chapter gives a brief summary of the results and conclusions presented in Chapters 3, 4, and 5. Following the summary and conclusions, the contributions from this dissertation are discussed.

6.1 Summary and Conclusions

In this dissertation an alternate fabrication sequence (Pinti et al. 2013) was developed for gated nanofluidic devices that relies on UV lithography, wet etching, and oxygen plasma bonding techniques (Fuest et al. 2015). In contrast to all previous devices with a similar device layout, the fabrication sequence developed here for ultra-low aspect ratio (ULAR) nanochannels is significantly simpler and therefore enables much broader accessibility to the microfluidics and nanofluidics community to develop the next generation of applications with gated micro-nanochannel devices. The gated nanofluidic device was in a planar configuration with the gate electrodes embedded in the top wall or

‘roof’ of the nanochannels. A planar design more easily allows incorporation of multiple electrodes at desired spacing along the nanochannel length. Moreover, the choice of implementing a ULAR nanochannels allowed use of 1-D theory as the nanochannel width and length were orders of magnitude larger than the nanochannel depth.

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The device consisted of three layers. The bottom layer had the micro- and nanochannel network, the intermediate layer was a PDMS dielectric layer that isolated the gate electrodes from the fluid in the channels, and the top layer or cover had the patterned array of electrodes and forms the 4th wall or roof of the nanochannels. The electrodes had an engineered size and spacing along the length of the nanochannel allowing investigation of the effect of the gate electrode location on the modulation of electrokinetic transport caused by the embedded electrode, an effect that had received limited attention in previous reports.

In this dissertation results are reported with only one electrode active at a given time. However, an independent potential can be applied to each of the embedded gate electrodes further opening up the possibility of using multiple electrodes at engineered locations to systematically alter the surface charge distribution along the channel length as well as the possibility of using multiple electrodes with time lagged signals, adding to versatility of the design.

As with previously reported gated nanofluidic device designs (Section 2.4), general fabrication techniques detailed in Section 2.3 were implemented or adapted to create a multi-step fabrication procedure for the gated nanofluidic device, where the use of existing techniques were primarily determined by the choice of substrate materials

(bottom and top layers). UV lithography was implemented with a modified spin recipe to allow fabrication of nanochannels on a non-planar substrate that already contained etched microfluidic channels. A second glass substrate was used for the electrode cover. A spun on PDMS layer isolated the electrodes from the fluid in the nanochannel and provided a

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surface to bond the electrode cover to the substrate with the channel network via oxygen plasma bonding. Successful device fabrication, with nearly all results in this dissertation reported for 16 nm deep x 30 µm wide x 5 mm long (or 2 mm long), was confirmed through optical micrograph images, SEM images, AFM measurements, fluorescence images, and electrical characterization of fabricated devices. Measured intrinsic nanochannel conductance for KCl was compared to a Poisson-Nernst-Planck coupled equation model for ion transport in nanofluidic channels to further verify device functionality.

Ionic transport through the nanofluidic devices was quantified through a current measurement. Two Keithley function generators in DC mode were used to supply independent axial and gate potentials. Axial and gate potentials were applied with respect to the same ground for a common reference. Axial potentials used in this dissertation generally ranged from +5 V to – 5 V with gate potentials ranging from +3 V to – 3 V. All experiments were conducted in an Earth grounded Faraday cage to minimize external electrical noise. A Keithley 6485 picoammeter was used to measure the current through the nanochannels. The intrinsic nanochannel conductance, 퐺푎 = 퐼/푉푎, was first measured with the gate electrode floating (푉푔 = 0 V). Ionic transport was governed by the surface charge at low concentration (푐푏푢푙푘 < ~1 mM KCl) while bulk or geometry governed transport behavior was observed at high concentrations (푐푏푢푙푘 > ~1 mM KCl). The transition between the two transport regimes occurred at the critical concentration (푐푡 ≈

1 mM KCl), in agreement with previously reported results for intrinsic nanochannel conductance.

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The effect of the gate electrode on ionic transport was quantified by monitoring the change in measured current in response to the gate potential. A fixed axial potential difference was applied between the two microchannel reservoirs and the gate potential was swept from 0 V to 3 V and from 0 V to -3 V. The measured current increased for an applied positive gate potential and decreased for an applied negative gate potential with respect to the current in the un-gated case (푉푔 = 0 V). The current modulation, or the ability to alter the current via the gate electrode, was demonstrated in the surface charge governed transport regime with a maximum effect of the gate electrode at the transition concentration between the surface charge governed and bulk transport regimes. At concentration above the transition concentration the effect of the gate electrode decreased as 푐푏푢푙푘 approached 100 mM. The electric double layer decreases as the bulk electrolyte concentration increases, where the thickness of the electric double layer has an inverse square root dependence on ionic strength. In the case of thin electric double layers, ionic transport in the nanochannel approaches the microfluidic case where the gate electrode controls only interfacial properties near the electrode.

In previous reports, the gate electrode has been used to modify the concentration of species in the channel to maintain system electroneutrality and thus alters the total available charge carriers (Karnik et al. 2005). In this dissertation, it was experimentally confirmed for the first time that the gate electrode additionally alters the electric field in the nanochannel by modifying the potential in the nanochannel near the gate electrode/dielectric/solution interface. The change in electric field was experimentally verified by systematically altering the magnitude and polarity of the applied axial and

219

gate potentials as well as the relative location of the gate electrode along the nanochannel length. For bulk KCl concentrations corresponding to the surface charge governed transport regime for intrinsic nanochannel conductance, the gate electrode was used to switch off the measured current for a fixed axial potential, where repeatable on/off switching was demonstrated. Switching behavior was thus caused by a change in the electric field within the nanochannel induced by the gate electrode, consistent with previous modeling reports (Liu et al. 2010; Ai et al. 2011).

Nearly all reports on gated nanofluidic devices to date have used monovalent symmetric electrolytes with the majority of experimental and modeling studies focusing on transport of KCl (Karnik et al. 2005; Fan et al. 2008; Kalman et al. 2009; Liu et al.

2010; Liu et al. 2010; Jin et al. 2011; Shin et al. 2012; Singh et al. 2012; Pardon et al.

2013; Guan et al. 2014; Lee et al. 2015), with limited evaluation of HCl (Fan et al. 2008;

Joshi et al. 2010) and buffer solutions (Jiang et al. 2011). The effect of local variation of surface charge in nanoscale conduits on transport of multivalent electrolytes and electrolyte mixtures, which form the basis for most actual biological systems or practical applications, has not yet been reported. In this dissertation, transport of two monovalent (KCl, NaCl) and two divalent electrolytes (MgCl2, CaCl2) was investigated to determine the effect of local variation of electrostatic properties in gated nanofluidic channels on ionic transport as a function of cation type. Nanochannels with a negative surface charge density such as the devices here are cation selective under conditions of interacting electric double layers, therefore, the cation was varied across electrolyte solutions for a fixed anion (chloride).

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The concentration dependent intrinsic nanochannel conductance (un-gated or floating gate case) was first investigated to not only provide validation against existing reports but also to demonstrate cation dependent surface charge regulation for two monovalent (NaCl and KCl) and two divalent (CaCl2 and MgCl2) electrolyte solutions. The intrinsic nanochannel conductance was measured as a function of cation type for pH 7 KCl,

NaCl, CaCl2, and MgCl2. In agreement with previous anomalous transport reports, no significant difference was observed for the intrinsic nanochannel conductance of KCl compared to NaCl despite 38% difference in ionic mobility of K+ and Na+. Conductance decreased for MgCl2 and CaCl2 at concentrations typically associated with surface charge governed transport for monovalent electrolytes (at 1 mM and 3.33 mM respectively), suggesting a decrease in the total surface charge density due to divalent cation adsorption to the negatively charged walls. An improved site binding model accounting for changes in pH confirmed that ion adsorption has a significant impact on the surface charge density at pH > 6 for KCl and at all pH values for CaCl2. Ion adsorption between the charged walls and the cations in the electrolyte regulate the surface charge density thus limiting the ability of the gate electrode to alter the surface charge density to concentrations near the transition concentration.

Comparison of MgCl2 and CaCl2 data indicated that the surface charge regulation is a function of cation type for divalent ions. Electrolyte mixtures of KCl and CaCl2 were studied to determine the effect of cation dependent surface charge regulation on the transport of electrolyte mixtures. Monovalent KCl and divalent CaCl2 were selected for further comparison due to the broader set of knowledge existing for these two electrolytes

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and the vital role of calcium ions in many biological transport systems with nanoscale critical length scales (Xia 1988; Li 2011; Jensen 2012). Data from KCl and CaCl2 electrolyte mixtures clearly indicated an affinity of Ca2+ for the wall, determined by a decrease in surface charge density when CaCl2 was added (between 0% CaCl2 composition and 25% CaCl2 composition) and a surface charge density that was independent of KCl concentration for % CaCl2 > 25%. At the transition electrolyte composition between a state where CaCl2 is significantly adsorbed to the surface (% CaCl2 > 25%) and no adsorption was observed (0% CaCl2) the gate electrode tunes the surface affinity for CaCl2 demonstrated by the gated conductance behavior.

6.2 Contributions

1. Development of a fabrication sequence for gated nanofluidic devices that relies on

photolithography, wet etching, and oxygen plasma bonding techniques to yield

sealed channels with a sub-20 nm critical length scale.

2. Experimentally verified that the gate electrode alters the electric field in the

nanofluidic channel. The gate potential is not limited to modulation of the surface

potential at the dielectric-electrolyte interface, but rather affects the potential in

the nanochannel near the gate electrode.

3. Demonstrated tunable control of the magnitude of the current using an embedded

surface electrode, where repeatable on/off switching was shown in the surface

charge governed regime.

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4. Performed a systematic study of two monovalent and two divalent electrolyte

showing a decrease in the total surface charge density due to divalent cation

adsorption to the negatively charged walls as a function of cation type.

5. Developed an improved site binding model for the surface charge density that

accounts for pH and gate potential that confirmed ion adsorption has a significant

impact on the surface charge density at pH > 6 for KCl and at all pH values for

CaCl2.

6. Determined ion adsorption between the charged walls and the cations in the

electrolyte regulate the surface charge density thus limiting the ability of the gate

electrode to alter the surface charge density to concentrations near the transition

concentration.

7. Demonstrated affinity of Ca2+ for the surface in electrolyte mixtures that was

independent of K+ concentration with an electrolyte composition above

25% CaCl2 and 75% KCl. The gate electrode had the greatest impact on ionic

transport near the transition composition where adsorption of Ca2+ became

significant.

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Chapter 7: Future Work

7.1 Pumping against a concentration gradient

Biological ion pumps use a ‘dual gated’ nanofluidic pore to pump electrolyte solutions against an electrochemical gradient. The dual gate approach prevents back flow of ions across the membrane due to the electrochemical gradient, thus preserving and even allowing increase of the concentration difference across the membrane (Gouaux et al.

2005). The multiple surface electrodes in the nanofluidic device can be utilized to mimic this pumping behavior, with applications in sample concentration and separations.

In this dissertation it was experimentally demonstrated that the gate electrode modifies the electric field in the nanochannel. The gate electrode can be thought of as a cathode with a negative potential applied and as an anode with a positive potential applied.

If we imagine a plug of fluid, the first electrode is set to a negative potential, attracting cations to accumulate near the electrode surface. Electrode 1 is then switched to a positive potential, repelling the cations. In order for the ions to pump against the electrochemical gradient, a second electrode located a little further down the channel must then have a higher net negative potential than the wall, so that the fluid plug continues down the channel rather than returning to the “low concentration” reservoir. An initial phase lag in the experiments could be 180°, but further experimentation and refinement of the electrode

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spacing is required to achieve pumping. The potential difference between the two microchannel reservoirs is a logarithmic function of the concentration gradient between the reservoirs. The potential difference between the reservoirs can be monitored to determine if pumping has been achieved. Potential measurements should be taken with the gate electrodes inactive so that possible electric fields generated by the gate electrodes do not affect the potential measurement.

7.2 Ion transport selectivity based on valence of the cation

Ion selectivity has been achieved by the sign of the valence (counter-ion vs. co-ion)

(Nishizawa et al. 1995) but, till date, selectivity of ions of the same polarity (i.e. Na+ compared to Ca2+) has not been demonstrated in an artificial system, even though biological ion channels perform such selective transport routinely. Until this point, experiments have been targeted towards flow control in gated nanofluidic device to demonstrate current modulation or gating and preferential direction of transport (i.e., dioding). Selectivity of ions of the same valence is the third and most elusive functionality of an ion channel.

Monte Carlo simulations show that modulation of the surface charge of a nanoscale channel is the key parameter influencing preferential transport of Ca2+ over Na+ (Boda et al. 2006). By increasing the magnitude of negative surface charge on the protein bilayer,

2+ Ca affinity was increased by up to an order of magnitude (Boda et al. 2006). In this dissertation, data from electrolyte mixtures indicated an affinity of Ca2+ over K+ for the charged wall, in agreement with the trends in the simulations performed by Boda et al.

Therefore, the first few layers of ions near the charged surface should be comprised by a predominant concentration of Ca2+ ions. By shrinking the size of the nanochannel from

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16 nm to ~1 to 2 nm the affinity of Ca2+ for wall may allow selective transport of Ca2+ over K+.

Since the gate can be used to modulate the surface potential in the channel, and by

Gauss’ law produce an effective surface charge (Jin et al. 2011), it is possible that if the dominating mechanism for selectivity is electrostatic in nature as indicated by Boda et al., that the gate electrode can be used to increase the surface charge density of the wall and therefore the affinity for Ca2+ and the channel selectivity. To test for ion selectivity two separate fluorescence based tests could be performed. First one side of the nanofluidic devices would be filled with an electrolyte solution with equal concentrations of NaCl and

CaCl2. The other microchannel, or receiving channel, will be filled with Fluo-4 dye dissolved in DI water, a fluorescent dye whose intensity increases upon binding with calcium ions. The change in fluorescence will be monitored with time to determine the concentration of calcium introduced into the receiving channel. The second test will follow the same format, only with CoroNa, a sodium sensitive dye, in the receiving channel.

Likely fabrication procedures and overall device design will need to be altered to achieve ~1-2 nm channels with an embedded gate electrode. One possibility is to use focused ion beam milling to create a pore in a membrane stack comprised of a Si handle wafer, insulating Si3N4 layer, Cr adhesion layer, and Au gate electrode. The Si handle wafer would be etched with KOH to limit the FIB milling to the Si3N4 / Cr / Au layers. The gate electrode could then be insulated and the pore shrunk down to ~1-2 nm using atomic layer deposition.

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7.3 PDMS v. Silica as the Gate Dielectric Material

In this dissertation, the magnitude of the PDMS surface charge was approximated to be the same as glass under all experimental conditions, an approximation which is often used in the literature (Kirby et al. 2004). No detailed experimental data was found despite an extensive literature search about the mechanism by which PDMS obtains a net surface charge density and how the surface charge of PDMS changes in response to a gate potential. A direct comparison between gating experiments utilizing the same device geometry and design parameters but simply substituting SiO2 for PDMS would gain fundamental insight into the charging mechanism of PDMS compared to glass. The main limitation is that fabrication procedures for glass to glass bonding must be developed for the gated nanofluidic devices. Two main challenges arise in the fabrication protocols.

Fusion bonding techniques would need to be developed for glass to glass bonding of the channel substrate to the electrode over with the SiO2 gate dielectric.

Fusion bonding depends on the cleanliness and planarity of the two substrates.

Challenges will arise from non-planarity of the top cover caused by the presence of the gate electrode which could lead to unbonded/leaking regions in the device. Additionally, the device reported in this dissertation uses borosilicate substrates while the gate dielectric will be silica. Differences in the thermal expansion coefficients between the two glass substrates and the dielectric layer lead to device cracking during fusion bonding. One option is using fused silica substrates for the micro- and nanofluidic networks and the top cover substrates. The gate dielectric material can then be deposited on both substrates so that the material properties are as closely matched as possible at the

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interface. A second option would be to use a sacrificial etch approach similar to Karnik et al. and Fan et al., thereby eliminating the bonding step. However, channels fabricated using sacrificial etch techniques are prone to collapse due to capillary forces during extraction of the etchant thus limiting the minimum critical dimension of the nanochannels.

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Appendix A: Nomenclature and Abbreviations

246

A.1 Alphabetical List of Abbreviations

Abbreviation Full Name 2-D Two dimensional AFM Atomic force microscope Al Aluminum Al2O3 Aluminum Oxide ALD Atomic layer deposition Ar+ Argon Ion ARC Anti-reflective coating Au Gold AZO Aluminum Doped Zinc Oxide BCl3 Boron Chloride BOE Buffered oxide etchant C Celsius Ca2+ Calcium ion CaCl2 Calcium Chloride (aqueous) CF3 Trifluoromethyl CF4 Tetrafluoromethane CH3 Methyl Group CHF3 Fluoroform Cl- Chloride Ion Cr Chromium CVD Chemical vapor deposition DC Direct current DI deionized DNA Deoxyribonucleic acid DRIE Deep reactive ion etching EC Electrolyte Composition EDL Electric double layer EOF Electroosmotic flow FET Field effect transistor FIB Focused Ion Beam Flow-FET Fluidic field effect transistor or gated fluidic device Ga+ Gallium Ion GLC Gate leakage current + H3O Hydronium HCl Hydrochloric acid HF Hydrofluoric Acid 247

IL Interferometric lithography IPA isopropyl alcohol ITO Indium Tin Oxide I-V Current - voltage K+ Potassium Ion KCl Potassium Chloride (aqueous) KOH Potassium Hydroxide LPCVD Low pressure chemical vapor deposition MD Molecular dynamics (simulations) MgCl2 Magnesium Chloride (aqueous) NaCl Sodium Chloride (aqueous) NH4F Ammonium Fluoride NMP N-Methylpyrrolidone O2 Oxygen gas OH- Hydroxide PC polycarbonate PDMS Polydimethyl siloxane PECVD Plasma enhanced chemical vapor deposition PET Polyethylene terephthalate pH Power of Hydrogen PIV particle image velocimetry PMMA Polymethylmethacrylate PNP Poisson-Nernst-Planck Pt Platinum RF Radio Frequency RIE Reactive Ion Etching RMS Root mean square S2 Oxide Growth SCG Surface charge governed SEM Scanning electron microscope Si Silicon SiO2 Silicon Dioxide Si3N4 Silicon Nitride SPR Surface Plasmon Resonance TiCl4 Titanium Tetrachloride TiN Titanium Nitride TiO2 Titanium Dioxide TiOH Titanium Hydroxide? TEM Transmission electron microscope UV Ultraviolet

248

A.2 Nomenclature

Symbol Full Name 푎 Diameter of the channel 퐴 Cross section area of the nanochannel 퐴푒 Area of the nanochannel roof covered by the gate electrode 퐶 Capacitance (of a parallel plate capacitor) 퐶퐸퐷퐿 Capacitance of electric double layer 퐶𝑖푛푠 Capacitance per unit area of the gate dielectric 퐶푆푡푒 푛 Capacitance per unit area of the Stern layer 퐶푤푎푙푙 Capacitance of nanochannel wall 푐푎 transition concentration where ion-associations between cations and the surface reduce the effective surface charge 푐푎푛 Concentration of anions in the bulk 푐푏푢푙푘 Bulk or prepared electrolyte concentration 푐푐푎푡 Concentration of cations in the bulk 100 Concentration of K+ ions in the 푐퐾+ nanochannel at an electrolyte composition of 100% KCl (Ch. 5) 푐𝑖 Concentration of species 𝑖 in the nanochannel 푏푢푙푘 푐𝑖 Bulk concentration of species 𝑖 푔푎푡푒푑 Concentration in the nanochannel of 푐𝑖 species 𝑖, with the gate electrode active 푛푎푛표 푐𝑖 Concentration in the nanochannel of species 𝑖 푢푛푔푎푡푒푑 Concentration in the nanochannel of 푐𝑖 species 𝑖, with the gate electrode floating ct Transition concentration between surface charge governed and bulk transport behavior in nanochannels 2+ [퐶푎 ]퐵 The bulk concentration of calcium ions [퐶푙−] Concentration of chloride ions in the nanochannel 퐷𝑖 Diffusion coefficient of species 𝑖 푒 Elementary unit of charge

249

퐸⃗ Electric field in the nanochannel 퐸푒푓푓 Effective Young’s modulus 퐸푥 Axial electric field 퐹 Faraday’s Constant 퐺푎 Intrinsic (axial) nanochannel conductance (퐼/푉푎) 퐺푏푢푙푘 Bulk conductance Intrinsic conductance of a mixture with an 퐺 퐸퐶 electrolyte composition (EC) 퐺푔 Gated nanochannel conductance Conductance in the surface charge 퐺푆퐶퐺 governed regime

퐺100% 퐾퐶푙 Intrinsic conductance of the 100% KCl case (Ch. 5) ℎ Nanochannel height ℎ푚𝑖푛 Minimum channel height + [퐻 ]퐵 Bulk proton concentration + [퐻 ]푆 The surface proton concentration 퐼 Current 퐼퐶푙− Ionic current due to chloride 퐼퐾+ Ionic current due to potassium 퐼푔푎푡푒푑 Measured current in the gated case 퐼푙푒푎푘푎푔푒 Gate leakage current 퐼푆 Ionic Strength 퐼푢푛푔푎푡푒푑 Measured current in the ungated case [퐾+] Concentration of potassium ions in the nanochannel + [퐾 ]퐵 Bulk potassium ion concentration 퐿 Length of the nanochannel L1 Distance from the inlet microchannel to the gate electrode m Total number of species i n Index of refraction of a material 푁푐ℎ Number of nanofluidic channels 푁𝑖 Molar flux of a species i − [푂퐻 ]퐵 The bulk concentration of hydroxide ions 푝 Pressure 푝퐾1 Equilibrium constant for deprotonation of SiOH 푝퐾푀 Equilibrium constant for monovalent ion adsorption 250

푝퐾퐷1 Equilibrium constant for divalent ion adsorption (neutralization of surface site) 푝퐾퐷2 Equilibrium constant for divalent ion adsorption (resulting in positive surface site) 푝푟표퐶푎2+ Proportion of Ca2+ in an electrolyte mixture 푝푟표퐾+ Proportion of K+ in an electrolyte mixture R Universal gas constant Rct Charge transfer resistance s seconds 푡 time 푡푑 Thickness of the dielectric T Temperature of the electrolyte solution 푄 Charge (stored by the capacitor) 푢⃗ Fluid velocity 푉 Voltage (generally) 푉푎 Axial potential 푉푑 Axial potential (Horiuchi et al.) 푉푔 Gate potential 푤 Nanochannel width 푧푎푛 Valence of an anion (general) 푧푐푎푡 Valence of a cation (general) 푧𝑖 Valence of species 𝑖 Γ Total number density of surface sites α Empirical parameter that accounts for potential change from the gated dielectric- electrolyte interface through the depth of the nanochannel Γ+ Number density of positively charged surface sites Γ− Number density of negatively charged surface sites − Γ푆𝑖푂 Number density of SiO- surface sites Γ푆𝑖푂퐶푎(푂퐻) Number density of SiOCa(OH) surface sites 2+ 2+ Γ푆𝑖푂퐶푎 Number density of SiOCa surface sites Γ푆𝑖푂퐻 Number density of SiOH surface sites Γ푆𝑖푂퐾 Number density of SiOK surface sites 휀0 Permittivity of free space 휀푒 Electrical permittivity of the medium 휀푅 Relative permittivity 251

휁 Zeta potential (potential at the slip plane) 휂 Fluid viscosity κ Inverse Debye length 휆 Wavelength of light 휆퐷 Debye length 휇 Ionic mobility (general) 휇+ Ionic mobility of a cation (general) 휇퐶푙− Ionic mobility of chloride 휇𝑖 Ionic mobility of a species 𝑖 휇퐾+ Ionic mobility of potassium 𝜌푒 Space charge density 𝜎 Surface charge density 휙 Potential distribution in the nanochannel 휙퐷푂푁 Donnan Potential 휙푆 Surface potential 휔 Maximum spin speed

252

A.3 Units

Abbreviated Unit Full Name cm Centimeter GΩ Giga ohms kΩ Kilohms KeV Kiloelectron Volt KPa Kilopascal KV Kilovolt M Molar MeV Megaelectron Volt mm Milimeter mM Millimolar mV Millivolt MΩ Mega Ohm’s nA Nanoamperes nL Nanolitres nm Nanometers pA Picoamperes S Siemens V Volts µm Micometers μM Micromolar

253

Appendix B: Device Characterization

254

B.1 SEM images of the etched channel network

A schematic representation of the channel network is shown in Figure 65. Colored coded locations are labeled on the schematic corresponding to the reservoir, the bend in the microchannel, the microchannel, and the micro- and nanochannel interface. These labels are used to identify the locations of the images taken from a fabricated channel network. Corresponding labels are placed in the upper left corner of each SEM image to indicate the location where the image was taken.

A B

D C

Figure 65. A schematic representation of the channel network. The color coded and labeled locations are used to identify the location where SEM and micrograph images were taken in the following figures.

255

10 µm

Figure 66. An SEM image of the fluidic reservoir etched into the borosilicate substrate. The location of the reservoir is marked by box A in Figure 65.

10 µm

Figure 67. An SEM image of the interface between the fluidic reservoir and the microfluidic channel. The location of the reservoir is marked by box A in Figure 65.

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100 µm

Figure 68. An SEM image of the bend in the microchannel. The location of the microchannel bend is denoted by box B in the schematic shown in Figure 65.

20 µm

Figure 69. An SEM image of the bend in the microchannel. The location of the microchannel bend is denoted by box B in the schematic shown in Figure 65.

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Nanochannels

20 µm Microchannel

Figure 70. An SEM image of the micro- and nanochannel interface showing two 227 nm deep nanochannels. The small etched region on the bottom of the microchannel denoted by the two light blue arrows occurs when the nanochannel is slightly misaligned. The photoresist in the microchannel is then exposed and the bottom of the microchannel is etched to the same depth of the nanochannel. Despite the slight misalignment, this channel slide had nanochannels that connected the right and left microchannels.

20 µm

Figure 71. SEM image of a microfluidic channel etched for 8 minutes in 4:1 DI water to 49% HF.

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B.2 Microchannel Etch Plot

The depth of microfluidic channels etched in 4:1 DI water to 49% HF as a function of the exposure time to the etchant is shown in Figure 72. Note with the exception of the 8 minute etch time used for all devices in this dissertation, only one sample was prepared for each etch time. The data shown here is intended as a guide to approximate etch time for a desired microchannel depth.

9 8 7 ) 6

 ( 5 4 3

Depth Depth 2 1 0 0 1 2 3 4 5 6 7 8 9 Etch Time (min)

Figure 72. Micochannel etch plot. The depth of the microchannel was measured after exposure to 4:1 DI Water to 49% HF with a profilometer.

B.3 Channel Fabrication Challenges

After the lithography step, the pattern defined in the photoresist is transferred to the Au/Cr etch mask by wet etching with potassium iodide and HCl based solutions for

Au and Cr respectively. The Au/Cr layers were etched until no visible remnants remain and then exposed in 10:1 buffered oxide etchant to etch the nanochannels. Patches of 259

unetched SiO2 were visible from SEM images of the etched channel. The chemical composition of the visible patches was confirmed with EDS. A 100% overetch, or twice the time needed to visibly remove the mask, was used. After implementing the overetch, patches were no longer observed. The metal mask was not removed before imaging

(Figure 73). Two insets show zoomed in images from the areas of the channel indicated by the respective red boxes. The upper inset shows a notch defect in the metal etch mask.

Figure 73. Patches of unetched SiO2 after exposure to 10:1 buffered oxide etchamt. The etched channel was 16 nm deep. The Cr/Au metal etch mask was not removed. A notch defect in the metal etch mask can be observed in the upper inset. The unetched areas occur from “micromasking” from portions of the Cr/Au metal mask that were not completely removed during lithography and Au/Cr etching of the nanochannel pattern. The image demonstrates the necessity of over etching Au/Cr masking layers.

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B.4 Electrode Characterization

Height = 29 2 nm

4 µm

5 µm

Figure 74. The electrode height was measured with an Asylum MFP-3D AFM. The electrode height was 29 ± 2 nm (nominal height 25 nm). The scan size was 4 μm x 5 μm

Figure 75. An SEM image of a patterned electrode on a glass substrate that has been sliced to expose the thickness of the metal layers. The locations of the electrode, the glass substrate, and the cut line are labeled on the image.

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Figure 76. An SEM image of a patterned electrode on a glass substrate that has been sliced to expose the thickness of the metal layers. The image was taken near the cut line in Figure 75.

B.5 Characterization of Electrical Testing Station

The inherent noise of the electrical test set-up was first characterized. Low terminals of the two voltage sources and the picoammeter were connected and the test leads later used for measurements were connected to the respective instruments. An axial voltage sweep was performed with the circuit “open” to characterize the current inherent to the instruments themselves. The measured noise does not depend on the axial potential applied. The slope of the measured noise current could be either a positive or negative value across runs. The average noise was 0.15 ± 0.02 pA (Figure 77).

262

0.20

0.15

0.10

0.05

Noise Current (pA) Current Noise 0.00 -10 -5 0 5 10 Axial Voltage (V)

Figure 77. Axial voltage sweep performed for an “open” circuit. Instruments and test leads were all connected with test leads placed inside an Earth grounded Faraday cage. The test leads were not connected to the micro- and nanofluidic device. The average “noise” current was 0.15 ± 0.02 pA.

To further characterize the noise of the system, a gate voltage sweep was performed on a dry device. The experimental setup was connected as shown in Chapter 3

Figure 38 but the device was not filled with an electrolyte solution. The resulting measured current had an average value of 0.14 ± 0.08 pA where the average value did not depend on the applied gate voltage (Figure 78). The measurement using the dry device confirmed that there are no unexpected current paths inherent to the experimental setup.

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0.30 0.25 0.20 0.15 0.10 0.05

Noise Current (pA) Current Noise 0.00 -10 -5 0 5 10 Gate Voltage (V)

Figure 78. A gate voltage sweep was performed on a dry micro- and nanofluidic device to characterize the noise of the measurement system. Gold wires were inserted into the dry reservoirs and a potential of 3V was set to the axial power supply. The gate electrode was connected to the gate power supply and the gate potential was swept from 0 to 10V and then from 0V to -10V. The current does not show any dependence on the applied gate potential and has an average value of 0.14 ± 0.08 pA. The noise measurement confirms that there are not any unexpected current paths inherent to the experimental setup.

B.6 Device Testing Protocols

Data for each electrolyte solution was collected in ascending order of concentration. To ensure that the channel was filled with the appropriate concentration of electrolyte, the device was rinsed three times with the next highest concentration.

Channels were dried in a vacuum desiccator after a rinse cycle, exposed to oxygen plasma, and then the desired concentration was introduced into the channel. Figure 79 shows three rinsing cycles for 1 mM KCl which was introduced into the channel after testing with DI water. Three axial sweeps were performed as part of each “rinsing” cycle. 264

0.04 1st Rinse 2nd Rinse 0.02 3rd Rinse

0.00

Current (nA) Current -0.02

-0.04 -10 -5 0 5 10 Axial Voltage (V)

Figure 79. Rinsing a micro- nanofluidic device with 1 mM KCl. The previous data run was done with DI water. Data was used after rinsing the channel 3x with 1 mM KCl to ensure the nanofluidic channels were filled with the appropriate electrolyte concentration

B.7 Device Design Changes

Two major device designs were used through-out this dissertation. Exploded view schematics of the two designs are given in Figure 80. Design 1 was used in Chapters 3 and 4, while Design 2 was used in Chapter 5.

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Design 1 Design 2

Glass 10-10 AA0.25 PDMS D KCl 1 mMChannels NaCl 0.20 Gold 0.15 Forward 0.10 10-11 0.05 Off

Current (nA) Current 0.00 Gold Reverse PDMS -0.05 Channels -2 -1 0 1 2 Glass Gate Voltage (V) 10-12

Axial Conductance (S) Conductance Axial

10-7 10-6 10-5 10-4 10-3 10-2 10-1 Figure 80: Exploded view schematics of the twoB major device designs used in this E Concentration (M) dissertation. Design 1 was used in Chapters 3 and 4 while Design 5 was used in 10-10 CaCl Chapter 5. It should be noted fabrication processes detailed in Chapter 3 and Appendix C 2 MgCl were not affected by the design change. SEM 2

10-11 Several design changes were made withC a comparison of dimensions across

designs given in Table 13. The most significant change to the design was the length ofA 10-12

Axial Conductance (S) Conductance Axial the glass cover. The length of the glass cover containing the electrode array was 10-7 10-6 10-5 10-4 10-3 10-2 10-1 increased from 50 mm in Design 1 to 75 mm in Design 2. The substrate with the etched Concentration (M) micro- and nanofluidic network was the same in both designs with a length of 50 mm.

Visible un-bonded regions between the fluidic reservoirs were frequently observed for

Design 1, likely due to the edge bead that formed during the PDMS spin step. Edge beads are a “pile up” of the coating material that forms at the edge of a substrate during spin coating. The extra material in this region prevented bond formation between the reservoirs. By increasing the length of the cover but not the channel substrate, the edge bead was sufficiently far from the bonding surfaces. While devices with leaks between the reservoirs were effectively eliminated, since device bonding is a manual process,

266

misaligned devices increased due to the awkward nature of manually bonding two glass plates of unequal size. Despite alignment issues, the number of useable devices post-bonding increased by more than a factor of 2 after the design change was made.

Table 13. A summary of device design parameters for Design 1 and Design 2. Gray shading indicates a value that changed between designs. Design 1 Design 2 Glass Cover Length 50 mm 75 mm Width 50 mm 50 mm Thickness 1 mm 1 mm

Electrodes Height 25 nm 25 nm Width 25 µm 25 µm Number of Electrodes 6 4 Space Between Adjacent 30 / 30 / 60 / 30 / 90 µm 30 / 60 / 90 µm Electrodes (Chapter 4 Figure 43)

Channel Substrate Length 50 mm 50 mm Width 24 mm 24 mm Thickness 0.17 to 0.25 mm 0.17 to 0.25 mm

Microchannels Length 3 cm 3 cm Width 50 µm 50 µm Height 8 µm 8 µm Nanochannels Length 5 mm 2 mm Width 30 µm 30 µm Height 16 nm 16 nm

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The length of the nanochannels was also decreased from 5 mm in Design 1 to

2 mm in Design 2. Shortening the nanochannels allows both microchannels to be seen in a single frame the Nikon Cool Snap H2Q camera and the Ti-U microscope with a 4x objective. Being able to capture both microchannels in a single frame is important for fluorescence based studies, which are part of potential future work for this project.

Due to the decrease in nanochannel length, the number of electrodes was reduced from 6 to 4. The number of electrodes is limited by the alignment tolerance needed for manual bonding procedures. The spacing between the first four electrodes was preserved between Designs 1 and 2. It should be noted fabrication processes detailed in Chapter 3 and Appendix C were not affected by the design change.

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Appendix C: Process Sheets

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C.1 Fabrication of Gated Nanofluidic Device

C.1.1 Channel Network Fabrication

Process for Borosilicate Cover Slips Substrate Cleaning with Piranha

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA - High Precision "CP" PEEK Tweezers)  Acetone ( > 200 mL)  IPA ( > 500 mL)  DI ( > 200 mL)  Borosilicate Substrates (Fisher Scientific 12543D No 2 Cover Glass 50x24 mm  Thomas Cover Glass Ceramic Staining Outfits (Thomas Scientific No. 8542E40)  Handeheld Timer  250 mL Pyrex “IPA” beaker  250 mL Pyrex “Solvent Waste” beaker  250 mL Pyrex “Piranha” beaker  250 mL Pyrex “DI Rinse” beaker  96% Sulfuric Acid (160 mL)  30% Hydrogen Peroxide (40mL)  Polystyrene Petri dishes (Fisher 08-757-100B Petri dishes 60x15mm)

Procedure

1. Rinse tweezers with Acetone, IPA, DI, then IPA and dry with N2. Solvents are disposed of in the organics waste bottle. Tweezers and glass slides can be rinsed directly over the waste bottle with the funnel inserted into the opening in the bottle, or in a separate 250 mL Pyrex “Solvent Waste” beaker 2. Rinse ceramic staining rack with IPA 3. Place staining rack in “IPA” beaker and cover with 200 mL of IPA 4. For each glass slide, rinse both sides with Acetone, IPA, DI, then IPA 5. Load rinsed glass slide into staining rack at a 45° angle. Be sure the glass slide is fully covered by the IPA 6. Place “IPA” beaker into the sonicator. Sonicate 10 minutes 7. Meanwhile prepare the Piranha solution a. Full personal protective gear should be worn when working with Piranha b. Put on gown and face shield. Test gloves with N2 before putting them on 270

c. Measure out 160 mL of 96% Sulfuric acid. Pour into “Piranha” beaker using “Sulfuric Acid” glass graduated cylinder d. Measure out 40ml of 30% Hydrogen Peroxide using “Hydrogen Peroxide” glass graduated cylinder. Do not pour into Piranha beaker yet e. Set the timer for 10 minutes f. Fill “DI Rinse” beaker with 200 mL of DI water 8. Remove “IPA” beaker from sonicator and place in the stainless steel tray lined with Berkshire wipes 9. Remove staining rack from the “IPA” beaker using the tweezers. Place in stainless steel tray on wipe. THOUROUGHLY DRY staining rack and glass slides with N2 in the stainless steel tray. 10. Rinse tweezers with DI water. Dry with N2 11. Pour Hydrogen Peroxide into the “Piranha” beaker 12. Slowly lower the staining rack in the Piranha solution. Full personal protective gear must be worn. 13. Start the timer 14. Rinse tweezers with DI water. Dry with N2 15. After 10 minutes, transfer staining rack to “DI Rinse” beaker. Be sure the glass slides are completely covered with DI water 16. Let stand in the DI water for 5 minutes 17. Meanwhile a. Rinse tweezers with DI water. Dry with N2 b. Aspirate the waste Piranha solution followed by a large (~800mL) amount of DI water 18. Rinse the “IPA” beaker with IPA. Fill with 100mL DI and 100 mL IPA 19. Transfer staining rack to “IPA” beaker 20. Aspirate the waste from the “DI Rinse” beaker. Wash both the “DI Rinse” and “Piranha” beakers in the dump rinse 21. Clean the tweezers with Acetone, IPA, DI, then IPA. Dry with N2. 22. Rinse each glass slide with IPA 23. Dry with N2 24. Store dry samples in a petri dish lined with a Berkshire wipe 25. Solvents are disposed of in the organics waste bottle NOTE: 12 borosilicate channel substrates fit in the ceramic staining rack and 14 fit in the evaporator at one time. Seven electrode cover substrates fit in the evaporator at once.

Evaporator Program for Metal Etching Mask (Channel Slides)

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Piranha cleaned cover slips in petri dishes 271

Procedure

1. Load Piranha cleaned samples being mindful to place the clips in areas where there will not be patterned features during photolithography steps. Clips placed too close to the features lead to defect formation during device etching. This can cause distorted or leaking channels post-bonding 2. Be careful not to overtighten the clips. Overtightening leads to stress fractures in the substrate. Substrates with stress cracks break during N2 drying 3. Run the Cr/Au deposition program (Program 2 on EVP03). YOU MUST CHECK ALL PROGRAM PARAMETERS BEFORE BEGINNING THE DEPOSITION. The program is listed below. 4. When the deposition has completed, wait an additional 5 minutes beyond the pre- programmed “FEED” for the metal film to cool 5. Remove Samples – label petri dishes with the mask thicknesses and date

Pg 1

Material Index Cr Au Rate 0.5 Å/s 0.5 Å/s Final Thickness 0.200 kÅ 1.000 kÅ Final Thickness Limit 0 kÅ 0 kÅ Time Limit 0:00 0:00 Co-Deposition No No Rate Watch Time 0 0 Rate Watch Accuracy 0 0 Crucible 5 4

Pg 2

Material Index Cr Au Rate Ramp 1 New Rate 2.0 Å/s 3.0 Å/s Start Ramp 0.050 kÅ 0.030 kÅ Ramp Time 0:00 0:45 Rate Ramp 2 New Rate 0.0 Å/s 0.0 Å/s Start Ramp 0.130 kÅ 0.900 kÅ Ramp Time 1:00 1:07

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NOTE: Formula for Ramp Down Time (Clean room manual) Ramp down at a thickness of 0.8 * final thickness Time (s) = (Final thickness (A) – Start ramp thickness (A))/(Previous Dep Rate(A/s) /2)

Process for Photolithography – Microchannels

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Acetone ( > 200 mL)  IPA ( > 300 mL)  DI ( > 250mL)  Hot plate  Cover slides with evaporated Cr/Au layer  S1813 Photoresist  ~15 Disposable pipettes (Fisher 13-711-9AM)  Timer  Aluminum block (in clean room)  Photolithography Mask  4” Wide Tape (in clean room)  Razor  Pyrex “MF-319” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “MF-319 DI Rinse” Petri Dish  MF-319 ( > 50 mL)

Procedure

1. Rinse tweezers with Acetone, IPA, DI, then IPA. Dry with N2 2. Rinse glass slides with metal mask on them with Acetone then IPA 3. Dry with N2 4. Set hot plate to 100°C. Use the uncovered hot plates, not the one attached to the coater 5. Set program for the coater. COT03 works the best for the slides as COT02 has too strong of a vacuum and bends the slides leading to uneven photoresist coats. The program for the microchannels has two steps. Adjust Program 4 so it has the spin parameters listed below.

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Spin Speed 300 rpm Acceleration 100 r/s Time 5 sec Spin Speed 3500 rpm Acceleration 5000 r/s Time 45 sec

6. Spin on photoresist (S1813) 7. Soft bake slides on the hot plate for 90 seconds 8. Place on aluminum block to cool before putting back in petri dish 9. Rinse the aligner mask with Acetone and IPA. Dry with N2 taking care to hold the mask securely 10. Cover the vacuum holes on the aligner tray with the 4” wide tape. Using a razor, smooth the tape down and cut air vents to get vacuum only under the slides. Ensure there are absolutely no bubbles or uneven regions of the tape. Note: Load the mask with the Cr side facing up and the anti-reflective coating (brownish color) facing down 11. Expose in the aligner. Alignment for microchannels can be performed visually 12. Do not expose less than 3 minutes after spin coating 13. The Aligner program is listed below

Name Marie_Channel.rcp Mask size 5” Mask Thickness 2.3 mm Substrate Size 4” Substrate Thickness 0.5 mm Resist Thickness 2 μm Separation Distance 30 μm Exposure Time 2.4 seconds Contact Mode Soft Contact

14. Pour MF-319 into MF-319 dish. Fill “MF-319 DI Rinse” dish with DI water 15. Develop in MF-319 for 1 minute 10 seconds with agitation (Wear protective gloves) 16. Move to DI Rinse dish 17. Immediately remove from DI Rinse dish and rinse with DI spray gun 18. Dry with N2 19. Confirm the sample is fully developed using the Bay 2 microscope

274

20. Hard bake on 115°C hot plate for 90 seconds 21. Place on aluminum block to cool before putting back in petri dish

Process for Wet Etching Microchannels

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Pyrex “Au Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Au Etch DI Rinse” petri dish  Transene Gold Etchant Type TFA (>50mL)  DI water (>200 mL)  Pyrex “Cr Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Cr Etch DI Rinse” petri dish  Cr-7 Chromium Etchant (>50 mL)  “Prakash Group Only” hot plate  Nalgene “HF only” 100 mL graduated cylinder  “BOE” Nalgene crystallization dish  “DI Water” Nalgene crystallization dish  Magnetic Stir Bar  49% Hydrofluoric Acid (HF) (25 mL)

Procedure

1. Full PPE must be worn while working with acids 2. Pour Transene Gold Etchant Type TFA into “Au etch” Pyrex Petri Dish 3. Fill “Au Etch DI Rinse” Pyrex Petri dish with DI water 4. Etch samples in TFA for 1 min 5 seconds with agitation 5. Move to DI Rinse dish 6. Immediately remove from “DI Rinse” dish and rinse with the DI spray gun 7. Dry with N2 8. Confirm that the Au has been fully removed from the microchannel pattern using the microscope in Bay 1 (light and dark field) 9. Dispose of Au etchant and DI water in the Au and Palladium etch waste container under the hood in Bay 1 10. Triple rinse Pyrex Petri dishes. Pour rinse waste into Au and Palladium etch waste container. Triple rinse again if there is any chance traces of Au etchant remain on either dish. Dry with Berkshire wipes 11. Pour Cr-7S Chromium Etchant into Cr etch Pyrex Petri Dish 12. Fill Cr Etch DI Rinse Pyrex Petri dish with DI water 275

13. Etch samples in Cr-7s for 22 seconds with agitation 14. Move to DI Rinse dish 15. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse 16. Dry with N2 17. Confirm that the Cr has been fully removed from the microchannel pattern using the microscope in Bay 1 (light and dark field) 18. Dispose of Cr etchant and DI water in the Metal etch waste container under the hood in Bay 1 19. FULL PPE MUST BE WORN WHEN WORKING WITH HF AT ALL TIMES 20. Ensure the hood is completely dry. All drops found on the hood after this point should be considered to be HF. 21. Find the “Prakash Group Only” hot plate and set the “BOE” Nalgene crystallization dish on the hot plate. Insert the stir bar. 22. DO NOT TURN ON THE HEAT AT ANY POINT IN THIS PROCESS 23. Measure out 100 mL DI water in Nalgene graduated cylinder. Pour into “BOE” Nalgene crystallization dish 24. Measure out 25 mL 49% HF using the Nalgene graduated cylinder. Pour into “BOE” Nalgene crystallization dish 25. Turn the stir speed to high (1200rpm) 26. Etch channels for desired time with agitation (typical 8 minutes for 50 μm wide x 8 μm deep channels). Use the timer on the hood NOT the handheld timer 27. Place in “DI” Nalgene crystallization dish 28. Immediately remove from the “DI Rinse” dish and rinse with the DI spray gun. 29. Dry with N2 30. Aspirate contents of BOE and DI Nalgene Crystallization dishes when finished. Clean the Nalgene dishes in the dump rinse 31. With tweezers over the dump rinse, rinse the stir bar with DI. Dry with N2.

Process for Photoresist Removal

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  250 mL “NMP” beaker  NMP ( > 300 mL)  Thomas Cover Glass Ceramic Staining Rack (Thomas Scientific No. 8542E40)  Methanol ( > 200 mL) 276

 IPA ( > 200 mL)

Procedure

1. Fill NMP Pyrex beaker with 200 mL of NMP 2. Rinse the Ceramic Staining Rack with IPA 3. Dry with N2 4. Place ceramic staining rack in NMP beaker 5. Using the NMP squirt bottle, rinse samples with etched microchannels with NMP paying special attention to the edges and microchannel area 6. Load into ceramic staining rack 7. Once all samples are loaded sonicate for 7 minutes 8. Rinse each sample with NMP, methanol then IPA 9. Dry with N2 10. When the samples dry they should evaporator relatively quickly, not leave a “streaking” pattern as they dry. If the sample does not dry properly repeat previous two steps. If the samples are not properly dried a green film forms on the glass following exposure to oxygen plasma. 11. Rinse ceramic staining rack with methanol and IPA. Dry with N2 12. Pour NMP into organic waste container. Triple rinse with Methanol and IPA 13. Load samples into oxygen plasma 14. Expose to oxygen plasma for 1 minutes at 100 W with a chamber pressure of 100 mtorr (10.0 sccm O2).

Process Sheet for Photolithography – Nanochannels

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Acetone ( > 200 mL)  IPA ( > 300 mL)  DI ( > 250mL)  Hot plate  Cover slides with microchannels and evaporated Au/Cr layer  S1813 Photoresist  15 Disposable pipette (Fisher 13-711-9AM)  ~Timer  Aluminum block (in clean room)  Photolithography Mask 277

 4” Wide Tape (in clean room)  Razor  Pyrex “MF-319” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “MF-319 DI Rinse” Petri Dish  MF-319 ( > 50 mL)

Procedure

1. Rinse tweezers with Acetone, IPA, DI, then IPA. Dry with N2 2. Rinse glass slides with microchannels on them with Acetone then IPA 3. Dry with N2 4. Place in O2 Plasma 5. Let the chamber pump down to less than 20 mtorr 6. Turn on the O2 at a flow rate of 10 sccm 7. Let the chamber pressure stabilize to 100 mTorr 8. Turn on the RF power to 100 W 9. Start the timer when the power reaches 100 W. Run for 1 minute 10. Set hot plate to 100°C. Use the uncovered hot plates, not the one attached to the coater 11. Set program for the coater. Use COT03 if possible since the vacuum on COT02 is too strong for the channel slides and can lead to an uneven photoresist layer. The program is three steps for nanochannels

Spin Speed 60 rpm Acceleration 20 r/s Time 4 sec Spin Speed 250 rpm Acceleration 50 r/s Time 5 sec Spin Speed 3500 rpm Acceleration 100 r/s Time 45 sec

12. Spin on photoresist (S1813). Apply it just over the microchannels and allow it to spread over the rest of the slide before spinning 13. Soft bake slides on the hot plate for 90 seconds 14. Place on aluminum block to cool before putting back in petri dish 15. Rinse the photolithography mask with Acetone and IPA. Dry with N2 being very careful not to drop the mask

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16. Cover the vacuum holes on the aligner tray with the 4” wide tape. Using a razor, smooth the tape down and cut air vents to get vacuum only under the slides. Ensure there are absolutely no bubbles or uneven regions of the tape. Note: Load the mask with the Cr side facing up and the anti-reflective coating (brownish color) facing down 17. Expose in the aligner. Alignment must be performed using the alignment markers. The alignment program, “Marie_channels.rcp” is listed below

Mask size 5” Mask Thickness 2.3 mm Substrate Size 4” Substrate Thickness 0.5 mm Resist Thickness 2 μm Separation Distance 30 μm Exposure Time 3.4 seconds Contact Mode Soft Contact

18. Develop in MF-319 for 1 minute 10 seconds with agitation (Wear protective gloves) 19. Move to DI Rinse dish 20. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse

21. Dry with N2 22. Confirm the nanochannels are fully developed using the microscope in Bay 2 23. Hard bake on 115°C hot plate for 90 seconds 24. Place on aluminum block to cool before putting back in petri dish

Process for Wet Etching Nanochannels

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Pyrex “Au Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Au Etch DI Rinse” petri dish  Transene Gold Etchant Type TFA ( > 50mL)  DI water ( > 200 mL)  Pyrex “Cr Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Cr Etch DI Rinse” petri dish  Cr-7 Chromium Etchant ( > 50 mL)  “BOE” Nalgene crystallization dish 279

 “DI Water” Nalgene crystallization dish  10:1 Buffered Oxide Etchant (BOE) (100 mL) Process

1. Full PPE must be worn while working with acids 2. Pour Transene Gold Etchant Type TFA into Au etch Glass Petri Dish 3. Fill Au Etch DI Rinse Pyrex Petri dish with DI water 4. Etch samples in TFA for 45 seconds with agitation 5. Move to DI Rinse dish 6. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse 7. Dry with N2 8. Confirm that the Au has been fully removed from the nanochannel pattern using the microscope in Bay 1 (light and dark field)’ 9. DO NOT Dispose of Au etchant until after the next process (metal etch mask removal) 10. Pour Cr-7S Chromium Etchant into Cr etch Glass Petri Dish 11. Fill Cr Etch DI Rinse Pyrex Petri dish with DI water 12. Etch samples in Cr-7s for 18 seconds with agitation 13. Move to DI Rinse dish 14. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse

15. Dry with N2 16. Confirm that the Cr has been fully removed from the nanochannel pattern using the microscope in Bay 1 (light and dark field) 17. DO NOT Dispose of Cr etchant until after the next process 18. FULL PPE MUST BE WORN WHEN WORKING WITH HF AT ALL TIMES 19. Measure out 100 mL 10:1 Buffered Oxide Etchant. Pour into “BOE” Nalgene crystallization dish. Note you do NOT need the hot plate or stir bar 20. Fill the “DI” Nalgene crystallization dish with DI water 21. Etch channels for desired time with agitation (typically 20 seconds for 30 μm wide x 16 nm deep channels) 22. Place in “DI” Nalgene crystallization dish 23. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse 24. Dry with N2 25. Aspirate the BOE and DI when finished etching. Run the dump rinse to clean the Nalgene crystallization dishes

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Process for Preparing Channel Slides for Bonding

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Pyrex “Au Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Au Etch DI Rinse” petri dish  Transene Gold Etchant Type TFA (>50mL)  DI water ( > 400 mL)  Pyrex “Cr Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Cr Etch DI Rinse” petri dish  Cr-7 Chromium Etchant ( > 50 mL)  Pyrex 250 mL “Aqua Regia” beaker  Pyrex 250 mL “DI Rinse” beaker  HCl (150 mL)  Nitric Acid (50 mL)  Thomas Cover Glass Staining Rack (Thomas Scientific No. 8542E40)  Glass 250 mL “IPA” beaker  IPA (>200 mL)

Process

1. Follow the Process for Removing Photoresist above 2. Confirm samples are properly fabricated in the microscope in Bay 1 (no defects or blockages in channels, etc.) 3. Using the Au etch Pyrex Petri Dish and Au Etch Rinse dishes, soak samples in Au etch for 2 minutes with agitation. 4. Move to Au DI Rinse dish 5. Rinse with the DI spray gun. Rinse the slide over the dump rinse 6. Dry with N2 7. Using the Cr etch Pyrex Petri Dish and Cr Etch Rinse dishes, soak samples in Au etch for 2 minutes with agitation. 8. Move to Cr DI Rinse dish 9. Rinse with the DI spray gun. Rinse the slide over the dump rinse

10. Dry with N2 11. Dispose of Au etchant in Au and Palladium etch waste bottle and Cr etchant in Metal Etch Waste bottle 12. Place 150 ml of HCl in the Pyrex Aqua Regia beaker. Full PPE must be worn while working with acids 13. Rinse ceramic staining rack with DI water 281

14. Dry with N2 15. Pour 50 ml of Nitric acid into Aqua Regia beaker 16. Load samples into the ceramic staining rack. Place the ceramic staining rack in the Aqua Regia. 17. Soak for 55 minutes 18. Fill DI water beaker with 200 mL of DI water 19. Dispose of Aqua Regia and DI water in the Metal Etch waste bottle. Add an additional 200mL of water to the waste container. Ensure the aqua regia is not bubbling in the waste bottle and that the proper vented cap has been used before capping the bottle. 20. Transfer ceramic staining rack to DI beaker. Let the samples soak in the DI Rinse for 5 minutes 21. Fill IPA beaker with 200 mL of IPA. Transfer ceramic staining rack to IPA beaker 22. Rinse each sample with IPA 23. Dry with N2 24. Channel slides are now ready for bonding NOTE: If you are unsure if the sample has been flipped, use the tweezer to lightly scratch the sample slide near the alignment marker. Avoid the micro- and nanochannel area. The alignment marker is the same depth as the microchannels and can be felt with the tweezers.

C.1.2 Process for Fabricating Electrode Covers

Process Sheet for Electrode Slide Glass Cleaning

Material

 Wafer tweezers (TDI International #TDI 4WFCPR-SA – High Precision “CP” PEEK Wafer Tweezers)  Alconox Powdered Precision Cleaner Manufacturer Catalog No. 1112 (1 packet)  DI water (>2000 mL)  Glass top covers (Fisher Scientific Plain Microscope Slides Catalog No 12-550C)  IPA ( > 1300 mL)  1 L Pyrex “IPA” Beaker  PFA 2” Mask Holder with handle (Entegris Inc. PFA holder #A41-01; PFA Handle #A08-0215)  1 L Pyrex “Piranha Clean” Beaker  96% Sulfuric acid (600 mL)  30% Hydrogen Peroxide (200 mL)  Handheld Timer  1 L Pyrex “DI Rinse” Beaker 282

Process

This process is for cleaning glass substrates that have been cut by the OSU glass shop. If using full sized samples, skip steps 1-3. 1. Scrub each side of slide with a clean room wipe soaked in 1% Alconox solution. Scrub each side vigorously for 45 seconds 2. Rinse with DI water and dry with N2 3. If there are any visible impurities on the surface repeat scrubbing process 4. Clean wafer tweezers with acetone/IPA/DI/IPA. Dry with N2 5. Clean PFA 2” mask holder with IPA 6. Place holder in “IPA” beaker and cover with 800 mL of IPA 7. For each glass slide clean both sides with acetone/IPA/DI/IPA 8. Load clean glass slide into staining rack that is submerged in the IPA. Be sure the glass slide is fully covered by the IPA (~800 mL) 9. Remove the mesh basket from the solicitor and place “IPA” beaker with slides into the bath. Sonicate 5 minutes 10. Meanwhile prepare the Piranha solution a. Full personal protective equipment must be worn when working with Piranha b. Put on gown and face shield. Test gloves with N2 before putting them on c. Measure out 600 mL of 96% Sulfuric acid. Pour into “Piranha” beaker d. Measure out 200 mL of 30% Hydrogen Peroxide. DO NOT pour it into the beaker yet e. Set the hood timer for 10 minutes f. Fill “DI Rinse” beaker with 800 mL of DI water 11. Remove “IPA” beaker from sonicator and place on a Berkshire wipe in the solvent hood 12. THOUROUGHLY DRY holder and glass covers with N2. The PFA sample holder can be transported to the acid hood by the handle 13. Rinse tweezers with DI water. Dry with N2 14. Pour the Hydrogen Peroxide into the “Piranha” beaker 15. Slowly lower the PFA holder in the Piranha solution. Full personal protective gear must be worn 16. Start the timer 17. Rinse tweezers with DI water. Dry with N2

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18. Transfer staining rack to “DI Rinse” beaker. Be sure the glass slides are completely covered with DI water 19. Let stand in the DI water for 5 minutes 20. Meanwhile a. Rinse tweezers with DI water. Dry with N2 b. Aspirate the waste Piranha solution followed by a large (~3-4 L) amount of DI water 21. Rinse the “IPA” beaker with IPA. Fill with 400 mL DI and 400 mL IPA 22. Transfer PFA holder to “IPA” beaker 23. Aspirate the waste from the “DI Rinse” beaker 24. Clean the Piranha and DI rinse beakers with the dump rinse 25. Clean the tweezers with acetone/IPA/DI/IPA 26. Rinse each glass slide with IPA 27. Dry with N2 28. Place in Polystyrene Petri Dishes lined with Berkshire wipes (Fisher #08757100D Petri dishes 100x15mm)

Evaporator Program for Electrode Covers

Materials

 Wafer Tweezers (TDI International #TDI 4WFCPR-SA)  7 Piranha cleaned top covers

Process

For more instructions on evaporation see Evaporator process for metal etching mask.

Pg 1

Material Index Cr Au Rate 0.5 Å/s 0.5 Å/s Final Thickness 0.070 kÅ 0.180 kÅ Final Thickness Limit 0 kÅ 0 kÅ Time Limit 0:00 0:00 Co-Deposition No No Rate Watch Time 0 0 Rate Watch Accuracy 0 0 Crucible 5 4

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Pg 2

Material Index Cr Au Rate Ramp 1 New Rate 0.0 Å/s 0.0 Å/s Start Ramp 0.000 kÅ 0.000 kÅ Ramp Time 0:00 0:00 Rate Ramp 2 New Rate 0.0 Å/s 0.0 Å/s Start Ramp 0.000 kÅ 0.000 kÅ Ramp Time 0:00 0:00

NOTE: A deposition rate of 0.5 Å/s is used for the Cr and Au evaporation for the electrode covers. The deposition rate is not increased in order to avoid cracking of the metal layers.

Process Sheet for Photolithography – Electrodes

Materials

 Wafer Tweezers (TDI International #TDI 4WFCPR-SA)  IPA ( > 300 mL)  DI ( > 250mL)  Hot plate  Cover slides with evaporated Au/Cr layer  S1813 Photoresist  ~15 Disposable pipette (Fisher 13-711-9AM)  Handheld Timer  Aluminum block  Photolithography Mask  Pyrex “MF-319” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “MF-319 DI Rinse” Petri Dish  MF-319 ( > 50 mL)

Process

1. Clean tweezers with acetone/IPA/DI/IPA 2. Rinse glass slides with metal mask on them with acetone/IPA 3. Dry with N2 4. Set hot plate to 100°C. Use the uncovered hot plates, not the one attached to the coater 285

5. Set program for the coater. Typically, program N is used on COT02. COT02 is used since the vacuum on COT03 is often not strong enough to hold the slides and will fling them around inside the coater. The program is two steps for electrode slides

Spin Speed 300 rpm Acceleration 100 r/s Time 5 sec Spin Speed 3500 rpm Acceleration 5000 r/s Time 45 sec

6. Drop the photoresist onto the electrode substrate avoiding the corners 7. Spin on photoresist (S1813) 8. Soft bake slides on the hot plate for 90 seconds 9. Place on aluminum block to cool before putting back in petri dish 10. Expose in the aligner. Use the 5” mask holder. The table outlines the recipe called “Marie_covers.rcp”. Note: Load the mask with the Cr side facing up and the anti- reflective coating (brownish color) facing down

5 4” Mask Thickness 2.3 mm Substrate Size 2” Substrate Thickness 1 mm Resist Thickness 3 μm Separation Distance 350 μm Exposure Time 2.6 seconds Contact Mode Soft Contact

11. Develop in MF-319 for 1 minute with agitation (Wear protective gloves) 12. Move to DI Rinse dish 13. Immediately remove from the DI rinse dish and rinse with the DI spray gun. Rinse the slide over the dump rinse 14. Dry with N2 15. Confirm the pattern has been fully developed with the microscope in Bay 16. Hard bake on 115°C hot plate for 90 seconds 17. Place on aluminum block to cool before putting back in petri dish

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Process for Wet Etching Electrode Array

Material

 Wafer tweezers (TDI International #TDI 4WFCPR-SA)  Handheld Times  Pyrex “Au Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Au Etch DI Rinse” petri dish  Transene Gold Etchant Type TFA (>50mL)  DI water (>200 mL)  Pyrex “Cr Etch” petri dish (Fisher 150x15mm 08748E {bottom}, 08749E {top})  Pyrex “Cr Etch DI Rinse” petri dish  Cr-7 Chromium Etchant (>50 mL)  1 L “PR Removal” Pyrexbeaker  NMP (800 mL)

Process

1. Follow process for wet etching microchannels steps 1-13 (Au and Cr etching) with ADJUSTED ETCH TIMES 2. Au etch time – 6 seconds 3. Cr etch time – 12 seconds 4. Follow Process for Removing Photoresist. Use 1 liter “PR Removal” beaker in place of 200 mL “NMP” beaker with 800 mL NMP

Process for Drilling Glass Slides

Material

 Print out of photolithography mask  Top covers with patterned electrode array  Sharpie  Parallel set  Vice  Blank top covers (Fisher Scientific Plain Microscope Slides Catalog No 12-550C)

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 3/32” diameter diamond core drill bit (McMaster #2868A46 Diamond-Core Drill Bit for Nonmetal Material 3/32” OD, .043” ID, 2” Length)  Palmgren Drill Press  DI water ( > 700 mL)  Paper towels

Process

1. Align top cover with patterned electrode array over image of photomask. Mark location of fluidic access ports on the slide with a Sharpie 2. Place parallels in vice. Place marked slide on a small stack (5-7 slides) of sacrificial blank glass slides of the same size. 3. Place stack of slides with marked slide on top between the parallels. Tighten the vice so that the top slide will not vibrate while drilling. Over tightening, however, will cause the slide to break when the drill bit breaks through the slide. 4. Visually align the drill bit to the first Sharpie mark. Turn on the drill and slowly lower the drill bit without making contact with the glass slide to make sure the drill bit is aligned to the sharpie mark when it is on. Turn off the drill. Re-align the sample if necessary 5. Spray DI water over the surface of the glass slide 6. Turn on the drill (flip black and yellow switch on the front of the drill up) and slowly bring the drill bit in contact with the glass 7. Drill through the slides while constantly cooling with DI water. After every 30 seconds of drilling raise the drill bit slightly and spray DI to cool the surface and remove shards of glass. 8. Drill through the glass slowly. Drilling through too fast will cause the glass to break. 9. When drilling, the particles of glass will make the DI water white. By constant cleaning, it is easy to control the speed of drilling and to know whether the glass is drilled through. When there is white liquid between the working slide and the sacrificial slide, stop drilling. Loosen the vice and clean the working slide and the first sacrificial slide with lab wipes. If glass particles are present between the working slide and sacrificial slide, the vibration they make will easily break the slide when drilling the rest of the holes. 10. Repeat for each fluidic access hole, turning off the drill when readjusting the position of the vice 11. When finished drilling be sure to completely dry the sample stage and drill stand with lab wipes. There should not be any water on the stand, stage, vice, parallels or in the holes of the stand 288

12. Drilled slides should be sonicated for 15 minutes in a 0.01% Alconox solution (200 ml DI, 20 mg Alconox). Please see sonicator process sheet for further instructions.

Note: If slides are breaking excessively, secure the alumina cleaning stick with the vice and drill into it 5-8 times. This only needs to be done approximately every 50 slides. Excessive use of the cleaning stick will strip the diamond coating from the drill bit. If the cleaning stick is not sufficient, replace the diamond core drill bit (available from McMaster)

Process for Sonicating Drilled Slides

Materials

 3 – 250 mL “Alconox” Pyrex beakers  DI water (>600 mL)  3 weigh trays (Fisher 08-732-117)  60 mg Alconox (Alconox Powdered Precision Cleaner Manufacturer Catalog No. 1112)

Process

1. Drilled glass slides should be sonicated for 15 minutes in a 0.01% Alconox solution by weight (200 mL DI, 20 mg Alconox) 2. Prepare solution in three separate 250 mL beakers dedicated for this purpose 3. Place one drilled slide in each beaker 4. Take out basket from sonicator. Check that the water level is at the “operating level” line. If it is not, fill to the line with distilled water. 5. Replace basket and the cover (should have three holes in it) 6. Place one beaker in each of the holes. The rim should be wide enough to ensure the majority of the beaker is submerged but the beaker doesn’t fall into the basket 7. Turn on the rocker switch on the sonicator 8. Use the up/down arrows until the indicator light is next to “degas (min)” 9. Adjust the time to 15 minutes using the +/- key 10. Press the flat on/off switch 11. Sonicate slides for 15 minutes. 12. Remove slide from Alconox beaker. Rinse with DI. Dry with N2.

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13. Inspect each slide under the microscope using the 10x objective. If there are still visible particles, sonicate another 15 minutes 14. Repeat steps 12 and 13 until slides are free of particles 15. Alconox solution goes in the buffer waste container 16. Triple rinse the Alconox beakers with DI water. The waste from the rinsing also goes in the buffer waste container

Process for Spinning PDMS

Materials

 Wafer tweezers  Acetone ( > 50 mL)  IPA ( > 900 mL)  DI ( > 50 mL)  Pyrex 1 L “IPA” beaker  PFA sample holder  “Prakash Group” scale  Disposable pipette (Fisher 13-711-9AM)  Disposable Plastic cup  Handheld Timer  60g PDMS bulk (Sylgard 184 Silicone Elastomer Base Dow Corning Corporation)  6g PDMS Curing agent (Sylgard 184 Silicone Elastomer Curing Agent)  Aluminum foil  “Prakash Group Only” hot plate  Copper tape

Process

1. Rinse wafer tweezers with Acetone, IPA, DI, then IPA 2. Fill 1 liter IPA beaker with 800 ml of IPA 3. Rinse PFA sample holder with IPA. Place in IPA beaker 4. Rinse electrode slides with acetone/IPA 5. Load electrode covers into PFA sample holder 6. Sonicate electrode covers in IPA for 10 minutes 7. Rinse with IPA 8. Dry with N2 9. Retrieve the Prakash group scale and plug it in inside the organics hood 290

10. From bay 2, get a clean photoresist dropper 11. Place a plastic cup on the scale and tare the scale 12. For three devices, measure out 60g bulk and 6g Curing agent into a plastic cup. Typically, use about 20g of monomer per slide but do not exceed 60g or the cup will spill over in the vacuum chamber 13. Mix by hand thoroughly for 10 minutes using a photoresist dropper to stir 14. Place in the vacuum chamber to de-gas for 1 hour 20 minutes a. Release a little of the gas after 5, 10 and 15 minutes 15. Cover the “Prakash group only” hot plate with aluminum foil. Ensure the foil is as flat as possible. Set to 75°C 16. Program bench top coater (coater 2). The program has 3 steps and is typically program “M” a. Press F1 b. Press “delete step” if the program has more than 1 step c. Use the left and right arrows to toggle between parameters; the up and down arrows to change the values d. Press F1 when finished editing the program

Spin Speed 60 rpm Time 0:08 (Min:Sec) Acceleration (001 Acl) Spin Speed 300 rpm Time 0:05 (Min:Sec) Acceleration (002 Acl) Spin Speed 1000 rpm Time 1:00 (Min:Sec) Acceleration (002Acl)

17. Immediately prior to spin coating the PDMS, treat the top covers with an oxygen plasma. Place top covers (electrode side up) into the plasma chamber. Pump down to < 20 mtorr. Turn on the oxygen flow rate to 10.0 sccm. Adjust until the chamber pressure is 100 mtorr. Turn on the power to 200W. Run for 3 minutes. 18. Cover drilled holes by placing copper tape on the back side of the electrode slide 19. Spin PDMS onto electrode slides a. Center the electrode slide on the smaller chuck b. Press the “vacuum” button c. Use a photoresist dropper to fill drilled holes with uncured PDMS d. Close the lid 291

e. Press “Run” f. When finished, cover the entire slide with PDMS g. Close the lid h. Press “Run” 20. Place electrode slides to cure on a 75°C hot plate for 24 hours

Process for Oxygen Plasma Bonding

Materials

 Sample tweezers (TDI International #TDI 2ABCPR-SA)  Wafer tweezers (TDI International #TDI 4WFCPR-SA)  Acetone ( > 25 mL)  IPA ( > 25 mL)  DI ( > 25 mL)  Top covers with cured PDMS  Completed channel slides  Handheld Timer  Polyurethane black rod (McMaster 3/4” diameter 6”long #8695K521)

Process

1. Rinse tweezers with Acetone, IPA, DI, then IPA 2. Dry with N2 3. Rinse channel slides to be used with Acetone then IPA 4. Dry with N2 5. Pump down empty O2 plasma chamber to 16 mtorr 6. Turn on O2 with a flow rate of 10.0 sccm (chamber pressure 100 mtorr) 7. Set the RF power to 200W. Run for 3 minutes. 8. Adjust the RF power to 60 W. 9. Turn off the RF power (DO NOT move the dial back to zero. Just toggle the switch on and off) 10. Turn off the gas and vent the chamber 11. Remove the copper tape from the electrode slide 12. Insert channel slide and electrode slide with cured PDMS bonding side up 13. Pump down the chamber to 16 mtorr 14. Turn the O2 flow rate to the instrument maximum (50.0 sccm) 15. Turn on the O2. Wait for the chamber pressure to stabilize to 270mTorr

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16. Turn on the RF power. Start the timer when the power is 60W and the plasma is lit. Run the process for 30 seconds 17. Turn off the RF power, the O2 gas and vent the chamber 18. Remove channel slide and electrode slide 19. Visually align the reservoirs of the channels slide to the fluidic inlets of the electrode slide. Press together, avoiding the channel areas. The oxygen plasma treatment decays with time so the bonding should be performed as quickly as possible 20. Roll with polyurethane tube 21. Press any unbonded regions together with tweezers. Unbonded regions are identified by Newton Rings. Be careful to avoid pressing directly on the micro- or nanochannels. Pay special attention to the area in between the reservoirs on either end 22. Place in 60°C oven for 1 hour to strengthen bond 23. Place device on a metal block to cool before placing it back in the petri dish

C.2 Processes for Gated Nanofluidic Device Testing

C.2.1 Preparation for Device Testing

Process for Plasma Treating Device before Testing

Materials

 Gated nanofluidic device  Nitrile Gloves

Process for Herrick Oxygen Plasma Cleaner (W491)

1. Turn on the oxygen tank. Always wear gloves when touching the inside of a vacuum chamber. 2. Open the O2 valve, then the purge valve to vent the chamber 3. Wait for the door to open (DO NOT FORCE THE DOOR OPEN) 4. Close the purge valve, then the O2 valve 5. Place samples inside the Harrick Plasma chamber 6. Close the door, hold it closed and turn on the Edwards RV3F pump (black switch on left of pump). Only the RV3F pump may be used with the oxygen plasma system. The RV3F uses only Fomblin oil which is not a hydrocarbon oil. Using a

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pump with the oxygen plasma system that has hydrocarbon oil IS A SIGNIFICANT SAFETY HAZARD AND MUST NEVER BE DONE. The pump is not attached to the “Pump” switch on the plasma since the initial current spike when the pump is turned on blows a fuse in the plasma system. 7. Shut off the O2 tank 8. Wait for the chamber pressure to reach < 30 mtorr 9. Open the purge valve and the O2 valve 10. Wait until the O2 line is purged (flattened). The chamber pressure will start to decrease again once the line is fully purged. 11. Close the O2 valve and the purge valve 12. Turn on O2 tank 13. Turn off O2 tank 14. Wait until the vacuum chamber pressure reaches < 30mTorr 15. Repeat the O2 line purge (Steps 9 – 11) 16. Turn on the O2 tank and leave it on 17. Open the purge valve (the pressure will increase again) 18. Wait until the chamber pressure reaches 50 mTorr 19. Close the purge valve 20. Wait until the chamber pressure reaches < 30 mtorr 21. Open the O2 valve 22. Open the purge valve and adjust so that the pressure inside the chamber is 600 mTorr 23. Turn RF power level dial to required setting (usually High for device cleaning before testing). NOTE: This is the ideal case. The dial on the plasma is wearing out. LEAVE IT ON HI. 24. Switch on the “Power” switch. Turn off the lights in the room. After about 1 minute you will see a blue / white plasma in the chamber. If it looks purple there is nitrogen in the chamber. If there is Nitrogen in the chamber : Turn off the plasma power. Proceed from step 19. 25. When you see the plasma is on start the timer 26. Expose the device to the oxygen plasma for 10 minutes 27. Turn off the “Power” switch 28. Set the RF power level dial to “OFF” (no longer applicable) 29. Turn off the pump 30. Open the purge valve completely 31. Wait until the door opens (DO NOT FORCE THE DOOR OPEN) 32. Close the purge valve and the O2 valve 33. Wearing gloves, remove the sample

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34. Close the door, hold it closed and turn on the vacuum pump 35. Shut off the O2 tank 36. Open the purge and O2 valve for about 6-8 seconds so that the O2 line is not fully pressurized but not flat 37. Wait until the chamber pumps down to 200 mTorr 38. Turn off the pump 39. !!! DOUBLE CHECK THE O2 TANK IS CLOSED!!!

Process for Making an Electrolyte Solution for Nanofluidic Device Testing

Materials

 Safety: Gloves and googles  2 – 250 mL beakers dedicated for HCl  2 – 250 mL beakers dedicated for the electrolyte solution (i.e. KCl)  1 – 100 mL Graduated Cylinder  1 – Disposable Spatula (G – 1985 – P – 01)  Pellets of desired salt o NaOH: Fisher Scientific S318-500 Sodium Hydroxide 500g o Mg(OH)2: Fisher Scientific M342-500 Magnesium Hydroxide 500g o Ca(OH)2: Fisher Scientific C88-500 Calcium Hydroxide 500g o KOH: Fisher Scientific P250-500 Potassium Hydroxide 500g o MgCl2: Fisher Scientific M33-500 Magnesium Chloride Hexahydrate 500g (must account for water molecules in weight measurements) o CaCl2: Sigma-Aldrich Calcium chloride C8106-500G  2 – disposable pipettes (Fisher 13-711-9AM)  Parafilm (PM-996)  Kim wipes (34155)  Concentrated HCl (Fisher A144C-212)  Basic scale (Ohaus V32XH2)  Scientific balance (Ohaus EP214C)  3 – disposable weighing dishes (Fisher 08-732-117)  pH meter (Fisher 402985)  3 – pH calibration solutions, one for each pH level o Red acid – YSI Inc. Buffer Solution pH 4.00 YSI3823 o Yellow neutral – YSI Inc. Buffer Solution pH 7.00 YSl3822 o Blue base – YSI Inc. Buffer Solution pH 10.00 YSI3821  Wash bottles filled with deionized water  Water purifier (Millipore ZRQVP030)

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Procedure

1. See part B for dilution procedure for 0.1 mM 2. See part C for procedure for pH controlled solutions of divalent electrolytes near the solubility limit of Ca(OH)2 and Mg(OH)2. Use for 10 mM and 100 mM 3. Place 250 mL dedicated beaker on scale then zero the scale 4. Turn on Millipore DI stream. Make sure that the reading on the filter is 18.2 MΩ-cm 5. Fill the 250 mL beaker with 150 mL of water. Confirm volume is 150 mL by weighing 150 g. Wipe off excess H2O off of the outside of the beaker 6. Zero another 250 mL beaker on the scale 7. Fill a 250 mL HCL dedicated beaker with 50 mL of water using the previous weighing procedure, this will be used to dilute the concentrated HCl 8. Using a disposable spatula, place MOH pellets in 1st weighing dish, be careful not to place any pellets that have been touched by the spatula back in their container because they may be contaminated. The spatula can be dipped in the container only once. If you need more salt you must use a new spatula. 9. Cover the weighing dish with the salt pellets with 2nd weighing dish 10. Crush the pellets into powder using a hammer 11. Place 3rd weighing dish on the scale, then zero the scale 12. Using the spatula, carefully weigh the needed amount of MOH salt 13. In order to transfer an accurate amount of reagent to the 150 mL of deionized water, pour a small amount of the 150 mL of water into the weighing dish and swirl the liquid around in order to pick up all stray salt particles 14. Pour the liquid back into the electrolyte dedicated beaker. 15. Repeat steps 13-14 three times to ensure all salt has been dissolved 16. If making a divalent electrolyte, sonicate the MOH solution for 5 minutes 17. Repeat steps 12-13 until all salt particles have been collected in the water 18. Pour 50 mL of this new solution in the other electrolyte dedicated beaker as a backup in case the neutralization of the solution fails 19. Cover the 50 mL of MOH solution with parafilm to avoid contamination 20. Before measuring the pH of the solution, the pH meter must be calibrated properly 21. Remove the pH probe from its storing liquid. Confirm that the acidic pink calibration solution used to store the pH probe is full and free of particulates. The probe solution must be changed once every two weeks. Note: the pH probe cannot be dry/left out of solution for more than 1

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minute. Do not hold probe upside down (internal water must stay near measurement bulb) or ever place it on a table/bench top 22. Rinse the probe with DI water 23. Dry the pH probe using a kimwipe, however be careful not to dry the actual bulb itself 24. Turn on the probe 25. In order to calibrate the probe the probe must be placed in all 3 calibration solutions 26. A small amount of each calibration solution should be in each of the 3 date scintillation vials. Make sure to read the date on the calibration solutions. If they are more than 7 days old they must be thrown away in the buffer waste bin 27. Obtain new buffers and label the date on the containers 28. Put pH meter into calibration mode by pressing the “cal” button 29. Place pH probe in pink (4.0) calibrating solution. Wait until it stabilizes. Press enter. Remove probe, then rinse and dry. 30. Repeat with yellow (7.0) then blue (10.0) then rinse and dry after each solution. 31. The pH probe is now ready to be used 32. The following procedures must be performed carefully under a fume hood 33. Place about 1 mL of concentrated HCl in a dedicated HCl beaker 34. Using a dropper, add 12 drops of the concentrated HCl to the beaker holding 50 mL of DI water 35. Gently stir the HCl solution with dropper 36. Place the pH probe in the MOH solution 37. Carefully drop diluted HCl and or concentrated HCL (see next page) solution into the MOH solution until you get a desired pH of 7±0.02 38. Be sure to stir very well after every drop of acid to ensure a correct measurement 39. Note: After a few drops the pH will drop very quickly. As pH approaches 8/9 pH very quickly. 40. If you go past the pH 7 mark, you may use the backup MOH solution and attempt to bring the pH back up 41. For 0.1 and 1 mM solutions, usually bringing the pH back up works as long as the pH 5 mark has not been exceeded 42. If you cannot get the pH to raise significantly, you will have to repeat the entire procedure from the beginning aside from the acid preperation 43. Once a pH of 7 is reached cover MCl the solution with parafilm 44. Label the film with the date, solution name, concentration, pH, and temperature 45. Store near the nanofluidic device testing area

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46. In order to clean up, dispose of all pure HCL and diluted solutions in the acid waste bin under the fume hood. Triple rinse the dedicated beakers with DI water. Waste DI from rinsing goes in waste container. 47. Dispose of all of the excess MOH solutions in the buffer waste bin. Triple rinse the dedicated beakers with DI water. Waste DI from rinsing goes in waste container. 48. Dispose of all weighing dishes, spatulas, and droppers in the solid waste bin. Droppers should not be full of fluid. 49. Be careful not to touch the lip of the glass ware to any of the waste surfaces 50. Store the glassware lip down on towels to dry 51. Rinse the pH probe before putting it back in pink storing solution. Dilution Procedure for 0.1 mM MOH 52. Make 150 mL 1mM MOH “parent” solution 53. Measure 15 mL of “parent” solution with graduated cylinder 54. Add to 135 mL of DI 55. You now have 150 mL of 0.1mM MOH Process for 10 mM and 100 mM pH controlled divalent electrolytes 56. Make 150 mL of 10 mM (100 mM) M(OH)x solution 57. Make 150 mL of 10 mM (100 mM) MClx solution 58. The MCl solution should be slightly acid and the MOH solution should be slightly basic 59. Add MOH solution to MCl solution 1 drop at a time, stirring well after each addition, until the solution is at pH 7

C.2.2 Device Testing

Process for Ungated Device Testing

Materials

 Keithley 6485 Picoammeter  2 Keithley 3390 Arbitrary Waveform Generators (Function Generators)  Prepared electrolyte solution  Disposable pipette (Fisher 13-711-9AM)  Freshly plasma treated gated nanofluidic device  Kim Wipes  Alfa Aesar 99.9% pure gold wires corresponding to the desired electrolyte (2 short, 1 “U” wire)  Corresponding test leads

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 Computer with Labview

Process

1. Turn on the picoammeter and the function generator at least 30 minutes before beginning device testing. Connect a coaxial able to the output of each instrument. Ensure both instrument are connected to the computer. Make sure the test leads enter the Faraday cage through the small side holes. 2. Press the utility button on the function generator. Press the DC soft key. NOTE! VERY IMPORTANT! The output voltage is TWO TIMES the reading in DC mode on the front panel of the function generator. 3. After removing the device from the oxygen plasma, load the electrolyte solution into the microchannels 4. Use a clean dropper and place one drop of electrolyte solution in one reservoir of each microchannel 5. Use the Edwards RV8 pump with the long hose attachment. Seal the hose over the dry reservoir for each microchannel. Hold for 10 seconds. The pump is not designed to pump liquid. Ensure as little liquid as possible goes into the pump. Ensure the hose is very long. 6. Add a drop of electrolyte to each reservoir. Dry off excess with a KimWipe. Excess electrolyte can create a conduction path on top of the device 7. Use microscope to confirm the microchannels and reservoirs are completely full 8. Locate gold wires dedicated for the electrolyte solution being used for testing 9. Place the device in the Faraday cage on top of a 1 mm thick glass slide. This will prevent current paths from the cables connected to the gate electrodes to the cage. 10. Clip the “HI” (red) lead from the Keithley 6485 picoammeter coaxial cable onto the “U-shaped” gold wire. Insert one end of the Au wire into each reservoir of one microchannel. Only the co-axial cable can be used. Do not use alligator to banana leads to increase the length of the cable. This will introduce measurement noise. 11. Connect the HI (red) side of the Keithley 3390 function generator to two banana to alligator cables. This won’t introduce additional measurement noise. Clip a gold wire into each alligator clip. Place the wires in the other two microchannel reservoirs (they should be in the SAME MICROCHANNEL) 12. Connect black leads of picoammeter and function generator. The picoammeter is now in series with the device and the function generator. Ensure the clips don’t contact the Faraday cage. Place a 1 mm thick glass slide under the clips. 13. Open LabView program. Instruments must be on before the program is opened. Click file folder icon. Select a .CSV file for the data to be saved. 14. Adjust Start and stop voltage, voltage step size, and time at each step 15. Run the program. The voltage, time, and measured current will be saved in the .CSV file. The time is taken from a LabView counter.

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Process for Gated Device Testing

Materials

Process

1. Turn on the picoammeter and both function generators at least 30 minutes before beginning device testing. Connect a coaxial able to the output of each instrument. Ensure the picoammeter and the function generator that’s going to be used to supply the gate potential are connected to the computer. Make sure the test leads enter the Faraday cage through the small side holes. 2. Press the utility button on the function generators. Press the DC soft key. NOTE! VERY IMPORTANT! The output voltage is TWO TIMES the reading in DC mode on the front panel of the function generator. 3. After removing the device from the oxygen plasma, load the electrolyte solution into the microchannels 4. Use a clean dropper and place one drop of electrolyte solution in one reservoir of each microchannel 5. Use the Edwards RV8 pump with the long hose attachment. Seal the hose over the dry reservoir for each microchannel. Hold for 10 seconds. The pump is not designed to pump liquid. Ensure as little liquid as possible goes into the pump. Ensure the hose is very long. 6. Add a drop of electrolyte to each reservoir. Dry off excess with a KimWipe. Excess electrolyte can create a conduction path on top of the device 7. Use microscope to confirm the microchannels and reservoirs are completely full 8. Use a razor to scrape the PDMS from the electrode contact pads corresponding to the gate you would like to use

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9. Cut 2 small (~2cm) lengths of the copper wire. This wire is covered in an insulative coating that must be scraped off with a razor 10. Using a small square of copper tape, attach the copper wore to the electrode intended for testing. One wire should be attached to each contact pad. Ensure the copper tape does not touch multiple contact pads 11. Use the electrical tape to cover all copper on the bottom on the device so as not to form a short to ground 12. Locate gold wires dedicated for the electrolyte solution being used for testing 13. Place the device in the Faraday cage on top of a 1 mM thick glass slide. This will prevent current paths from the cables connected to the gate electrodes to the cage. 14. Clip the “HI” (red) lead from the Keithley 6485 picoammeter coaxial cable onto the “U-shaped” gold wire. Insert one end of the Au wire into each reservoir of one microchannel. Only the co-axial cable can be used. Do not use alligator to banana leads to increase the length of the cable. This will introduce measurement noise. 15. Connect the HI (red) side of the Keithley 3390 function generator used to supply the axial potential (the one NOT connected to the computer) to two banana to alligator cables. This won’t introduce additional measurement noise. Clip a gold wire into each alligator clip. Place the wires in the other two microchannel reservoirs (they should be in the SAME MICROCHANNEL) 16. Connect the HI side of the second function generator to two more banana to alligator cables 17. Connect black leads of picoammeter and both function generators. The picoammeter is now in series with the device and the axial function generator. The gate and axial potentials are now applied with respect to the same ground for a common reference. Ensure the clips don’t contact the Faraday cage. Place a 1 mm thick glass slide under the clips. 18. Close the door of the Faraday cage. NEVER OPEN THE FARADAY CAGE WHILE THE TEST IS RUNNING. Do not bump or move the test leads. Don’t move anywhere near the Faraday cage while the test setup is running. 19. NOTE ON SAFETY: Close the Faraday cage with ALL POTENTIALS OFF. Reach in through the side of the cage to turn on the axial potential. The function generator should be on the opposite side of the cage, nowhere near the bare wires. NEVER OPEN THE CAGE WHILE THE POTENTIAL IS ON. ENSURE BOTH GATE AND AXIAL POTENTIALS ARE OFF BEFORE OPENING THE CAGE. If the Labview program freezes with the voltage on and you can’t 0 the voltage using the program, shut off the function generator. 20. Open LabView program. Instruments must be on before the program is opened. Click file folder icon. Select a .CSV file for the data to be saved. 21. Turn on the axial potential by pressing the “output” button 22. Adjust Start and stop voltage, voltage step size, and time at each step for the gate potential 23. Run the program. The gate voltage, time, and measured current will be saved in the .CSV file. The time is taken from a LabView counter.

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24. When finished testing, dry the device in the glass vacuum desiccator for at least 15 minutes

Modifying the setup for gate leakage current test

Materials

Process

1. Connect a U-shaped copper wire to one gate electrodes with copper tape and electrical tape (see above) 2. Connect the HI side of the picoammeter to the center of the U-shaped copper wire 3. Connect one function generator to the computer. The Hi side of the function generator can be connected to a. Left microchannel b. Right microchannel c. All four reservoirs using banana to alligator test leads and Au wires 4. Run the voltage sweep. The measured current is now the leakage current

Notes on Device Testing

5. ALWAYS start with the lowest concentration of electrolyte. For example, once a 10 mM solution of KCl has been added to a device it cannot be used for concentrations lower than 10 mM KCl

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6. When moving to the next highest electrolyte concentration, treat the device in the plasma. Run device testing. Dry the device. Repeat with the same concentration. The first run LIKELY HAS A CONCENTRATION that is the average of the previous and the new concentration. Ideally data taken on the third testing run with a given concentration should be used 7. The plasma degrades the PDMS. This causes PDMS cracking around the reservoir which receives the most exposure. Plasma treatment is primarily a diffusion based process but pressure gradients between the inside of the channel and the chamber also contribute. Eventually the device will fail, evident by significantly increased axial conductance or gate leakage (compared to expected values for a given concentration). Take this into consideration when designing the parameter space 8. DI conductance of a newly fabricated device can be measured to serve as a reference point between devices. DI conductance depends on surface charge density, channel width, channel length, and number of “open” channels. 9. Use dedicated devices for each electrolyte and dedicated Au wires to avoid contamination / unreliable results (if comparing electrolytes). Use the DI conductance / calibration point

NOTE ON NOISE: Whenever a new setup is designed, connected, or used run a noise measurement. This ensures that there are not stray current paths between instruments or other sources of noise (triboelectric effects, etc.). Connect all test instruments, test leads, and the computer that will be used in the device testing setup. Place the test leads in the Faraday cage. Ensure they are not touching the cage. Run the Labview program with the circuit “open” i.e. the clips should not be connected to the device. The noise current should be consistent with instrument specifications and should be independent of the applied potential. If this is not the case, troubleshoot the system. Repeat this measurement with the setup connected to a dry device. USE A BRAND NEW NEVER TESTED DEVICE. Confirm it is dry in the microscope. Sometimes water condenses in the channels post-bonding. This measurement will ensure there are not stray current paths through the device, or from the test leads to the Faraday cage.

How to Turn on the Microscope

Process

1. Remove the dust cover 2. Turn on the microscope. Ensure the white, circular key on bottom black panel is pushed in. 3. Turn on the camera power supply (black rocker switch on black box connected to camera) 4. Turn on the camera using the black rocker switch on the back of the camera 5. NEVER BUMP THE CAMERA. ENSURE THERE IS NOTHING ANYWHERE NEAR IT THAT VIBRATES. Even when it’s off 303

6. Turn on the lamp. Flip the rocker switch on the short gray box to the right towards the back of the microscope 7. Turn on the Mercury lamp if doing fluorescence experiments. The lamp is ready to be used as soon as it is turned on. It cannot be turned off for at least 30 minutes (i.e. leave it on. Repeated on and of switching destroys the bulb) 8. Use the dial on the right side of the microscope to select “Eyepiece” or “L” for the camera 9. Ensure the camera is on before opening the Nikon software. There are two versions of the Nikon software installed. One works and one doesn’t. 10. Press the green triangle “play” button to turn on the live feed 11. Objectives below the stage are adjusted manual 12. Course and fine focus are adjusted using the large and small knobs located on both sides of the microscope 13. Fluorescence requires filters. Green filter is for Rhodamine. Filters are located below the objectives. Rotate the thumb wheel to select a filter. NOTE: Dye emission is pH dependent

C.3 Supplementary Process Sheets

SC-I Clean for Electrode Slides

Materials

 Hot plate  Sample tweezers (TDI International #TDI 2ABCPR-SA)  Acetone ( > 25 mL)  IPA ( > 50 mL)  DI ( > 1125 mL)  Glass Top Covers  Sample holder  “BOE” Nalgene beaker  10:1 Buffered Oxide Etch (50 mL)  “DI Rinse” Nalgene beaker  “SC-I” beaker  Hydrogen Peroxide (30 mL)  Ammonium Hydroxide (3 mL)  Thermometer and thermometer holder

Process

1. Set hot plate to 300⁰C in chemical hood 2. Clean tweezers with acetone/IPA/DI/IPA 304

3. Clean glass slides with acetone/IPA 4. If glass was cut in the glass shop, lightly scrub with acetone soaked swabs to remove and visible debris. Rinse with acetone/IPA 5. Dry glass with N2 and place in sample holder 6. Add 350 mL H2O to “BOE” beaker 7. Place sample holder in “BOE” beaker 8. Put on gown and face shield. Test gloves with N2 before putting them on 9. Measure out 50 mL of 10:1 Buffered Oxide Etch 10. Add BOE to DI water in “BOE” beaker 11. Sonicate 1 min 12. Transfer sample holder to “DI Rinse” beaker filled with 400 mL DI water 13. Let stand for 2 minutes 14. Aspirate out BOE waste 15. Sonicate slides in “DI Rinse” beaker for 5 minutes 16. Add 300 mL DI and 30 mL Hydrogen Peroxide to “SC-I” beaker a. Measure out 3 mL of Ammonium Hydroxide b. Use a disposable pipette if the container is very full 17. Place “SC-I” beaker on the hot plate a. Add the sample holder b. Add the Ammonium Hydroxide 18. Set timer for 30 minutes a. When the temperature of the solution reaches 70⁰C, lower the hot plate temperature to 150⁰C (about 8 minutes) b. Adjust hot plate temperature to keep the solution temperature as close to 73⁰C as possible. It should spend at least 10 minutes at this temperature 19. Remove “SC-I” beaker from hot plate 20. Sonicate 5 minutes 21. Fill “IPA” beaker with 200 mL IPA and 200ml DI water 22. Transfer sample holder to “IPA” beaker 23. Let stand 3 minutes 24. Aspirate DI/Hydrogen Peroxide/Ammonium Hydroxide solution, diluting with DI 25. Rinse each slide with IPA 26. Dry with N2

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Instructions for Asylum AFM

Process

1. Computer should be on and remain on. Software can have issues if the computer is shut down. 2. Sign in: Password is data 3. Open the AFM software 4. After the software boots a pop-up will appear. Click template. 5. Turn on the second monitor if it’s not already on 6. Turn on the lamp (located under AFM table) 7. Turn on the AFM (green rocker switch on front) 8. Load the sample on the stage 9. Raise the tip slightly on the optical head. If your thumb is pointing in the direction of the tip, it raises according to the right hand rule using the thumb wheel on the front of the optical head. 10. Position the optical head over the sample with the three legs positioned in the appropriate holes 11. Turn the laser on by turning the key on the back of the computer to the on position 12. Adjust the position of the laser on the cantilever beam. The cantilever should be in view on the second monitor. If it is not press the button on the front of the monitor until it says SVideo3. You may need to adjust the mirror by using the thumb screws behind the mirror to get the cantilever in view on the screen. Use the thumb wheels on the upper right side and upper back side of the optical head to adjust the laser in x and y respectively. You want an amplitude of 6.3-6.5. 13. The thumb wheel on the upper left adjusts the detector position. Adjust the position of the detector until the deflection is 0. 14. Close AFM doors and secure the top latch 15. Go to the “tune” tab. Press auto tune 16. Confirm in the main menu that the scan mode is set to “AC mode” (tapping) 17. Press “engage” on the master menu (the one that shows the amplitude and deflection of the cantilever). 18. Z voltage should read 150 when there is no contact between the tip and sample. Amplitude should be 1.0 19. Slowly lower the tip using the thumb wheel (CCW). 20. When the tip is close to the sample it will begin to interact with the sample causing a damping effect. The amplitude will be ~0.94. 21. Continue lowering the tip until the Z-voltage is between 60 and 70 306

22. Now you are ready to start scanning 23. Set the scan size. Note a scan size of 5 microns refers to a 5 micron by 5 micron square scan on the sample 24. Set scan rate (0.57 Hz is a good number) 25. X/y offset can be adjusted to scan the area of interest on the sample. To make larger adjustments and change the area of interest “withdraw” the tip and use the x/y thumb screws to move the sample stage. “Engage” the tip before scanning. The stage CANNOT be translated when the tip is engaged. You can focus on the sample to help find the area of interest by turning the wheel just in front of the mirror that sits behind the optical head. The screws on the back of this mirror adjust the area you can see with the camera. 26. The following parameters are adjusted so that the trace and retrace follow the same path as exactly as possible. Some good rule of thumb values are; Set point = 691mV; Integral Gain = 9.69; P Gain = 2.09. Note: The AFM tries to hold a constant feedback signal equal to the set point. If the set point is set too high the tip will be in too hard of a contact with the surface and may break. 27. Once the appropriate parameters have been defined press scan 28. You must stop the scan else when the AFM has finished the first scan it will take another (and another…) 29. Do not change the set point, gain, x/y offset or sample position while scanning. 30. When you are finished press “withdraw”. This is a VERY IMPORTANT step as it turns off the Z voltage. 31. Raise the cantilever by rotating the thumb wheel on the front of the optical head CW 10-12 times 32. Turn off the laser (Key on the back of the computer) 33. Open the AFM doors 34. Remove the optical head being careful not to bump the mirror 35. Remove sample 36. Turn off the AFM (green rocker switch) and the light (below AFM stage) 37. Close the doors 38. Close the software 39. DO NOT SHUT OFF COMPUTER

Notes on the AFM software:

1. In the master panel on the height tab: save the image with no changes (i.e. no flattening) 2. Once the scan is finished it will save the image as whatever you have entered as the file name. You can change this on the master panel before the scan finishes. 307

3. Double click on an image in your folder to analyze it 4. “3D” button shows a 3D topographical image 5. “M” brings up the screen to flatten. This must be done to correct for the fact that no surface (and therefore your sample surface) is truly flat. This must be corrected for by the software. 6. “A” brings up the screen to do analysis of the image including surface roughness and cross section. Make sure you flatten the image before analyzing or your numbers will be wrong. Image can be masked to choose a section to measure the surface roughness. The whole image won’t work when scanning a channel as it will call your etched channel “roughness”. 7. To measure a cross section; Click draw. Position two cursors on image to define a line. When the cross section window comes up drag and drop cursors A and B from the bottom tool bar to desired points to measure dx and dy. 8. Export a data report by clicking Lx

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Appendix D: Matlab Codes

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%Picoammeter Data %The code works by looking for a change in the voltage value or a decrease in the time stamp %(column 1 in .csv file) clc; clear; format long filename=input('filename?') M = csvread(filename); I=M(:,1); %vector containing all values of first column of Excel Sheet - Voltage J=M(:,2); %vector containing all values of second column of Excel Sheet - Time K=M(:,3); %vector containing all values of third column of Excel Sheet - Current i=1; j=1; while i<=length(I); n=1; B(n)=K(i); while (i

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%Calculation of Chemical Surface Charge %summation of all of the charged cites times the fundamental unit of %charge clear %Experimental Parameters pH=6; Kb=1e-3; %bulk concentration of K+ in moles/liter Cab=(1/3)*10^(-3); %bulk concentration of Ca2+ in moles/liter Hb=10^(-pH); %bulk concentration of protons in mol/liter OHb=10^(-14+pH); %bulk concentration of OH in mol/liter

%ionic strength of 2:1 electrolyte for Grahame below zcat2=2; zan2=-1; ccat=Cab*1000; can=2*ccat; ionics=0.5*(zcat2^2*ccat+zan2^2*can)%for CaCl2

%Constants e=1.609e-19; %Fundamental Unit of charge epse=78.54*8.854187817e-12; %permitivity F=96485; %Faraday T=298; %temp R=8.315; %gas constant B=F/R/T;

%Guess a range for the surface potential - 25mV or so for pH 7 glass psi=linspace(-0.2,0.0,20000);

%Boltzmann Distribution - assumed for all ions in solution Hs=Hb.*exp(-B.*psi); %surface activity of H+ gam=4.8e18; %total number of cites per m^2

% Derived from the law of mass action pK1=8; %deprotanation pK2=1; %protanation pKM=3; %ion exchange / monovalent adsorption pKD1=2.5; %divalent ads 1 - SiOH + OH- + Ca2+ react to SiO2HCa+ + H+ pKD2=6.3; %divalent ads 2 - SiOH + Ca2+ react to SiOCa+ + H+

K1=10^(-pK1); K2=10^(-pK2); KM=10^(-pKM); KD1=10^(-pKD1); KD2=10^(-pKD2);

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A1=K1./Hs; %gamÔ- = A1*gamÔH - deprotonation A2=Hs./K2; %gamÔH2+ = A2*gamÔH - protonation AM=KM.*Kb./Hb; %gamÔK = AM*gamÔH - ion exchange / monovalent ads AD1=OHb.*Cab.*KD1./Hb; %divalent adsorption 1 AD2=Cab.*KD2.*exp(-psi.*B)./Hb; %divalent adsorption 2

%Use as many of the "A" equations as desired to write equations for sig %Full form is sig = e*gam(charged cites)/(1+gamÔK+charged cites) %being careful of the sign %Comes from gam = gamÔH + charged cites+gamÔK

%Surface Charge From Surface Chemistry

%General sig1=-e*gam.*A1./(1+A1); %deprotonation only sig2=e*gam.*(A2-A1)./(1+A1+A2); %deprotonation and protonation

%Monovalent sig3=-e*gam.*(A1)./(1+A1+AM); %deprotonation, K+ ads

%Divalent sig4=e*gam.*(-A1)./(1+A1+AD1);%deprotonation, protonation, Ca2+ 1 sig5=e*gam.*(AD2-A1)./(1+A1+AD2);%deprotonation, protonation, Ca2+ 2 sig6=e*gam.*(AD2-A1)./(1+A1+AD1+AD2);%deprotonation, protonation, Ca2+ both

%Mixture sig7=e*gam.*(A2+AD1+AD2-A1)./(1+A1+A2+AD1+AD2+AM);%deprotonation, protonation, K+, Ca2+ both

%plot(psi,sig1,'-r',psi,sig2,'-b',psi,sig3,'-g',psi,sig4,'- k',psi,sig5,'-c',... %psi,sig6,'-y',psi,sig7,'-m')

%Surface Charge from one integration of Poisson Boltzmann %(Grahame Equation)

%Monovalent sigM=sqrt(8*R*T*epse*Kb*1000).*sinh(B.*psi./2);%converted Kb to mol/m^3

%2:1 Electrolyte CaCl2 sigD=-sqrt(2*ionics*R*T*epse).*sqrt(exp(-2.*B.*psi)+exp(B.*psi)-3); sigD2=sqrt(2*ionics*R*T*epse).*sqrt(exp(-2.*B.*psi)+exp(B.*psi)-3);

%figure plot(psi,sig5,'-b',psi,sig4,'-r',psi,sig6,'-m',psi,sigD,'-k')

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Appendix E: Permission to Reprint

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Please refer to the supplemental file for the permissions to reprint.

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