Limit of Detection of Silicon Biofets

Abstract

Limit of Detection of Silicon BioFETs

Nitin K. Rajan

Yale University

2013

Over the past decade, silicon nanowire/nanoribbon ﬁeld-eﬀect transistors (NWFETs) have demonstrated great sensitivity to the detection of biomolecular species, with limits of detection

(LOD) down to femtomolar concentrations. Several well known factors limit the LOD; among them, screening effects, efficiency of the biomolecule-specific surface functionalization, binding kinetics and equilibria, and the delivery of the analyte to the sensor surface. Recently, the noise properties of such biosensors have been receiving more attention, both as a factor that determines the LOD as well as a diagnostic tool to extract information about the electronic properties of the FET sensors.

However, the signal-to-noise ratio (SNR) of these bioFET sensors, and the device parameters that determine the LOD, are not well understood.

We discuss our experiments on applying noise spectroscopy to silicon NWFETs with the goal of understanding and improving the detection limit of such devices. Using low frequency noise measurements and modeling, we are able to compare different devices/material systems and quantify the effect on device performance of different process parameters. We also consider the effects of temperature on the noise generating mechanism and investigate the fundamental origin of 1/f noise in these devices.

We then introduce SNR as a universal performance metric, which includes both the eﬀects of noise and signal transduction, and we show that the SNR is maximized at peak transconductance due to the eﬀects of 1/f noise, and not in the subthreshold regime where sensitivity is maximized.

We also correlate the LOD predicted by the measurement of the SNR to pH sensing experiments, highlighting the relevance of this metric for the ultra-sensitive detection of biomolecules. The eﬀects on the SNR, of surface functionalization, gating scheme and device scaling are also considered and

i quantiﬁed, yielding interesting results which will have a profound impact on the design of sensors with lower LOD.

The nanowire-based devices have shown a theoretical LOD of 4 electronic charges, ignoring the eﬀects of screening. Using these devices, with very good performance in terms of SNR, we were able to measure and extract the binding kinetics of protein interactions, which have never been done with NWFETs. Binding constant (KD) determination is a critical parameter for biomolecular design and has until now been primarily assessed by surface plasmon resonance (SPR). The KD determines the magnitude of the sensor signal for a particular concentration of analyte and therefore, is an important factor in determining the smallest measurable concentration. Utilizing the low LOD and reproducibility of sensing signals from our bioFETs, we study the reaction kinetics of low and high

KD systems and demonstrate the viability of the bioFET platform as a potential replacement for

SPR.

Our investigation of different solution gate electrodes and their noise performance show that both the accuracy of biosensing results and the LOD are significantly affected by the choice of the solution gate electrode. A full reference electrode is difficult to integrate into a miniaturized system and pseudo reference electrodes require careful control of the sensing buffer in order to avoid measurement artifacts. We finally propose and demonstrate some intial results on the integration of an on-chip Ag/AgCl pseudo reference electrode for improved noise performance and better LOD, especially under fluid flow conditions.

ii Limit of Detection of Silicon BioFETs

A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy

by Nitin K. Rajan

Dissertation Director: Mark A. Reed

December 2013 Copyright c 2014 by Nitin K. Rajan

iv To my grandfather,

Dharma V. Rajan

v Vitae Non Scholae Discendum

vi Acknowledgments

I acknowledge my advisor, Mark Reed, ﬁrst and foremost. This thesis would not have been possible without his guidance and constant support, especially when experiments did not work out as planned. I am deeply grateful for the freedom I enjoyed, under Mark’s guidance and encouragement, to explore various ideas. A lot of them did not work out and are not mentioned in this thesis but they resulted in stimulating discussions between Mark and myself, and helped shape my research methodology. This modus operandi of thinking outside the box and trying out diﬀerent ideas, which is a cornerstone of his research philosophy, kept my inquisitive spark alive and made graduate school both intellectually rewarding and plenty of fun.

I am indebted to Professor T. P. Ma for his suggestions and insightful comments regarding my thesis. He is not only a brilliant scholar but also an excellent teacher, and will serve as a model for my future academic career. Professor Tarek Fahmy has been an invaluable asset and collaborator for the Reed Lab during my Ph.D. and I really hope it stays that way for many years to come.

I am grateful for Tarek’s genuine interest in my thesis as well as his friendship during the past six years. Last but deﬁnitely not least, I would like to thank Professor Robert Schoelkopf for his helpful suggestions and unwavering support.

My journey in the academic world would not have been possible without the support of my family. My parents Ashok Rajan and Radha Rajan, made the sacriﬁce of having their son be two oceans away, so I could study Physics in the US. My father constantly pushed me to develop my critical thinking and taught me, at an early age, to ask questions. My mother taught me

vii to be patient, as she spent countless hours helping me study when I was very young. I am sure the completion of this latest chapter of my life makes them even more proud and they can rest assured that it was all worth it. My sister, Neeha Rajan, deserves a special mention for making me laugh more than anybody else in the world. Graduate school can be hard sometimes, but having somebody with such an iridescent personality in one’s life makes it easier, brighter.

Throughout the years, my path has crossed those of many other graduate students and post- docs. I am extremely thankful for what I learned from them as well as for their friendship. I cannot name them all here, but I have to acknowledge the part they played in my growth as a scholar and more importantly, as a human being. Aleksandar Vacic was a true friend and colleague, who took me under his wing when I first started in the lab and taught me the ropes of the lab which set the foundation for this thesis. He was a great mentor and I always enjoyed the stimulating discussions we had about research, politics, religion and philosophy. As he would like to say, we worked hard and played hard. Weihua Guan’s friendship has been equally invaluable over the years. Within the lab, he is a prolific scientist and I am thankful for the numerous discussions we have had and for what I have been fortunate enough to learn about the process of rigorous scientific thinking. Beyond the lab, the adventures we had made graduate school a very lively period and sometimes even a surreal one. Xuexin Duan and I started collaborating as soon as he joined the lab as a post-doctoral researcher. His scholarship is commendable, his patience is remarkable and his sensitivity makes him a great person to have as a friend. I enjoyed working with him and taking long afternoon breaks discussing science as well as life. Having perspective is extremely important in graduate school and

Xuexin helped me in acquiring some. Another post-doc who was intrumental in my development as a researcher is Eric Jung. His scholarship is well recognized and his simplicity and work ethic are both admirable. I am honored to have known him and I am grateful for his friendship.

Other graduate students at Yale who have been important during my graduate school career, even if our paths crossed only brieﬂy, are: Ryan Munden, David Routenberg, Monika Weber,

Mary Mu, Sylvia Li, Shari Yosinski, Sonya Sawtelle, Zak Kobos, Ben Leung, Xiao Sun, Danti

Chen, Ge Yuan, Daniel Mugaburu, Andrew Zhang, Ricardo Monsalve, Mariana Melo-Vega, Laurie

viii Lomask, Manuel Clemens, Brian Shotwell and Zuhair Khandker. Graduate school has also been an opportunity for mentoring undergraduate students and in the process I have had the honor to work with and eventually built friendships with some truly amazing and brilliant students. They made research more interactive and less lonely, and I am forever thankful to them: Cathy Jan, Jin

Chen, Bo Fan, Shashwat Udit, Vijay Narayan, Paschall Davis and Kara Brower.

None of this thesis would have been possible without the support of many Ithaca College faculty members who I worked closely with and learned so much from. Professors Bruce Thompson, Beth

Clark Joseph, Ali Erkan, Matt Sullivan, Luke Keller, David Brown and Marty Sternstein helped shape my interests and my ability to pursue them, through their teaching, advising and genuine support. My friends, from my college years, deserve a lot of gratitude for being caring and supportive companions during that time: Reuben, Adhish, Elvis, Maksim, Semeret, Innocent, Tendai, Jani,

Goodmore, Doreen, Cathy, Nuha, Alex, Sigurd and Nirbhik.

Finally, I would like to thank the administrative and research support staﬀ at Yale University.

Vivian Smart has brightened so many of my days with her snappy comments and her great sense of humor. She was always genuinely interested in helping me with ordering, shipping or simply bearing with me whenever I needed a break from lab. Arlene Ciocola was always very professional and a pleasure to talk to. The cleanroom staﬀ, namely Michael Power, Chris Tillinghast and Jim

Agresta were always helpful and willing to go the extra step whenever I needed assistance with the cleanroom or with lab equipment and parts. Michael Rooks also deserves a special mention for his assistance and training with the YINQE facilities, as well as his genuine interest in my research projects.

I am very sad to leave the Reed lab, but I am also excited by the current crop of graduate students who without doubt, will be very successful. To you then, whenever the journey gets tough, I hope this quote from Randy Pausch helps:

Experience is what you get when you didn’t get what you wanted. And experience is

often the most valuable thing you have to oﬀer.

ix Contents

List of Figures xiii

List of Tables xxviii

1 Introduction 1

1.1 Overview...... 1

1.2 Performance Metrics...... 4

2 Theoretical Considerations6

2.1 Working Principle of an ISFET...... 6

2.2 pH Sensing...... 9

2.3 Biomolecular Detection...... 12

2.4 Low-Frequency Noise...... 15

3 Device Fabrication and Electrical Characterization 19

3.1 Nanoribbon Device Fabrication...... 19

3.2 Multiplexed Detection Setup Gen.1...... 25

3.3 Multiplexed Detection Setup Gen.2...... 27

3.4 Low Frequency Noise Measurement...... 28

3.5 Lock-in Ampliﬁer Measurements...... 30

3.6 Summary...... 35

x 4 Low Frequency Noise of BioFETs 37

4.1 Introduction...... 37

4.2 Eﬀects of Etching Process on BioFET Characteristics...... 38

4.3 Temperature Dependence of 1/f Noise Mechanisms...... 44

4.4 Random Telegraph Signals...... 49

4.5 Summary...... 58

5 Signal-to-Noise Ratio as a Performance Metric 60

5.1 Introduction...... 60

5.2 Sensitivity...... 61

5.3 Optimal Operating Regime for BioFETs...... 68

5.4 Inﬂuence of surface functionalization...... 75

5.5 Gate Coupling...... 78

5.6 Device Scaling...... 81

5.7 Summary...... 87

6 Binding Aﬃnity Considerations 89

6.1 Introduction...... 89

6.2 BioFET as an aﬃnity sensor...... 92

6.3 Binding Kinetics Simulator and SNR...... 93

6.4 High KD Case...... 98

6.5 Low KD Case...... 100

6.6 Summary...... 103

7 Reference Electrode 105

7.1 Introduction...... 105

7.2 Electrode requirements for pH sensing...... 106

7.3 Electrode noise and its eﬀects on SNR...... 112

xi 7.4 Inﬂuence of the reference electrode on charge sensing...... 116

7.5 Outlook on integration of on-chip reference electrode...... 118

7.6 Summary...... 121

8 Conclusions 123

References 128

xii List of Figures

1.1 Schematic of a typical bioFET measurement. The baseline current is changed by

the binding of analyte molecules (green cirlces) due to the additional electric ﬁeld

induced by the charged analyte...... 2

2.1 Schematic of a device and the experimental setup...... 7

2.2 This ﬁgure shows an example of how the applied potential Eref is distributed

throughout the diﬀerent layers of materials involved in the ISFET device structure

as well at the solid-liquid interfaces...... 8

2.3 Circuit model of a typical ISFET sensing setup, showing the voltage drops across

the double layer and silicon device...... 10

3.1 Fabrication Process Flow for Silicon Nanoribbon FET Devices...... 20

3.2 (a) Optical micrograph of a 3.3 mm x 3.3 mm die which is the smallest die we used

in this thesis. (b) Optical image of a larger die size, 6.6 mm x 6.6 mm, which makes

it easier to integrate an external micro-reference electrode into the ﬂuidic cell. The

four on-chip Pt electodes are also clearly visible, extending into the middle of the die. 21

3.3 (a) Optical micrograph of a single nanoribbon device with length and width of 20 µm

and 2 µm respectively. (b) Image of a ﬁve-channel device with each channel being

20 µm long and 2 µm wide. (c) A 10-ﬁngered device with L = 10 µm and W = 1 µm. 22

xiii 3.4 Optical micrographs showing devices where the SU-8 passivation windows were not

completely cleared. The problem is more signiﬁcant for smaller openings. Treating

the devices to oxygen plasma can be used to get rid of the SU8 residues...... 23

3.5 (a) Scanning electron micrograph of a single metallized nanoribbon device, without

the SU-8 passivation layer. (b) SEM image of an array of parallel nanoribbon devices

with the SU-8 passivation layer opening clearly visible in the center. The metal leads

to each device can also be easily seen...... 23

3.6 Scanning electron micrograph of a nanowire device with width of 200 nm and length

of 4 µm...... 24

3.7 Transfer characteristics for a solution gated bioFET device, showing the low threshold

voltage (≈ 1.1V) as well as the low gate leakage current (shown in red and ≈ 20 pA) 24

3.8 Ampliﬁer circuit using an operation ampliﬁer (LT1012) for current to voltage

conversion of the drain current ﬂowing through the bioFET device...... 25

3.9 Photograph of the experimental setup using a connector box, an 8-channel ampliﬁer

stage and a connection panel which interfaces to the NI DAQ card...... 26

3.10 Main Display panel for Labview software designed to concurrently measure 8

recording channels...... 26

3.11 PCB board with assembled components for portable sensing measurements consisting

of on-board ampliﬁcation channels as well as biasing voltages...... 27

3.12 Gate leakage current measurement circuit for PCB board setup Gen.2. The

sense resistor was chosen such that the circuit is optimized for leakage current

measurements around 1 nA. The voltage after the resistor is measured by Analog

Input (AI) of the DAQ card. The leakage current is then calculated from (Vgs −

Vmeas)/Rsens...... 28

3.13 Modiﬁed periodogram method for estimating the power spectrum of a signal. The

algorithm consists of two user deﬁned parameters which are the length of each

periodogram (M) and the degree of overlap (D) between periodograms...... 29

xiv 3.14 (a) 1/f spectra for a bioFET device biased in strong accumulation, interfaced using

the three measurement setups outlined in this section. It is clear that the Portable

setup (Gen.2) performs just as well as the single channel low noise measurement

setup for low frequencies whereas the multi-channel setup (Gen.1) has a very high

noise background. (b) Noise proﬁle for the same bioFET device (extracted at f = 1

Hz) showing the dependence of the noise on the gate bias voltage or drain current.

Again, the portable sensing setup has a similar performance to the single channel

setup except for low current values...... 31

3.15 Normalized noise power spectra of the conductance of a bioFET device as measured

by a lock-in ampliﬁer. The 1/f reference (dashed line) shows that the intrinsic 1/f

noise of the DUT is not aﬀected by the choice of the AC modulation frequency.... 33

3.16 SNR and DC transconductance (gm) as a function of gate voltage in the case of a

DC source-drain bias...... 34

3.17 SNR and AC transconductance (gm, G) as a function of gate voltage in the case of

an AC modulation of the source-drain bias...... 35

3.18 pH calibration curve for a bioFET sensor using the lock-in technique. The AC

current response (proportional to the conductance at Vds = 0) of the PSD is plotted

as function of time, showing the stability of the time traces when an AC source-drain

modulation is used...... 36

4.1 Summary of Hooges parameter (αH ) for diﬀerent nanowire materials as well as

sub-micron MOS structures utilizing high-k dielectrics. Included is our best SOI

silicon nanowire device (red circle). The dash-dotted line shows the ITRS roadmap

speciﬁcation of αH for the 45nm technology node (Adapted from [46])...... 39

xv 4.2 SEM images of two nanowires (NWs) etched using an orientation dependent wet etch,

TMAH, and the other one etched using a dry RIE etch chemistry involving Cl2.

TMAH etches (100) planes faster than (111) planes and the resulting trapezoidal

shape can be clearly seen in the SEM image. The device etched using Cl2 has a more

rectangular cross section as expected from an anisotropic RIE etch...... 40

4.3 Plot of noise amplitude, A, as a function of the drain-to-source voltage (Vds) at a

ﬁxed gate voltage, clearly showing that A is independent of the drain current if the

number of charge carriers remains unchanged...... 41

4.4 Typical dependence of 1/f noise spectra on gate voltage for a TMAH-etched device,

from which the noise amplitude A, at each gate voltage (13 - 25 V), can be extracted.

The inset shows 1/A plotted as a function of Vg, where the slope of the line is used

to calculate αH ...... 42

4.5 (a) Measured Hooge parameters for three sets of devices. Each set was etched using

either TMAH or Cl2 or CF4. The box plot shows the 25th percentile, the median, and

the 75th percentile (the mean is indicated by asquare marker). The average values

of αH were 0.0021 for the TMAH devices, 0.015 for the Cl2 devices, and 0.017 for

the CF4 etched devices. (b) Measured subthreshold swing for three sets of devices,

etched using either TMAH or Cl2 or CF4. The average value for the TMAH devices

was 1.0 V/decade. For Cl2 etched devices, the average was 2.6 V/decade, and for

CF4 devices, the average was 3.0 V/decade...... 43

4.6 Typical noise spectra measured for a device at diﬀerent gate voltages (22 - 40 V)

from subthreshold to strong inversion. The exponents of the 1/ f spectra all lie in

the range 0.8 < β < 1.2. The ﬂattening of the noise spectra is due to background

noise from the measurement setup...... 45

xvi 4.7 Normalized drain current noise amplitude at f=1 Hz (A) is plotted against drain

2 current (Id). Measurements at room temperature (300 K) compared to the gm/I

curve clearly indicate that the device follows the correlated ∆n-∆µ noise model. For

measurements carried out at 100 K, the noise amplitude is consistent with a carrier

number ﬂuctuation noise ( ∆n) model as indicated by the change in slope compared

to the 300 K data in the strong inversion region...... 46

4.8 (a) The data show the gradual change of the slope in the strong inversion regime

as temperature is lowered at T=300, 250, and 100 K, respectively. The data points

for 250 and 100 K have been scaled for easier visualization of the change. (b) The

data are ﬁtted using the correlated ∆n-∆µ noise model, conﬁrming the change in the

noise generating mechanism as the temperature decreases. The Coulomb scattering

coefficient, α, is also extracted from linear fits to the data at 250 and 300 K. The fit

to the data at 100 K clearly indicates that the correlated model is no longer valid at

that temperature...... 47

4.9 Plot of mobility as a function of temperature for 2 NW devices, showing the increase

in mobility as temperature is decreased due to suppressed phonon scattering..... 49

4.10 Evolution of the normalized noise power spectral density from room temperature

(300 K) to 120 K for a NW device. At certain gate voltages and at low temperature

(120 K), only a few traps are active and contribute to the noise spectrum, which

consequently changes from a 1/f spectrum (with the dotted line representing a 1/f

least-squares ﬁt) to a Lorentzian superimposed on a 1/f trend, evident for the larger

frequencies (with the solid line representing a Lorentzian least-squares ﬁt with a

corner frequency of 25 Hz)...... 50

4.11 Illustration of RTS in a current-time trace, showing two discrete current levels with

characteristic times τ0 and τ1, representing the low and high current states respectively. 51

xvii 4.12 Computed results showing how the addition of Lorentzian spectra due to discrete

two-level trapping systems can and indeed does result in 1/f noise spectra for an

ensemble of such traps...... 51

4.13 A segment of drain current versus time measurement for a NW bioFET device

showing the discrete two-level switching, indicating the activity of a single trap

resulting in RTS...... 52

4.14 Normalized noise spectra at diﬀerent gate voltages showing the typical Lorentzian

spectra associated with RTS. As the voltage is increased to 27 V, it is clearly seen

that the Lorentzian spectrum is changing to a 1/f spectrum, indicating a gate voltage

dependence of the RTS...... 53

4.15 Histogram of current values showing the bimodal distribution characteristic of a two-

level switching signal. The changes in trap occupancy as the gate voltage is varied

can be seen as changes in the populations of the “low” and “high” current states.

From the changes evident in the histograms, we conclude that the active trap in this

case is an acceptor trap, that is the trap is charged when ﬁlled and neutral when

empty...... 55

4.16 Plot of the capture (τc) and emission (τe) times as a function of gate voltage at

a temperature of 130 K. The inset shows the typical distribution of times which

follow a Poisson distribution. An exponential or Poisson ﬁt allows us to extract the

characteristic emission and capture times...... 56

4.17 Arrhenius plot of the characteristic emission time (τ0) and capture time (τ1) as

a function of temperature. From the slope, the thermal activation energy of the

capture and emission processes can be extracted.Ea, e = 250 meV and Ea, c = 180

meV...... 56

4.18 Arrhenius plot of the corner freqency (estimated from the noise power spectra) at

diﬀerent temperatures. The linear ﬁt shows that fc can be modeled by a thermally

activated process with an activation energy of 230 meV...... 57

xviii 4.19 Relative amplitude of RTS plotted as a function of the inverse of drain current

(1/Id). The linear ﬁt shows that the data agrees well with the 1/N dependence of

relative RTS amplitude. The large changes in the level of the RTS noise is attributed

to changes in the scattering coeﬃcient α, resulting in diﬀerent levels of mobility

scattering...... 58

5.1 (a) Normalized current data for a pH change from pH 7.1 to pH 7.9 at diﬀerent bias

points (diﬀerent Id levels). (b) Corresponding Id-Vg curve, where the bias points used

in (a) are indicated with crosses. For measurements done closer to the threshold

voltage, the resulting ∆I/I is larger as can be seen from Equation 5.1 and the

experimental data in (a). The relative noise level is also larger...... 63

5.2 Plot of device reponse (∆I) as a function of the transconductance (gm at diﬀerent

gate voltage bias) for a pH change from 7.1 to 7.9. From the linear least squares ﬁt,

the pH sensitivity of the device was extracted as 39 mV/pH...... 64

5.3 Illustration of the competitive desorption process of surface bound streptavidin

molecules using a high bulk concentration of D-biotin molecules. The surface bound

streptavidin consists of unbound sites that are available to molecules in the bulk

solution. By introducing D-biotin to the bulk, the strength of that interaction is

enough to pull the streptavidin molecules away from the surface bound biotin molecules. 64

5.4 BioFET response to streptavidin binding (20 pM) in 0.01X PBS, followed by

competitive desorption using 1mM D-biotin. The initial current drop is due to the

positive charge of streptavidin and the subsequent restoration of the baseline current,

on addition of D-biotin, shows that the competitive desorption strategy works. The

sampling rate used was 1000 Hz...... 65

xix 5.5 (a) Normalized current response due to 20 pM of Streptavidin in 0.01X PBS at

diﬀerent gate voltage values (bias points) for a sampling rate of 1000 samples/s. One

can see that the normalized response is a function of the gate bias, as expected, and

so is the relative noise level (which increases for the lower drain currents). (b) Id-Vg

curve for a biotin functionalized bioFET device, indicating the bias points used for

the sensing measurements in (a) using color coded crosses...... 66

5.6 Plot of the measured signal-to-noise ratio (at a f = 1Hz) as a function of gate bias

voltage. Even though the relative signal change is larger for small overdrive voltages

as can be seen in Figure 5.5, the SNRmeas is lower...... 67

5.7 Plot of the absolute bioFET response as a function of transconductance (gm) at

diﬀerent gate voltage bias points. From the slope of the linear ﬁt to the data, the

surface potential change of 100 mV can be extracted for 20pM of streptavidin binding

in 0.01X PBS...... 67

5.8 (a) Normalized current noise power density at f= 1Hz is plotted against drain current.

The noise proﬁle does not change signiﬁcantly with changes in PBS (phosphate

buﬀered saline) concentration or by changing the electrolyte to KCl (potassium

2 chloride). The proportionality to (gm/Id) conﬁrms that our data are well ﬁtted by

the number ﬂuctuation model. (b) Signal-to-noise ratio (as deﬁned in text) is plotted

against solution gate voltage to highlight the regime at which SNR is maximized. (c)

Transconductance values extracted from I-V measurements are also plotted against

solution gate voltage to point out that maximum SNR occurs close to the point of

peak transconductance...... 69

xx 5.9 (a) Signal-to-noise ratio (as deﬁned in text) is plotted against solution gate voltage

to highlight the regime at which SNR is maximized. The pH of the solution is varied

showing the independence of the peak SNR value on pH, except for the location of

the peak which shifts as the threshold voltage shifts with pH. (b) Transconductance

values extracted from I-V measurements are also plotted against solution gate voltage

to point out that maximum SNR occurs close to the point of peak gm. Peak gm also

shifts with gate voltage due to changes in Vth caused by the diﬀerent pH...... 71 √ 5.10 The gate voltage noise ﬂuctuations ( SV ) are plotted against solution gate voltage

(limited to the linear regime of operation). The absence of a linear dependence

indicates that number ﬂuctuations are the dominant cause of the noise of these

bioFET devices. The dip in the data also highlights the region of maximum signal- √ to-noise ratio (1/ SV ), which is again shown to occur around the region of peak

transconductance...... 72

5.11 Plot of the signal-to-noise ratio (SNR) and the device transconductance (gm) as a

function of solution gate voltage, highlighting the observation that SNR is maximum

at the point of peak transconductance. The maximum SNR for this device is 11 000

which translates to a minimum detectable pH change of 0.01...... 73

5.12 Current vs time data showing the device response at diﬀerent pH values. From the

Id-Vg curve and the pH response curve, the sensitivity is determined to be 24.9 mV/pH. 74

5.13 pH sensing experiment to investigate the limit of detection (LOD) of the bioFET

sensor, showing the successful detection of a change in 0.07 pH with a measured

signal-to-noise ratio of ≈ 3.5...... 74

xxi 5.14 (a) Comparison of the normalized current noise power as a function of drain

current, for APTES functionalized devices vs. un-functionalized bioFETs (bare

oxide surface). The APTES functionalization results in a signiﬁcant reduction in the

current noise power density. (b) The extracted SNR compared for the functionalized

and bare oxide devices, showing the improvement that results from bioFET surfaces

chemically modiﬁed with APTES...... 76

5.15 Normalized noise proﬁle for a bare oxide device compared to the same device after

poly-L Lysine (PLL) functionalization. The noise proﬁle is unchanged, which is

consistent with the electrostatic interaction of the positively charged PLL with the

negative silicon oxide surface...... 78

5.16 Optical image of a device showing the PDMS microﬂuidic channels functionalized

with FITC (green) and channels functionalized with TAMRA (yellow). There is no

leakage of ﬂuorophors between channels as evidenced by the high contrast of the image. 79

5.17 SNR plotted as a function of solution gate bias for diﬀerent surface functionalization

schemes, demonstrating that the SNR varies minimally for the diﬀerent types of

surface modiﬁcations after the ﬁrst step of APTES functionalization...... 79

5.18 Measured peak transconductance (gm) plotted for diﬀerent device dimensions,

showing that gm scales with the ratio W/L as predicted by Equation 5.3. The

R2 value of the linear least squares ﬁt is 0.9947...... 82

5.19 Peak SNR is extracted and plotted for diﬀerent device dimensions, showing that peak √ SNR scales with WL as expected from Equation. The R2 value of the linear least

squares ﬁt is 0.9988...... 83

5.20 Results from a 2D simulation of the SNR of 2 bioFETs, both with a 50% surface

coverage of bound analyte molecules. The length of the device is increased from 30

to 50 a.u., resulting in an increase in the device area and consequently an increase in

the SNR from 4.7 to 6.1 a.u., which correlates very well with our experimental results. 84

xxii 5.21 Simulation results for the SNR calculated at 50% surface coverage of bound analyte

molecules, for diﬀerent device areas. The simulation conﬁrms our experimental

ﬁndings that SNR is linearly proportional to p(area)...... 85

5.22 SNR as a function of diﬀerent number of rows and columns, keeping area constant

at 900 a.u. The small diﬀerences in SNR show that the layout is not as signiﬁcant

as the total surface area available for binding...... 86

5.23 Peak SNR extracted for measurements carried out on nanowire bioFETs fabricated

using e-beam lithography, of diﬀerent widths ranging from 60 nm to 2 µm...... 87

6.1 Langmuir isotherm plotted on a semi-log scale for analyte-receptor systems of

diﬀerent KD values. The dashed line indicates a certain detection limit which

occurs, for a particular charge per analyte (Z), at a surface coverage of 40%. The

detection limit in terms of concentration is then obviously dependent upon the

binding equilibria of the analyte-receptor system...... 91

6.2 Real-time sensor responses of HMGB1-DNA binding. Each curve represents the

measurement of a diﬀerent DNA concentration from multiple devices, and sensor

responses are normalized by the transconductance and oﬀset such that all traces

start at zero. The dashed lines represent the linear least squares ﬁt to the data using

Equations 6.2 and 6.3 from which values for kon and koff are estimated...... 94

6.3 Plot of the ﬁtting parameter konρ0 + koff as a function of DNA concentration. The

linear ﬁt indicates good agreement of the data with our binding model and the from

the slope of the line, we can extract the value for kon (i.e. k1)...... 95

6.4 Langmuir isotherm plotted using the data obtained from the real time current traces

of DNA binding to HMGB1. The isotherm is used to extract a value for the KD of

105 nM using Equation 2.24...... 95

xxiii 6.5 Simulation results based on the parameters given in Table 6.1, showing the binding

kinetics for diﬀerent device areas (and therefore diﬀerent numbers of receptor sites)

in the case where the analyte concentration (ρ0) is much larger than the KD ..... 97

6.6 Simulation results for binding curves corresponding to diﬀerent device areas and thus

diﬀerent numbers of receptors. Here, we consider a high KD system of 1 nM and an

initial bulk analyte concentration of 1 fM, yielding a very low occupation probability

and thus, low numbers of bound molecules at the end-point of detection...... 98

6.7 Coverage ratio extracted as from the binding curves in Figure 6.6 and plotted as a

function of number of receptor sites. Coverage ratio remains constant at 10−6 since

there are always enough molecules in the reaction volume to populate the increasing

number of sites on the surface...... 99

6.8 Coverage ratio extracted from the simulated binding curves for a high KD system

(1 fM) and plotted as a function of number of receptor sites. The coverage ratio

is no longer a constant quantity and instead decreases with increasing the surface

area, since the number of molecules in the bulk are limited and is smaller than that

required for conjugation to the increasing number of receptors...... 101

6.9 SNR as a function of device area, for the case of a low KD (1 fM) and limited

analyte molecules such that the coverage ratio is no longer constant (see Figure 6.8).

This results in a SNR that does not increase with p(area) but instead is

maximized at some intermediate device area. The results are shown for two diﬀerent

analyte concentration showing that the optimal device size depends on the target

concentration of analyte...... 102

6.10 Coverage ratio as a function of the analyte concentration in the regime of low KD

(1 fM) and limited number of analyte molecules. As the number of receptors is

increased (that is device area is decreased), the 106 receptors curve approaches the

Langmuir isotherm given by Equation 2.24...... 103

xxiv 7.1 pH response of a bioFET device using a Pt wire as the solution gate electrode (pseudo

reference electrode) at two diﬀerent bias points. The change in the current does not

correspond to changes in the surface charge of the bioFET (TRIS buﬀer used at

pH 7.45 and pH 7.95), but rather is a measurement artifact due to the interfacial

potential at the reference electrode itself changing with pH...... 107

7.2 Current response (∆I) at diﬀerent bias points plotted as a function of the

corresponding transconductance (gm), showing that the potential change involved

in the switching of the two well controlled buﬀers is consistent and repeatable. The

slope of the linear ﬁt line gives a “pH response” of 39 mV/pH...... 108

7.3 Id-Vg curves for two bioFET devices, demonstrating the diﬀerence in the interfacial

potential of the Pt electrode as compared to that of the Ag/AgCl electrode. The

larger interfacial potential of the Pt electrodes translates into a more negative

threshold voltage when the transfer characteristics are measured...... 110

7.4 (a) pH response of a bioFET using Ag/AgCl as a pseudo reference electrode and

10mM HEPES as the pH buﬀer solution. The extracted pH sensitivity is 12.2 mV/pH

(b) pH response of a bioFET using Ag/AgCl and 10mM TRIS as the buﬀer solution

with an extracted sensitivity of 24.6 mV/pH. This shows the inﬂuence of the buﬀer on

the potential changes that are measured due to the response of the pseudo reference

electrode itself to [Cl–]...... 110

7.5 Id-Vg curves of bioFET sensors for diﬀerent pH values of the PBS buﬀer solution,

showing the expected negative Vth shift for smaller pH values...... 111

7.6 Current-time trace for a bioFET device using the back-gate (BG) as a pseudo

reference electrode, showing the lack of response due to the potential change at

the electrode cancelling the change at the device surface...... 112

7.7 SNR as a function of solution gate voltage for a Pt electrode (red) compared to

Ag/AgCl electrode (black)...... 113

xxv 7.8 pH sensing results for the Ag/AgCl electrode under ﬂuid ﬂow conditions of 50

µL/min. The switching spikes correspond to the switching on/oﬀ of the electronic

solenoid valves...... 115

7.9 1/f noise spectra for the bioFET biased in strong accumulation, comparing the

spectra of the Pt electrode to the spectra of the Ag/AgCl electrode under no ﬂow

conditions as well as 50 µL/min ﬂuid ﬂow. The spectra for the Pt electrode is noisier

for high frequencies and the noise power increases by a larger amount than the noise

power of the Ag/AgCl electrode, when the ﬂow is switched on as we expected from

earlier measurements...... 115

7.10 1/f spectra for a bioFET biased in strong accumulation, comparing the noise of the

Pt electrode to that of a miniature Ag/AgCl reference electrode, under no ﬂow and

50 µL/min ﬂuid ﬂow conditions...... 116

7.11 Schematic of the experimental setup used to examine the changes in interfacial

potential occuring for various test electrodes upon addition of charged biomolecules,

by meauring the changes in the open circuit potential...... 117

7.12 Open circuit potential (Voc) of the Pt and Ag/AgCl electrodes measured against

a full Ag/AgCl reference electrode, showing the transients and voltage shifts upon

addition of 1 mg/mL of PLL...... 118

7.13 Open circuit potential (Voc) measurement for two full Ag/AgCl reference electrodes

upon addition of 1 mg/mL of Poly-L-Lysine (PLL). The transient is due to the

manual addition of PLL and the voltage change is 0.1 mV...... 119

7.14 The optical micrograph on the left shows patterned Ag metal deposited by e-beam

evaporation on to a silicon substrate. After the treatment with bleach, a thin layer

of AgCl is formed resulting in a darker color. The open circuit potential can be used

to conﬁrm the successful conversion of Ag to AgCl as the potential changes from 200

mV to 36 mV...... 120

xxvi 7.15 Open circuit potential (Voc) measured w.r.t a Ag/AgCl reference electrode as a

function of time, demonstrating the small amount of drift for the on-chip Ag/AgCl

pseudo reference electrode...... 120

7.16 (a) Response of the open circuit potential of the on-chip Ag/AgCl pseudo electrode

(measured w.r.t a reference Ag/AgCl electrode) upon addition of sodium hydroxide

(NaOH), showing that pH changes do not aﬀect the electrode potential as long as [Cl–]

remains constant. (b) Response of the on-chip Ag/AgCl electrode upon an increase

in [Cl–], showing that the electrode potential is indeed responsive to changes in the

chloride concentration...... 121

xxvii List of Tables

5.1 Table showing the average values of the measured SNR and extracted trap densities

for measurements carried out using the top gate silicon oxide, back gate silicon oxide

and top gate aluminum oxide dielectrics...... 81

6.1 Table showing the parameters and their typical values for the binding kinetics

simulations using Matlab’s ODE solver. The area of the bioFET device is given

by A, in units of cm2...... 96

xxviii Chapter 1

Introduction

1.1 Overview

The ability to detect very low concentrations of small molecules such as protein and DNA at a low cost has tremendous applications for medicine and basic biochemistry[1,2,3]. Currently most standard techniques rely on optical characterization methods[4,5] which involve tagging (i.e. labeling) the analyte of interest with a fluorescent molecule. This is not optimal for three main reasons: (1) Attaching a separate molecule to the analyte might influence the latter’s functionality, i.e. the way the analyte binds to other molecules[6]. (2) Pre-processing of samples does not allow the real-time monitoring of changes in analyte concentration and (3) Tagging with fluorophors and reliable optical detection requires a larger sample volume[7]. Alternatively, field-effect sensors such as silicon nanowire/nanoribbon biosensors (BioFETs) have shown great promise as a potential platform for direct, label-free detection of bio-molecules with ultra-high sensitivity and scalability[8,

9, 10, 11]. With the use of micro/nano-fabrication, sensor characteristics can be controlled and true multiplexing and addressing can be achieved. This paves the way for multi-component detection and analysis for Point-of-Care devices utilizing smaller sample volumes and having faster read-outs.

The structure of a BioFET is similar to that of a MOSFET, but instead of having a metal or polysilicon gate electrode, the gate dielectric in the BioFET case is directly exposed to solution.

1 The gate material (usually silicon oxide, silicon nitride or aluminum oxide) is modified with surface receptors specific to the analyte that one wishes to detect. Most biomolecules are charged when in solution, the charge being dependent on the pH. Therefore, when the analytes bind to the receptors, the field-effect due to the charges now bound close to the surface induces opposite charges within the semiconductor channel, which is then detected as a change in current or conductance. The principle of operation of a bioFET is shown in Figure 1.1, where the current rises as the analyte binds to the receptor. The first realization of a bio-sensor utilizing these principles happened in the

1.5µ

ISD (A)

1.0µ SD I

500.0n -50 0 50 100 150 200 Time (sec)

1.5µ

ISD (A)

1.0µ SD I

500.0n -50 0 50 100 150 200 Time (sec)

Figure 1.1: Schematic of a typical bioFET measurement. The baseline current is changed by the binding of analyte molecules (green cirlces) due to the additional electric ﬁeld induced by the charged analyte.

1970s with the concept of an Ion Sensitive Field Eﬀect Transistor (ISFET)[12]. However, due to the large size of ISFETs, a lot of molecules were needed to achieve a good signal to noise ratio[13] and therefore most of the research on this topic focused on the detection of pH changes. Work carried out on ISFETs eventually led to the pioneering work by Cui et al.[14] which made use of chemical vapor deposition (CVD) to grow silicon nanowires (10 -20nm) and use them as pH sensors as well as bio-sensors to detect proteins (streptavidin) down to picomolar concentrations. Further work on CVD grown semiconductor nanowires showed highly sensitive and real-time detection of

2 proteins[15, 16], DNA[17, 18] and single viruses[19]. However, the bottom-up approach to creating bioFETs suﬀers from two major drawbacks. Firstly, high density fabrication and integration is complicated by the need to align and/or contact the grown nanowires[20] using unconventional and low yield methods. Secondly, the grown nanowires have a large variance in their physical and electrical characteristics[21]. For true multiplexing capabilities, in the presence of a global gating scheme, the device characteristics need to be similar so that the sensitivity can be optimized for every single device in a multi-device array[13]. The desire to better control device characteristics on a wafer scale led to the top-down approach of using conventional micro-fabrication processes to create nanowire like structures using ultra-thin silicon-on-insulator (UT-SOI) wafers. The devices are deﬁned in the active silicon layer using either optical or e-beam lithography and the rest of the silicon is subsequently etched away using wet-etching[11, 22, 23, 24] or dry RIE etching[10, 25, 26].

Recently, there has also been resurging interest in wider sensors (larger than 1um) with nanometer thicknesses based on SOI, called nanoribbons or nanoplates, which involve a simpler and cheaper fabrication process relying on relaxed-dimension optical lithography. The sensing results from these devices indicate comparable sensitivity to nanowire systems[27, 28], the thickness of the nanoribbons being the critical dimension. Our research group has therefore focused on the top-down approach for better control and uniformity in bioFET characteristics and performance. We have explored both the nanowire as well as the nanoribbon device architectures and have had promising results with both of them. Our study on the detection of the cancer markers PSA and CA15.3 showed the immense potential of having devices with uniform characteristics across a wafer[29]. Due to similar threshold voltages across multiple devices, the devices could be biased at approximately the same operating regime by a single global solution-gate voltage. This allowed for the simultaneous measurement of 8 devices in parallel, greatly increasing the amount of data for a given experiment.

3 1.2 Performance Metrics

The most commonly used performance metric has been the “sensitivity” of the sensor during a certain measurement which is deﬁned as the change in the signal normalized by the original value of the signal (∆I/I) or in other words, the relative signal change. The origin of this metric can be traced back to the pioneering work on nanowire biosensors[14] wherein the authors claimed:

“. . . binding to the surface of a nanowire (NW) or nanotube (NT) can lead to the depletion or accumulation of carriers in the bulk of the nanometer diameter structure (versus only the surface region of a planar device) and increase sensitivity to the point that single-molecule detection is possible.” This argument exploits the higher surface to volume ratio of nanowires as compared to planar ISFETs to justify the increased sensitivity as deﬁned by ∆I/I and led to greater interest in the ﬁeld of nanowire FET sensors, with single molecular detection being somewhat of a holy grail. Theoretical work attempting to understand and provide guidelines for improving the performance of FET-based sensors therefore focused heavily on modeling how the “sensitivity”

(i.e. the relative signal change) varies with parameters such as bias conditions, doping densities and fluidic considerations[13, 30, 31, 32]. This definition of “sensitivity” should not be confused with the true definition of the sensitivity, which is the change in signal for a certain change in the measurand. In the specific case of bioFETs, measuring changes in the source-drain current,

∆(current) S = (1.1) ∆(analyte concentration)

The change in current can further be expressed as a product of the change in surface potential and the transconductance (gm). We note here that normalizing sensing results by gm has been shown to result in smaller device-to-device variations[29, 33], since the normalized signal becomes solely dependent on the change in surface potential (which is independent of the bias conditions).

Expressing the sensitivity as deﬁned in Equation 1.1 is more relevant to the potential applications of the sensor and allows people to focus on improving the signal transducer which is the bio- recognition layer. The surface coverage density of the functionalization layer as well as the density

4 of active chemical groups in that layer both determine the change in surface potential per unit change in analyte concentration[16]. Deﬁning sensitivity as such will allow more attention to be paid to extracting and displaying the proper calibration curves (the slope of the calibration curve being the sensitivity[34]).

Until very recently[35, 36], little attention had been paid to the fact that the measurement itself is a measurement of ∆I and what ultimately limits the smallest change that can be resolved by the bioFET sensor is the current noise (δi). The latter can be measured, characterized and modeled using established techniques/models in the MOSFET community[37, 38, 39, 40]. Therefore, if the goal is ultra-sensitive detection, the performance metric has to include both the magnitude of the signal as well as the noise properties of the sensor and its environment. In this thesis, we have tried to combine the noise analysis and modeling tools of the semiconductor device community, with the rather novel ﬁeld of FET biosensing to come up with more relevant and accurate ways to guide the fabrication and/or selection of bioFET sensors with the lowest limit of detection.

With this aim in mind, noise measurement and noise characterization represent valuable tools in being able to predict the smallest measurable signal, or in other words, the detection limit of bioFETs, as well as guiding the fabrication of “better” sensors. In our view, three factors currently determine the limit of detection of a particular sensor: (1) the intrinsic device noise which depends on the fabrication process and material quality, (2) charge screening, especially when physiological conditions (100mM ionic concentration) cannot be avoided and (3) binding equilibria between receptor and analyte molecules which dictate how much of the analyte binds to the surface receptors at steady-state conditions, for a given bulk concentration. This thesis mostly focuses on the ﬁrst limitation. Chapters 4 and 5 focus on noise characterization of our bioFETs and using

SNR as a performance metric, respectively. Chapter 6 covers binding kinetic measurements carried out using our platform, as well as simulation results based on modeling low and high KD systems.

Finally, Chapter 7 deals with the solution gate electrode and how sensing results can be aﬀected by the choice of the electrode and the buﬀer composition.

5 Chapter 2

Theoretical Considerations

2.1 Working Principle of an ISFET

To understand the working principle of any FET based biosensor, we need to revisit the work of Bergveld[12]. His invention, the Ion Sensitive Field Eﬀect Transistor (ISFET) is basically a

MOSFET(metal oxide semiconductor field effect transistor) with the gate electrode (solution gate) separated from the gate dielectric by the electrolyte solution. Figure 2.1 shows the device structure for an SOI ISFET, which can be transformed into a bioFET by functionalizing the surface of the dielectric with receptor molecules specific to the analyte of interest. Consequently, any binding event, involving charged analyte species, changes the electrostatics of the system and alters the potential distribution from the solution gate electrode to the ground of the device. The potential distribution for a certain bias voltage Eref is shown in Figure 2.2. Any alteration to this potential distribution is then detected as a change in the drain-to-source current (Ids), which is related to the change in surface potential at the dielectric-solution interface(ψ0).

The drain-to-source current (Ids) in the ohmic region, for low drain-to-source voltage (Vds) is given by[41]: W I = µ C (V − V ) V (2.1) ds L eff ox g t ds

6 Figure 2.1: Schematic of a device and the experimental setup

where W and L are the width and length of the device respectively. µeff is the eﬀective mobility for carriers in the silicon, Cox is the oxide capacitance per unit area, Vg is the applied gate voltage and Vt is the threshold voltage, which is given by:

ΦM ΦSi Qit − Qb + Qf Vt = − − + 2φf (2.2) q q Cox

ΦM and ΦSi are the metal and silicon work functions respectively. Qb, Qf and Qit are the bulk depletion charge, ﬁxed oxide charge and interface charge at the Si/Si02 interface respectively, all per unit area. φf is the fermi potential diﬀerence between the doped silicon and instrinsic silicon.

In the case of an ISFET, since the gate voltage is applied via a reference electrode, the threshold voltage (Vt) has to be modiﬁed to include additional potential drops at the interface of the reference electrode and the solution and at the interface between the solution and the gate dielectric.

sol ΦSi Qit − Qb + Qf Vt = Eref − ψ0 + χ − − + 2φf (2.3) q Cox

Electrolyte Solution Silicon Solution Gate Solution Gate DielectricGate

Eref

φs1 φs2 φox φSi Potential Vb

Distance from gate

Figure 2.2: This ﬁgure shows an example of how the applied potential Eref is distributed throughout the diﬀerent layers of materials involved in the ISFET device structure as well at the solid-liquid interfaces.

This equation is diﬀerent from Equation 2.2 in that the work function of the metal (ΦM ) is now replaced by the potential applied to the solution by the reference electrode, namely Eref . The potential drop between the reference electrode and the electrolyte is contained within the value of

Eref (In most cases, this potential drop is negligible compared to the applied voltage, and thus,

Vapplied ≈ Eref ) . The additional potential diﬀerence at the gate dielectric/solution interface is

sol sol given by ψ0 + χ . χ is the surface dipole moment of the solution which is generally regarded as a constant. ψ0 is the potential contribution due to the charged surface groups on the gate dielectric surface and therefore, ψ0 is a pH dependent quantity and is the essence of how the ISFET can be used as a pH sensor. Before going into the theory behind pH sensing, it is worthwhile to note that bio-molecular sensing can also be included in this model of the ISFET by considering ψ0 to be a function of the number of bound charged analyte molecules. It is also important to keep in mind that even though Equation 2.3 considers the case of a constant Eref , the choice of the reference electrode is crucial in ensuring that Eref is indeed constant during a particular measurement.

8 Otherwise, the ∆ Vt measured cannot be linked solely to changes in ψ0. For instance, in Figure 2.2, a change in current can either be due to the dielectric surface building up charges, resulting in a change in φs2, or the change in current can be due to fouling of the reference electrode producing changes in φs1.

2.2 pH Sensing

The theory of pH sensing is based on the site-binding/site-dissociation model[42] and involves the following surface hydroxyl groups and their corresponding reactions:

Ka − + A−OH )−−−−* A−O + Hs (2.4)

+ Kb + A−OH + Hs )−−−−* A−OH2 (2.5)

+ The concentration of hydrogen ions directly near the surface ([H ]s) determines the state of the hydroxyl groups on that surface. The surface concentration of hydrogen ions is related to the bulk concentration by: q ψ [H+] = [H+] exp(− dl ) (2.6) s b k T

+ where [H ]b is the bulk concentration of hydrogen ions, k is the Boltzmann constant, T is the temperature and ψdl is the potential diﬀerence between the dielectric surface and the bulk of the solution. A circuit model of the sensing experiment is shown in Figure 2.3. The bulk of the silicon is assumed to be grounded at some point (usually at the source contact) and ψ0 is the potential at the gate dielectric surface. This potential is subject to change when the charge at the dielectric surface (Q0) changes. The charge separation in the double layer at the interface of the oxide and electrolyte is modeled as a simple capacitor, Cdl. Figure 2.3 illustrates the charge sharing picture of charges binding at the surface of the gate dielectric. The surface charge is compensated by charges in the double layer as well as charges in the silicon. Under such an approximation, the potential

9 Figure 2.3: Circuit model of a typical ISFET sensing setup, showing the voltage drops across the double layer and silicon device.

diﬀerence, ψdl can be related to the oxide surface charge per unit area, σ0, by the following:

Cox Cnw σ0 = σdl + σnw = Cdl ψdl + ψ0 (2.7) Cox + Cnw

where Cnw is the capacitance of the nanowire, which is only signiﬁcant in the presence of a depletion region within the silicon. Henceforth, in order to simplify the mathematics, we will consider the case where Cnw is much larger than Cox, which is often the case for our measurements which are carried out in the strong accumulation or strong inversion regimes. Rewriting ψ0 as a function of the applied solution gate voltage, Vsg, we obtain:

σ0 = ψdl(Cdl + Cox) + Vsg Cox (2.8)

We can alternatively write σ0 as a function of ψ0 which yields the following:

σ0 = ψ0(Cdl + Cox) − Vsg Cdl (2.9)

σ0 is also related to the areal density of charged surface groups:

+ − σ0 = q([A−OH2 ]−[A−O ]) (2.10)

10 where the total areal density of surface groups is given by:

+ − Ns = [A−OH2 ] + [A−OH] + [A−O ] (2.11)

Taking the logarithm on both sides of Equation 2.6 and combining with Equations 2.10 and 2.11, we obtain the following equation:

1 1 2 2 + Ka qψdl −1 σ0 1 ln [H ]b − ln = + sinh (2.12) Kb kT qNs 4KaKb

+ Re-writing Equation 2.12 using the relation pH = − log10[H ]b,

1 2 qψdl −1 σ0 1 2.303 (pHpzc−pH) = + sinh (2.13) kT qNs 4KaKb

where pHpzc is the pH value at the point of zero charge(pzc), that is when the surface of the oxide is electrically neutral (σ0 = 0 and ψdl = 0). Equation 2.13 can be combined with Equation 2.8 to give the following general equation in the presence of charge sharing and applied solution gate bias:

qψdl −1 q Cox 2.303 (pHpzc−pH) = + sinh 0 ψdl + Vsg (2.14) kT kT β Cox + Cdl

0 where β is given by: 2 1 0 2q N (K K ) 2 β = s a b (2.15) kT (Cdl + Cox)

0 It is evident from Equation 2.15 that β , being proportional to the areal density of surface groups and how easily these groups associate or dissociate to give a charged surface, relates to the reactivity

0 of the surface. For a good pH sensing surface, we expect β to be large, more speciﬁcally, we expect

0 qψdl β kT , which results in the following approximation,

0 kT β Cox ψdl = 2.303 0 pHpzc−pH − Vsg 0 (2.16) q β + 1 (Cox + Cdl)(β + 1)

11 The surface potential ψ0 which is given by Vsg + ψdl can now be deﬁned, resulting in the Nernst equation for pH sensing, with the solution gate bias taken into account:

0 kT β Cox ψ0 = 2.303 0 pHpzc−pH + Vsg 1 − 0 (2.17) q β + 1 (Cox + Cdl)(β + 1)

0 For a large value of β , a unit change in the pH value produces a surface potential change of 59.9 mV, which is called the Nernst limit. This value is not possible with silicon dioxide as the sensing surface but is routinely achieved with other gate dielectrics such as aluminum oxide and tantalum oxide. It is important to note that this is a fundamental limit of a sensing surface and despite many attempts to go beyong this limit, the only successful strategy involves ampliﬁcation of the signal giving an ”apparent” surface sensitivity that exceeds the Nernst limit. The fundamental limit to the surface sensitivity, however, remains unchanged.

2.3 Biomolecular Detection

The detection of charged molecules can be described using an analogous model to the one developed in the previous section. The main difference to note is that with charge detection we consider the charges induced in the silicon channel as opposed to the potential set-up at the surface of the gate dielectric. In principle, both approaches should yield the same results except for the effects of screening. In the case of pH sensing, the reactive groups (hydroxyl groups) are close to the surface and within the Debye length for most electrolyte concentrations used. However, when trying to detect charged analyte molecules, the surface has to be modified and functionalized with specific receptors, which have lengths of about 10 nm or longer. In such a case, the Debye length has to be optimized by choosing the right ionic concentration for the buffer solution.

s r0kT λD = 2 (2.18) 2NAq I

12 where r is the relative permittivity of the electrolyte, 0 is the vacuum permittivity, NA is

Avogadro’s number and I is the ionic concentration in mole per m3. For a certain charge Q at a certain distance d (due to the thickness of the functionalization layer), the eﬀective charge

Qeff that can be detected by the bio-sensor is given by:

−d Q0 = Q exp (2.19) λD

This charge Q0 is then shared as before between the double layer on the solution side and the semiconductor channel on the device side, as depicted in Figure 2.3. From Equation 2.9, we conclude that any binding event which changes the surface charge, in turn changes the surface potential ψ0 and these two quantities are related to each other by:

1 ∆ψ0 = ∆σ0 (2.20) Cdl + Cox

We have described how the surface potential of the device changes after a certain number of receptors are conjugated. The physics of this conjugation is quite complex if one includes the effects of diffusion, mass-transport, non-specific binding, multiple binding sites, etc. For the sake of simplicity, a lot of insight can be obtained by considering the case of one-to-one binding (which is generally what is sought after in the design of bioFETs) with the addition of a two compartment model[43], to distinguish between reaction-limited and diffusion-limited regimes.The basic differential equation governing the binding kinetics of a receptor-analyte pair is given below:

∂N = k ρ (N − N) − k N (2.21) ∂t on s max off

where N is the number of conjugated receptors, Nmax is the total number of receptors available, kon and koff are the association and dissociation rate constants, respectively. ρs is the local concentration (in mol/L) of analyte molecules, right above the layer of receptors, to be distinguished from the bulk concentration of analyte, ρ0, far away from the reaction layer(reaction zone). The

13 two-compartment model was developed to analyze the depletion of analyte molecules in the reaction zone and the subsequent diffusion of analytes from the bulk into that region or compartment. This diffusion is modeled by a diffusion rate constant, km and is represented by the following differential equation: ∂ρs 1 = [km (ρ0 − ρs) − konρs (Nmax − N) + koff N] (2.22) ∂t VNA

where V represents the volume of the reaction zone in L and NA is the Avogadro number. We can consider the case of a reaction-limited experiment, which means that the reaction proceeds slowly enough such that the local concentration is always equal to the bulk concentration (ρs = ρ0). In such

dN a case, at equilibrium ( dt = 0), Equation 2.21 produces a simple equation for N at equilibrium:

kon ρ0 Nmax Neq = (2.23) koff + kon ρ0

koff The above equation can be re-written in terms of the equilibrium dissociation constant KD = , kon

ρ0 Neq = Nmax (2.24) ρ0 + KD

Therefore, for a given bulk analyte concentration ρ0 and knowing the equilibrium dissociation constant KD, the equilibrium number of bound molecules can be estimated by using Equation 2.24, assuming the conjugation is reaction-limited. Otherwise, Equations 2.21 and 2.22 need to be solved numerically to ﬁgure out Neq. After Neq is determined, the bound surface charge(Qbound) can be estimated by knowing the charge per molecule, which is determined from the iso-electronic point

(pI) of the analyte molecule and the pH of the electrolyte. Screening can then be accounted for using Equation 2.19 and the change in surface potential (ψ0) can be formulated as:

1 Z ρ0 Ns −d ∆ψ0 = exp (2.25) Cdl + Cox KD + ρ0 λD

14 where Z is the charge per analyte molecule, which is pH dependent and Ns is the areal density of surface receptor molecules, which is related to the eﬃciency of the functionalization. Ns = Nmax/A where A is the area of the gate dielectric surface functionalized with receptors and exposed to the solution containing analytes. It is very important to note that Equation 2.25 was derived by assuming that ρs is constant and equal to ρ0, which is true in most analyte-receptor systems that are reaction-limited, that is with high KD (>1nM). In the case of strong binding systems (low

KD, <1pM), the number of surface bound molecules at equilibrium does not necessarily follow

Equation 2.24 since ρs is time-dependent and decreases as more analyte molecules bind to the surface.

2.4 Low-Frequency Noise

The smallest measurable signal is determined by the noise level of the bioFET sensor. Since the device is essentially a MOS (metal-oxide-semiconductor) transistor, the noise at low frequencies (<

10kHz) is dominated by ﬂicker or 1/f noise[39][44] which has the following general form:

S A I = (2.26) I2 f

2 SI is the power spectral density of the drain current noise (in A /Hz), I is the drain current and A is a constant of proportionality which diﬀers based on the noise model that is used. The quantity

2 SI /I is the normalized noise power density (the noise power is normalized by the power dissipated

2 by the device, assuming a resistance of 1 ohm) and at a frequency of 1Hz, A = SI /I and is deﬁned as the noise amplitude. The noise amplitude is the only quantity necessary to deﬁne the

1/f noise spectrum completely and is the quantity that contains the details of the noise generating mechanisms and properties. Hooge’s model for instance[45], is based on an empirical equation, where A = αH /N, such that: S α I = H (2.27) I2 f N

15 where N is the number of charge carriers in the material and αH is called Hooge’s parameter and is material speciﬁc. αH is dimensionless and is a measure of the quality or equivalently the

“noisiness” of the material/device. Typical values are in the range 10−6 to 10−3. This model is commonly used in the linear (ohmic) region of a FET device and helps to compare across different device architectures and materials[46]. To represent devices and the drain current noise from the subthreshold regime to the strong accumulation/inversion regime, the number fluctuation (∆N) model is more accurate. The ∆N model is a physical model which assumes that the origin of the current fluctuations is the trapping/de-trapping process of charge carriers tunneling to/from traps and defect levels in the oxide close to the semiconductor interface. These fluctuations in the number of charge carriers in the channel are modeled as fluctuations in the flatband voltage:

2 λ k T q Not SVFB = 2 (2.28) WLCox f where λ is the characteristic tunneling distance, which is material dependent (for silicon oxide, it is on the order ot 10−10 m). This model assumes a spatially uniform trap density within a few kT

−1 −3 of the Fermi level. Not is the oxide trap density in units of eV m . Therefore, SVFB is usually constant for a given device at diﬀerent drain currents, unless the trap distribution, Not, varies with gate voltage. The normalized drain current ﬂuctuations are then given by:

S g2 I = m S (2.29) I2 I2 VFB

2 Equation 2.29 accurately models the noise proﬁle (plot of SI /I vs. I) in the subthreshold regime, where gm/I is a constant, resulting in a ﬂat region (since SVFB is usually weakly dependent on the gate bias voltage). The ∆N model predicts a normalized noise power density that varies as

2 1/I in the strong inversion/accumulation regime (for a constant gm). However, many devices do not display this trend. In fact, the dependence varies between 1/I2 and 1/I[47][48], that is the actual data lies somewhere between what is predicted by the ∆N and ∆µ models. To account for

16 this, a third model was developed, called the correlated number-mobility fluctuation (∆N − ∆µ) model[47]. The physical basis for this model is that trapped charges not only influence the number of charges in the channel, but also influence the mobility, since charged traps also act as Coulombic scattering centers which result in mobility fluctuations as the trap occupancy fluctuates. In the

∆N − ∆µ model, the gate voltage noise power density is given by:

p p SV g = SVFB [1 ± α µeff Cox (Vg − Vt)] (2.30)

where α is the Coulombic scattering coeﬃcient and the plus or minus signs depend on whether the trap is charged or neutral, respectively, when it is occupied. For α = 0, we recover the number

ﬂuctuation model of Equation 2.29, with SV g = SVFB. For a non-zero α, the deviation from the number ﬂuctuation model becomes more pronounced in the strong inversion/accumulation region, that is when the gate overdrive voltage (Vg − Vt) is large. In such a case, the normalized noise

2 β power increases for large drain current values and SI /I ∼ 1/I where 1 < β < 2.

Any bio-sensing experiment, for a given analyte-receptor system at a certain concentration, results in a change in the surface potential (ψ0) given by Equation 2.25. The noise (δi) in such a measurement, if the noise spectrum follows a 1/f spectrum, is calculated as:

Z f2 Z f2 2 SI (f = 1Hz) f2 (δi) = SI df = df = ln × SI (f = 1Hz) (2.31) f1 f1 f f1

Consequently, the signal-to-noise ratio of such a measurement (SNRmeas) can be deﬁned as:

∆I gm × ∆ψ0 SNRmeas = = √ p (2.32) δi BW SI (f = 1Hz)

where SI (f=1Hz) is the drain current noise power spectral density at f=1Hz and BW is a bandwidth related term which depends on the largest (f2) and smallest (f1) frequencies sampled, BW = √ ln f2 . For typical sensing measurements, BW is a weak function of the measurement bandwidth f1 and ranges from about 3.5 to 3.8 It is obvious that the smallest ∆ψ0 that can be measured will

17 have SNRmeas = 1. Of course, for reliable detection, we usually consider SNRmeas ≥ 3, but since we are discussing the limit of detection, it makes sense to consider the smallest possible SNRmeas which results in an observable signal. With SNRmeas = 1, we are led to deﬁne a metric that we shall name, for lack of a better term, SNR,

gm 1 SNR = p = √ (2.33) SI (f = 1Hz) SVFB

√ Equation 2.33 deﬁnes SNR as the SNRmeas for a unit voltage change in ψ0 and for BW = 1. Based on this deﬁnition of SNR, it is clear that the limit of detection (LOD) is given by 1/SNR, which

p √ is the gate voltage referred noise amplitude ( SV g or SVFB). The LOD can thus be extracted via a combination of DC and noise measurements, even before any actual sensing experiments are carried out. In this thesis, we will make the case for using SNR as a performance metric which takes into account the signal transduction as well as the noise limitations of bioFET sensors.

18 Chapter 3

Device Fabrication and Electrical

Characterization

3.1 Nanoribbon Device Fabrication

Improving on earlier generations of nanowire/nanoribbon FETs[49][50], this fabrication process includes a top-gate oxidation step (alternatively this could be replaced by an atomic layer deposition step) which greatly improves device lifetime and stability. The passivation layer was also changed back to SU-8, to allow the use of organic solvents during the biofunctionalization procedure. A passivation layer of around 2µm was found to be stable against electrolyte diﬀusion and protected the devices and the metal leads for several weeks. The general process ﬂow is shown in Figure 3.1.

We start with a 4-inch silicon-on-insulator (SOI) wafer from SOITEC (Active layer: 70 nm, P-Type

10 Ω cm, Buried Oxide Layer: 145 nm, Handle Layer: 500 µm, P-Type 15 Ω cm). Following RCA cleaning of the wafer (SC-1 and SC-2), the first step is to thin down the active layer using sacrificial oxidation, followed by silicon oxide removal using dilute hydrofluoric acid (HF:H2O, 1:10). The

ﬁnal active layer thickness is chosen such that it is close to the Debye length of silicon at that

15 doping concentration (for Na = 1x10 , λDebye = 40 nm) in order to maximize sensitivity[28][51].

19 Active Si BOX 1. Thin wafer Si Handle Implant TOX 2. Etch alignment marks Al SU-8

3. Ion implantation

4. Mesa definition

5. Oxidation

6. Metallize and liftoff

7. Passivate w/ SU-8

Figure 3.1: Fabrication Process Flow for Silicon Nanoribbon FET Devices

Step 2 involves patterning and etching the alignment marks into the handle silicon layer, using

SF6O2/C4F8 chemistry which etches silicon at a very fast rate (∼ 600 nm/min) and also etches silicon oxide (∼ 120 nm/min). In order to obtain a device with ohmic contacts, the source and

+ drain regions are implanted in Step 3 at the Cornell Nanofabrication Facility using BF3 at 10 keV for a ﬁnal dose of 2 − 5 x 1015 cm−2. Not shown in Figure 3.1 is the etching of the back-gate contacts through the active silicon and the BOX, which are also implanted. The dopant atoms

◦ are then thermally activated by heating the wafer at 900 C for 10 minutes in a N2 atmosphere.

Following dopant activation, the devices are deﬁned in the active silicon layer (Step 4) using optical lithography (minimum device width = 1µm) and subsequent etching using an Inductively Coupled

◦ Plasma (ICP) etch with Cl2. The devices are then oxidized at 1100 C in a dry O2 environment to create a top oxide (TOX) of about 20 nm as shown in Step 5. Aluminum contacts and leads are then patterned via optical lithography followed by a brief buﬀered oxide etch (BOE) to get rid of the top-oxide in the source/drain contact regions. The aluminum is then evaporated using an

20 (a) (b)

Figure 3.2: (a) Optical micrograph of a 3.3 mm x 3.3 mm die which is the smallest die we used in this thesis. (b) Optical image of a larger die size, 6.6 mm x 6.6 mm, which makes it easier to integrate an external micro-reference electrode into the fluidic cell. The four on-chip Pt electodes are also clearly visible, extending into the middle of the die. electron beam evaporation system and the final pattern is obtained by a lift-off process resulting in an aluminum thickness of 200 nm (Step 6). Not shown in the process flow of Figure 3.1 is a second metallization step for the on-chip pseudo-reference electrode (consisting of 5 nm of Ti followed by 50 nm of Pt). As will be discussed in Chapter 7, the on-chip Pt electrode was found to lead to erroneous results and was therefore initially abandoned for an external reference electrode and has now been modified to be a silver metal (Ag) layer which is to be further oxidized to AgCl. To improve the quality of the metal-semiconductor contact, thermal annealing is carried out in a tube furnace at

◦ 470 C, in a N2 atmosphere for 10-15 minutes for the formation of ohmic contacts and in order to reduce the contact resistance. Longer times and slightly higher temperatures might be required if the current-voltage characteristics are not linear and the contact resistance is much higher than about 1 kΩ, as measured between back-gate contacts. The ﬁnal step (Step 7) is the passivation of the metal leads such that they are not exposed to solution. This is achieved by patterning a 2

µm-thick SU-8 layer (hard baked at a ﬁnal temperature of 150 ◦C) with openings on top of the device channels. Optical micrographs of completed dies are shown in Figure 3.2. Each fabricated wafer consists of single silicon channels between the source-drain contacts as well as multiple silicon channels with common source and drain contacts (see Figure 3.3). These “multi-ﬁngered” devices

21 (a) (b)

(c)

Figure 3.3: (a) Optical micrograph of a single nanoribbon device with length and width of 20 µm and 2 µm respectively. (b) Image of a five-channel device with each channel being 20 µm long and 2 µm wide. (c) A 10-fingered device with L = 10 µm and W = 1 µm. were used for the studies on device area dependence and were found to be more robust that the single devices, which we believe to be due to the larger separation between the metal leads and the edge of the passivation window opening. Figure 3.3 also shows the passivation window opening in the SU-8 layer more clearly. The SU-8 processing can be a little tricky and it is very important to ensure that firstly, the SU-8 is not over-exposed and secondly, that the wafer is developed with significant agitation to ensure that the smaller openings are completely cleared. Figure 3.4 shows devices where the SU-8 windows were not completely cleared. In order to get rid of the residual

SU-8, the devices had to be exposed to oxygen plasma for roughly 4-5 minutes at 220W (or until the windows were visibly clean of any SU8 residues). Over-exposure to oxygen plasma results in a very thin SU-8 passivation layer which leads to signiﬁcant leakage current from the metal leads to the solution gate electrode. Therefore, care should be taken when carrying out this step.

Scanning electron microscope images of completed nanoribbon devices are shown in Figure 3.5, showing very smooth sidewalls which are very important for low-noise and high transconductance devices. Similar sidewall characteristics were obtained for nanowire devices as shown in Figure 3.6.

These devices were fabricated using electron beam (e-beam) lithography at the Cornell Nanofabri- cation Facility (CNF). The measurements carried out in this thesis involve both measurements on nanowire as well as nanoribbon devices. The nanowire devices were used for the dry, temperature based measurements described in Chapter 4 and the nanoribbon devices used for solution gated

22 (a) (b)

Figure 3.4: Optical micrographs showing devices where the SU-8 passivation windows were not completely cleared. The problem is more signiﬁcant for smaller openings. Treating the devices to oxygen plasma can be used to get rid of the SU8 residues.

(a) (b)

Figure 3.5: (a) Scanning electron micrograph of a single metallized nanoribbon device, without the SU-8 passivation layer. (b) SEM image of an array of parallel nanoribbon devices with the SU-8 passivation layer opening clearly visible in the center. The metal leads to each device can also be easily seen. measurements of Chapter 5. Based on previous sensing results[52], we obtain very good sensitivity with the nanoribbon devices and additionally the device characteristics are more uniform for the optically deﬁned nanoribbon FETs[29]. We also found that the optical lithography process (i.e nanoribbon fabrication) resulted in more robust bioFET devices, with low turn-on voltages (between

0V and -5V) and low leakage currents (∼ 30pA) when exposed to high salt concentrations (100 mM

NaCl). Figure 3.7 shows a typical Id-Vg curve for a solution gated nanoribbon device showing the low leakage current as well as the low turn-on voltage.

23 Figure 3.6: Scanning electron micrograph of a nanowire device with width of 200 nm and length of 4 µm.

Figure 3.7: Transfer characteristics for a solution gated bioFET device, showing the low threshold voltage (≈ 1.1V) as well as the low gate leakage current (shown in red and ≈ 20 pA)

24 RGain= 1Mohm

Vds DUT - + Vout

Figure 3.8: Amplifier circuit using an operation amplifier (LT1012) for current to voltage conversion of the drain current flowing through the bioFET device.

3.2 Multiplexed Detection Setup Gen.1

After the wafer fabrication, the wafer is diced into individual dies, with each die consisting of a number of devices (from 14 devices upto a maximum of 32) that are individually addressable.

Therefore, in order to get the most out of our sensing measurements and verify the repeatability of these measurements, we need to have a way to monitor a number of devices concurrently. Thus, we developed a multiplexed detection setup to concurrently measure 8 devices. Each amplification channel consists of an operational amplifier configured as a current-to-voltage converter which feeds into a National Instruments Data Acquisition (NI DAQ) Card as depicted in Figure 3.8. The gain resistor (Rgain = 1 MΩ) was chosen to accomodate typical drain currents of ∼100 nA such that the gain would be 106 (1 µA of input current produces 1 V of output voltage). In order to interface with the electrical measurement setup, the die has to be wirebonded and packaged in a ceramic

DIP holder (Spectrum Semiconductor Inc.). The device can then be hooked up to a connector box, ampliﬁer box and DAQ card as shown in Figure 3.9. The measurement of 8 channels is then carried out and recorded using a Labview program (designed in-house) as can be seen in Figure 3.10.

Concurrent sensing measurement results, using this multiplexed detection setup, have been shown previously[29].

25 Connector Box Op-Amp I-V Converter Box DAQ Card

Figure 3.9: Photograph of the experimental setup using a connector box, an 8-channel ampliﬁer stage and a connection panel which interfaces to the NI DAQ card.

Figure 3.10: Main Display panel for Labview software designed to concurrently measure 8 recording channels.

26 Figure 3.11: PCB board with assembled components for portable sensing measurements consisting of on-board ampliﬁcation channels as well as biasing voltages.

3.3 Multiplexed Detection Setup Gen.2

In order to further improve the portability and the noise performance of the measurement setup, the ampliﬁcation stage was combined with the connector box (interfacing to the DIP holder) in a custom designed printed circuit board (PCB). The PCB design involved eight ampliﬁcation channels, based on the same circuit as in Figure 3.8, with on-board switches for individual channels and individual op-amps. The board was connected to the DAQ card via a 68-pin VHDCI connector from NI and custom Labview software was written to interface and extract data from the 8 channels concurrently.

The ﬁnal assembled PCB board is shown in Figure 3.11. The board supplies both the drain-to- source voltage (Vds) as well as the gate-to-source voltage (Vgs). There is an external BNC connector and an associated switch to allow for an external gate voltage source since the on-board voltages are limited to 10V. There is also a gate leakage current measurement circuit which relies on a shunt resistor to convert the current into a voltage that can be subsequently measured by the analog-to-digital converter (ADC) of the NI DAQ card. The schematic of the leakage current

27 - AI 31 +

AO 1

(VGS) RSens= 100Mohm

Figure 3.12: Gate leakage current measurement circuit for PCB board setup Gen.2. The sense resistor was chosen such that the circuit is optimized for leakage current measurements around 1 nA. The voltage after the resistor is measured by Analog Input (AI) of the DAQ card. The leakage current is then calculated from (Vgs − Vmeas)/Rsens. measurement circuit is shown in Figure 3.12. The smallest leakage current than can be measured by this circuit is around 100 pA. The voltage after the sense resistor (Rsens ) is measured by one of the analog inputs (AI) of the DAQ card and the voltage drop is used to calculate the leakage current, Ileak = (Vgs − Vmeas)/Rsens, which is then used to determine whether a certain bioFET can be used.

3.4 Low Frequency Noise Measurement

We utilize the same data acquisition capabilities outlined in the previous sections to measure a large number of drain current values at high frequencies (typically 1000 Hz). To focus on the noise which makes up the fluctuations in the drain current, the measured signal is first filtered and then amplified using a low noise current amplifier from Stanford Research Systems (SR570). The bandpass filter used has corner frequencies of 0.03 Hz and 1000 Hz, which gets rid of the equilibrium DC signal and allows us to measure and record only the AC fluctuations in the current, that is the noise signal, within the bandwidth set by the bandpass filter. The output of the current amplifier is a voltage which can be fed into the NI DAQ card, interfaced again via a custom designed Labview program.

Noise analysis involves converting a time-domain signal into a signal in the frequency domain which essentially is a Fourier transform. The algorithm we use for our noise power spectrum extraction is

28 Figure 3.13: Modiﬁed periodogram method for estimating the power spectrum of a signal. The algorithm consists of two user deﬁned parameters which are the length of each periodogram (M) and the degree of overlap (D) between periodograms

Matlab’s pwelch method[53] which is a modified periodogram method for estimating the frequency domain power spectrum. Basically, the full signal is split up into smaller segments of data, based on what the user selects as the size of the periodogram (M), and an FFT is then carried out on each segment and finally averaged to obtain the power spectrum of the whole data set. The basic principles of the algorithm are depicted in Figure 3.13. The periodogram size (M) and the degree of overlap (D) between them, determines the number of periodograms generated. More periodograms implies smaller variance in the final power spectrum that the algorithm outputs whereas smaller sized periodograms implies that the frequency resolution of the final power spectrum is low.

Using our noise characterization tools, we can compare the noise performance of the diﬀerent measurement setups, while measuring the noise proﬁle of low noise device. The results of such a comparison are showin in Figure 3.14. It is evident that the portable sensing setup (Gen 2.) has a

29 similar performance to our low noise single channel measurement setup, which is as expected since the ampliﬁcation stage is closer to the devices. It is also important to note that the portable sensing setup fares worse when the frequency is high, due to the larger background noise of the op-amps we utilized in our PCB design. Also, for low current conditions, the noise amplitude is larger in the case of the Gen. 2 setup which is again most likely due to the higher noise contributions of the op-amps in our circuit. The multi-channel setup (i.e. Gen. 1) has a higher background noise level is general, though the eﬀect is more pronounced for low drain current.

3.5 Lock-in Ampliﬁer Measurements

The lock-in ampliﬁer is an instrument commonly used to make very sensitive, low-noise measurements. The working principle is that instead of measuring the DC response of a device where the

1/f noise contribution from other electronic components in the circuit is signiﬁcant, one measures the AC response of the device at a frequency which minimizes the noise contributions from those components. The voltage applied to the device under test (DUT) consists of a small AC modulation superimposed on a DC bias voltage:

Vin = VDC + vac sin(ωt + φsig) (3.1)

This results in a device current which also consists of a small AC current superimposed on a DC current level: d I I = I + v sin(ωt + φ ) (3.2) out DC d V ac sig where the term d I/d V is the conductance of the device. 1/f noise ﬂuctuations of the device itself can be modeled as ﬂuctuations in the conductance, G:

d I = G + δg(t) (3.3) d V

30 -2 10 (a) -4 10

-6 10 (1/Hz) 2 /I

I -8

S 10 Low Noise -10 10 Multi-Channel Portable-Sens

-12 10 -1 0 1 2 10 10 10 10 Frequency (Hz) 0 10 (b) Low-Noise Multi-Channel -2 Portable-Sens 10

-4 10 Noise Amplitude Noise -6 10

-8 10 -10 -9 -8 -7 -6 10 10 10 10 10 Drain Current (A)

Figure 3.14: (a) 1/f spectra for a bioFET device biased in strong accumulation, interfaced using the three measurement setups outlined in this section. It is clear that the Portable setup (Gen.2) performs just as well as the single channel low noise measurement setup for low frequencies whereas the multi-channel setup (Gen.1) has a very high noise background. (b) Noise proﬁle for the same bioFET device (extracted at f = 1 Hz) showing the dependence of the noise on the gate bias voltage or drain current. Again, the portable sensing setup has a similar performance to the single channel setup except for low current values.

31 The phase sensitive detector (PSD) of the lock-in ampliﬁer then essentially multiplies the current signal from the device (Iout) by a reference sine signal of the same frequency sin(ωt + φref ) and a low pass ﬁlter is subsequently applied (which gets rid of the non DC signals). The PSD output is then given by:

PSDout = vac cos(θ)[G + δg(t)] (3.4)

where θ = φsig − φref . Usually, the phase of the reference signal is adjusted to make the cosine term equal to 1. The output of the lock-in amplifier is then the AC current response of the device, vac × G. However, it is evident from Equation 3.4 that the output of the PSD includes the conductance fluctuations of the device, δg(t), which can be attenuated by the low pass filtering and this attenuation is no different than that obtained by low pass filtering in the case of a traditional

DC measurement. The normalized noise power spectrum from a lock-in ampliﬁer measurement with an a.c modulation frequency of 1 kHz is shown in Figure 3.15. The time constant on the

PSD was set at 10 ms which resulted in a corner frequency at 100 Hz as is evident in Figure 3.15.

Nonetheless, the 1/f noise spectrum is clearly visible below 100 Hz and supports the notion that the PSD output contains the conductance ﬂuctuations of the device as we showed in Equation 3.4.

To make sure that we are extracting the same noise performance from the lock-in amplifer as from the DC meaurement setup, we carry out measurements of SNR as a function of gate voltage. The definition of SNR in terms of current fluctuations is given in Equation 2.33 and if we write it in terms of conductance fluctuations, we obtain:

g 1 SNR = √m, G = √ (3.5) SG SVFB

where SVFB is the same quantity as that deﬁned in Equation 2.28. Therefore, SNR (as deﬁned in

Equation 2.33) is an equivalent metric whether one considers current or conductance fluctuations, since it reduces to the voltage source of the fluctuations, namely the noise in the flatband voltage

(SVFB) due to trapping/detrapping events. Figure 3.16 shows a typical plot of the DC SNR (DC

32 -4 10

-6 10 2 -8 /G

G 10 S ~ 1/f -10 10

-12 10 -1 0 1 2 10 10 10 10 Frequency (Hz)

Figure 3.15: Normalized noise power spectra of the conductance of a bioFET device as measured by a lock-in ampliﬁer. The 1/f reference (dashed line) shows that the intrinsic 1/f noise of the DUT is not aﬀected by the choice of the AC modulation frequency.

33 350 12000 SNR gm 300 250 10000 gm (nA/V) ) 200 -1 V 8000 150

SNR ( 100 6000 50 0 4000 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 Vsg (V)

Figure 3.16: SNR and DC transconductance (gm) as a function of gate voltage in the case of a DC source-drain bias.

source-drain bias voltage, Vds) as a function of gate voltage (Vg) as well as the DC transconductance

(gm) as a function of Vg. SNR can also be extracted in the case of an AC modulation of Vds, from the power spectrum of the conductance fluctuations as shown in Equation 3.5. The SNR and AC transconductance (gm, G) are plotted in Figure 3.17 as a function of Vg. It is evident that the SNR is the same as in the case of the DC measurement, which confirms that the 1/f noise fluctuations of the device are superimposed on the AC fluctuations when making a lock-in measurement and thus appear at the PSD output as highlighted in Equation 3.4. Therefore, the lock-in technique is very useful in reducing the 1/f noise contributions from external circuit elements, but not in reducing the fundamental 1/f noise of the DUT itself. This is in fact why it is possible to use a lock-in amplifier to carry out noise measurements of low-frequency resistance fluctuations[54]. One advantage of the lock-in amplifier setup in sensing experiments however, is the stability of the time traces as seen in Figure 3.18. In the case of a lock-in measurement, a DC source-drain bias is not needed, since the AC modulation is sufficient to extract the conductivity at Vds = 0. This in turn contributes to reduced electrochemical reactions at the source and drain contacts which most probably increases

34 35 12000 SNR gm 30 10000 25 g m,G ) -1 8000 20 (nS/V) V 15

SNR ( 6000 10 4000 5 2000 0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 Vsg (V)

Figure 3.17: SNR and AC transconductance (gm, G) as a function of gate voltage in the case of an AC modulation of the source-drain bias. the stability of the sensing experiment as well as impoves the lifetime of the bioFET devices.

3.6 Summary

In this chapter, we covered the fabrication of nanoribbon FET devices, with the main focus of improving reliability and yield and the instrumentation design to carry out sensitive, high- throughput measurements. By adding in a top-gate dielectric layer of silicon oxide (20 nm) and focusing on device widths that are 1 micron or larger, the critical dimension being the thickness

(≈ 40 nm), we are able to improve device uniformity and extend the lifetime of these devices to several weeks in an electrolyte environment, which allows for more reliable sensing data and more complex functionalization schemes. In order to increase the throughput of the measurement, an eight-channel ampliﬁer box was designed combined with software written in Labview to concurrently measure the drain current of 8 devices (Gen.1). A second generation of this multiplexed detection setup (Gen.2) was designed to combine the device interface with the ampliﬁcation circuit on a single PCB board. The relevant bias voltages were then applied via a NI DAQ card which was also

pH 8.13

pH 6.06 pH 6.06

pH 4.06 pH 4.06

pH 2.18 pH 2.18

Figure 3.18: pH calibration curve for a bioFET sensor using the lock-in technique. The AC current response (proportional to the conductance at Vds = 0) of the PSD is plotted as function of time, showing the stability of the time traces when an AC source-drain modulation is used. the interface used to measure 8 channels concurrently. Noise measurements were carried out using the same DAQ card for high sampling frequencies but only a single amplification channel (using a low noise current amplifier, SR570) for low noise current-to-voltage conversion. The different measurement setups were compared against each other for the measurement of a nanoribbon device and it was concluded that the portable sensing setup (Gen. 2) had very similar performance to the low noise, single channel measurement setup provided that (1) the frequency was low (< 10 Hz) and (2) the drain current was larger than 10 nA, which is very promising for the eventual design of a portable and sensitive point-of-care measurement setup. We also carried out measurements using a lock-in amplifer (LIA) setup, which allows one to choose a certain modulation frequency such that the noise pickup from other electronic components is minimized. Our measurements of SNR show that the bioFET device noise dominates for both the LIA and DC measurement setups (single channel measurement) and moreover, the choice of modulation frequency in the lock-in technique does not affect the amplitude of the resistance fluctuations measured at the output of the PSD, resulting in the same SNR for both DC and AC measurements.

36 Chapter 4

Low Frequency Noise of BioFETs

4.1 Introduction

For large area metal-semiconductor-oxide devices, the most common method of probing oxide/interface and mobile charges is the use of capacitance voltage measurements[41]. However, for nanoscale ﬁeld-eﬀect transistor(FET) devices, such measurements are very challenging owing to the small capacitance of these devices, which is easily overwhelmed by parasitic capacitances.

Alternative methods which are both sensitive and non-intrusive so as not to irreversibly alter the electronic properties of the devices are highly sought after. One such method involves the use of noise measurements which attempt to extract information from the dynamic processes involved in the interactions of channel electrons with defects, charge centers and interface states[38][55][56]. One of the major concerns with the down-scaling of electronic devices is the decrease in signal-to-noise ratio since the channel current becomes more prone to fluctuations due to surface/interface states as the surface to volume ratio is increased[57]. Therefore, not only do noise measurements serve as a way to quantify and hopefully reduce the noise fluctuations, but they also allow users to compare across different material systems, device architectures and measurement conditions, in order to identify devices with better noise performance. As researchers began to experiment with nanowire FETs based on different semiconductor materials with different mobilities and gate dielectrics, it became

37 obvious that there was a need for a metric to compare across different device characteristics as well as measurement conditions[46]. Such a metric is Hooge’s parameter, αH , defined in Section 2.4 which is independent of device parameters and measurement conditions[58]. This metric focuses on the noise performance only, but its power lies in the simplicity of its measurement/extraction and the universality of the parameter. Along those lines, a plot of the Hooge’s parameter for various material systems and device architectures will immediately shed light on which combinations result in the best, low-noise performance. Such a plot is shown in Figure 4.1. We can clearly see that devices based on bulk CMOS fabrication have a much lower αH value, on average, than “bottom-up” semiconductor nanowire-based FETs. Figure 4.1 also includes one of our “top-down” silicon-on- insulator (SOI) nanowires (width of 100 nm, height of 40 nm), highlighting the advantage of the top-down process in producing better quality devices with lower noise figures. In this chapter, we consider the use of low frequency noise analysis, namely 1/f noise models, to better understand the physical mechanisms behind current fluctuations in bioFET sensors and guide the fabrication of devices with lower noise figures, with the goal of improving the signal-to-noise ratio and the limit of detection of these devices.

4.2 Eﬀects of Etching Process on BioFET Characteristics

Silicon nanowire (Si NW) and nanometer-scale field effect transistors (FETs) have proven to be quite useful as chemical and biological FETs (bioFETs). However, efforts to fabricate such devices by top- down lithographic methods have often exhibited degraded electrical characteristics associated with the exposed silicon surfaces and high surface-to-volume ratio inherent in NW sensors[10][59][11].

These surfaces have most often been prepared by plasma-etching techniques, long known to cause surface states and bulk damage[60][23]. The presence of these defects has likely been the source of high levels of low frequency noise (LFN), diminished sensitivity, and threshold voltage hysteresis in NW sensors. Anisotropic wet etching has been previously proposed as a method for producing bioFETs with high-quality surfaces as compared to plasma-etched nanostructures. While devices

38 Figure 4.1: Summary of Hooges parameter (αH ) for diﬀerent nanowire materials as well as submicron MOS structures utilizing high-k dielectrics. Included is our best SOI silicon nanowire device (red circle). The dash-dotted line shows the ITRS roadmap speciﬁcation of αH for the 45nm technology node (Adapted from [46]).

39 200 nm

Figure 4.2: SEM images of two nanowires (NWs) etched using an orientation dependent wet etch, TMAH, and the other one etched using a dry RIE etch chemistry involving Cl2. TMAH etches (100) planes faster than (111) planes and the resulting trapezoidal shape can be clearly seen in the SEM image. The device etched using Cl2 has a more rectangular cross section as expected from an anisotropic RIE etch. have been fabricated using tetramethylammonium hydroxide (TMAH) to produce smoothly faceted

NW devices[23][61], it has not been demonstrated conclusively and quantitatively that the wet- etching process is responsible for the superior electrical performance of these devices. The only semi-quantitative comparison was carried out in our lab using pH sensitivity as the benchmark[11].

It was observed that the RIE etched device showed a lower signal change than what was expected for a TMAH etched device of the same dimensions, for the same change in pH of the buﬀer solution.

We veriﬁed these claims and placed them on more solid, quantitative grounds by comparing nominally identical bioFETs fabricated by TMAH anisotropic etching, as well as two common plasma-etching methods, namely Cl2 and CF4. SEM images of the etched nanowire channels are shown in Figure 4.2. The NW channels for the devices in this investigation were all nominally

100 nm wide and 2.5 µm long. The gate voltage was applied to the back-gate and drain-to-source voltage was kept constant at 0.1V for all measurements. The drain current in this case was measured with a Keithley 2636 source-meter at a sampling frequency of 25 Hz. The equilibrium DC signal was subtracted from the measured current values and the pwelch algorithm was applied to the data using software written in Matlab. The LFN of our devices follows Hooge’s equation given by

Equation 2.27. The frequency exponents for our devices were found to lie in the range 0.8< β <1.5.

1/f β noise is usually characterized by an exponent 0.8 < β < 1.2 [40]. The slightly higher exponents

40 Figure 4.3: Plot of noise amplitude, A, as a function of the drain-to-source voltage (Vds) at a fixed gate voltage, clearly showing that A is independent of the drain current if the number of charge carriers remains unchanged. encountered in our case, as can be seen in Figure 4.4, can be understood by the presence of RTS signals superimposed on the mobility fluctuation 1/f noise[62]. In the present situation, we do not expect to be able to observe RTS on top of 1/f noise since we will show that our devices satisfy the “rule of thumb” N > 1/αH [63]. Exceptions to the rule of thumb are possible in the case of inhomogeneous samples, which would explain additional RTS noise giving rise to a higher 1/f exponent than expected for pure 1/f noise[64][65]. Nonetheless, we confirm the validity of the mobility fluctuation model by observing the invariance of the noise amplitude A = αH /N on the drain current (refer to Figure 4.3), measured at a fixed gate voltage and varying Vds, as well as the linear dependence of 1/A on the gate voltage at fixed Vds (refer to inset of Figure 4.4). Since, in the determination of αH , we operate the devices in the linear region of the transfer curve, the number of carriers is given by: C N = (V − V ) (4.1) e g th where the back-gate capacitance C is determined from simulation results using Altas Device 3D from

Silvaco. The simulation was carried out by a former student[49] and the results of the capacitance voltage simulations were used to extract the value for αH . Therefore, from the slope of the inset

41 Figure 4.4: Typical dependence of 1/f noise spectra on gate voltage for a TMAH-etched device, from which the noise amplitude A, at each gate voltage (13 - 25 V), can be extracted. The inset shows 1/A plotted as a function of Vg, where the slope of the line is used to calculate αH . in Figure 4.4 which is equal to C , the Hooge’s parameter can be determined for each of the e αH

3 types of etched NW devices. The results are shown in Figure 4.5. The TMAH-etched devices have a considerably lower Hooge constant (close to an order of magnitude lower) than the plasma- etched devices and show smaller device-to-device variations. The average Hooge constant for the

−3 TMAH-etched devices is given by αH = 2.1 × 10 , which is comparable to the Hooge constant

−3 values reported for submicrometer MOSFETs with a metal/HfO2 gatestack (αH = 1.6 × 10 for

3 NMOS and αH = 6.9 × 10 for PMOS[66]. The average Hooge parameters for the plasma etched

−2 −2 devices are 1.5 × 10 for Cl2 devices and 1.7 × 10 for CF4 devices. An alternative approach based on a trapping/detrapping model[40][67] to analyze the noise measurement data makes use of the empirical relationship: M g 2 S = m (4.2) I 2 β Cox W L f

42 Figure 4.5: (a) Measured Hooge parameters for three sets of devices. Each set was etched using either TMAH or Cl2 or CF4. The box plot shows the 25th percentile, the median, and the 75th percentile (the mean is indicated by asquare marker). The average values of αH were 0.0021 for the TMAH devices, 0.015 for the Cl2 devices, and 0.017 for the CF4 etched devices. (b) Measured subthreshold swing for three sets of devices, etched using either TMAH or Cl2 or CF4. The average value for the TMAH devices was 1.0 V/decade. For Cl2 etched devices, the average was 2.6 V/decade, and for CF4 devices, the average was 3.0 V/decade. where M is the parameter to be extracted. W and L are the width and length of the channel, respectively, gm is the transconductance at the operating point of the measurement, and Cox is the gate capacitance per unit area. Using the aforementioned model, the average M parameter for the TMAH etched devices is M = (6 ± 2) × 10−24. Likewise, the average values for the plasma-

−24 −24 etched devices are M = (22 ± 10) × 10 for the Cl2 devices and M = (12 ± 4) × 10 for the CF4 devices. A similar trend is observed for the noise parameter M, where the TMAH-etched devices exhibit a lower noise ﬁgure than the plasma-etched ones.

The subthreshold swing measurements for each type of device are also shown in Figure 4.5(b).

Subthreshold swing, SS, is given by the following:

k T C + C + C SS = 2.3 ox d it (4.3) q Cox

43 where Cd is the depletion capacitance per unit area of the silicon channel and Cit is the capacitance per unit area associated with interface traps. The measured values of S are all quite high due to the thickness of the buried oxide (405 nm) serving as the gate insulator, which makes Cox small. However, the TMAH devices exhibit significantly lower average subthreshold swing and smaller device-to-device variation than either of the plasma-etched devices, which follows the trend exhibited by the values for αH. The differences in SS are attributed to the different values of Cit in the case of TMAH devices versus plasma etched devices. We attribute the lower noise figure and lower subthreshold swing, in the case of the wet-etched devices, to a lower density of surface states at the etched sidewalls. The differences in oxide capacitance and nanowire channel depletion capacitance are negligible and cannot account for the differences in the measured subthreshold swing, which we ascribe to variations in the interface state density. The noise and subthreshold swing measurements, therefore, together quantitatively confirm that wet-etching based methods yield smoother surfaces and consequently better electrical characteristics.

4.3 Temperature Dependence of 1/f Noise Mechanisms

The analysis of the previous section was focused on the linear regime of operation, which is where Hooge’s equation is applicable (see Equation 2.27). For a more complete modeling of the noise, from subthreshold to strong accumulation or strong inversion, the number ﬂuctuation model

(Equation 2.29) and the correlated number-mobility fluctuation model (Equation 2.30) are more relevant. To fully characterize the 1/f noise of our Si NWs, we carried out measurements from weak to strong inversion at low drain bias and at different temperatures (100 to 300 K). We observe a change in the noise mechanism as the temperature is lowered, from the ∆n-∆µ correlated model to the ∆n model. At certain gate voltages, the 1/f spectra evolve into Lorentzian spectra, indicative of random telegraph signal (RTS) noise. The NW channels were defined by a wet orientation dependent etch using tetramethylammonium hydroxide (TMAH), which we have shown yields better electrical characteristics and lower noise figures compared to dry etching techniques. The devices are used

44 Figure 4.6: Typical noise spectra measured for a device at diﬀerent gate voltages (22 - 40 V) from subthreshold to strong inversion. The exponents of the 1/ f spectra all lie in the range 0.8 < β < 1.2. The ﬂattening of the noise spectra is due to background noise from the measurement setup.

in the back-gated conﬁguration, where the gate voltage Vg is applied to the handle layer of the

SOI wafer. The source-drain bias was kept constant at 0.1 V and the drain current Id was fed into a current preamplifier (SRS 570), setup as a band-pass filter with cutoff frequencies at 0.03 and

1 kHz. The noise data was recorded using a National Instruments DAQ card at 1000 samples/s and the spectral power density estimated using the pwelch function in Matlab. The temperature dependent measurements were carried out in a Janis Instruments variable temperature cryostat.

With the DAQ card measurement setup, noise spectra were measured up to a frequency of 500 Hz, and typical spectra are shown in Figure 4.6.

2 The normalized drain current noise, SI/I at f=1 Hz (noise amplitude, A), is extracted and plotted

2 against Id in Figure 4.7. In the subthreshold region at 300 K, it is observed that SI/I is proportional

2 to (gm/I) , where gm is the transconductance extracted from the Id −Vg curve. Since the correlation does not hold as well in the strong inversion region, we conclude that the 1/f noise of our devices

2 follows the ∆n-∆µ correlated model. For measurements at 100 K, the SI/I versus Id plot indicates

2 a change in the dominant 1/f noise generating mechanism, since SI/I is now proportional to

45 Figure 4.7: Normalized drain current noise amplitude at f=1 Hz (A) is plotted against drain current 2 (Id). Measurements at room temperature (300 K) compared to the gm/I curve clearly indicate that the device follows the correlated ∆n-∆µ noise model. For measurements carried out at 100 K, the noise amplitude is consistent with a carrier number ﬂuctuation noise ( ∆n) model as indicated by the change in slope compared to the 300 K data in the strong inversion region.

2 2 2 (gm/I) even in strong inversion. The enhanced correlation between SI/I and (gm/I) indicates that at low temperature the correlated mobility ﬂuctuations are suppressed and carrier number

ﬂuctuations dominate the LFN[68]. The transition from the ∆n-∆µ correlated model to a purely

∆n model is a gradual transition as seen from the change in slope in strong inversion in Figure 4.8

(a). The data for T=250 K and T=100 K have been scaled to make the change in slope clearer, since the noise is subthreshold increases with decreasing temperature. Even though only the data for T=100 K is shown, the measurements carried out at T=200 K are proportional and show the same trend as the T=100 K data. This means that the transition happens over a small temperature range, between 200 K and 300 K. For the carrier number fluctuation model, including correlated mobility fluctuations, the gate-referred noise is given by Equation 2.30. For negligible correlated mobility fluctuations we expect Svg to be equal to the flatband-voltage noise density (SVFB), but for appreciable values of the scattering coefficient α and large number of carriers (i.e operating in

46 Figure 4.8: (a) The data show the gradual change of the slope in the strong inversion regime as temperature is lowered at T=300, 250, and 100 K, respectively. The data points for 250 and 100 K have been scaled for easier visualization of the change. (b) The data are fitted using the correlated ∆n-∆µ noise model, confirming the change in the noise generating mechanism as the temperature decreases. The Coulomb scattering coefficient, α, is also extracted from linear fits to the data at 250 and 300 K. The fit to the data at 100 K clearly indicates that the correlated model is no longer valid at that temperature.

47 strong inversion), we expect a linear relationship between Svg and Vg. We therefore investigated how well the data in Figure 4.8(a) fits the correlated ∆n-∆µ model as temperature is lowered. For the measurement at 300 K in Figure 4.8(b), the data confirm what we expect, with Svg directly proportional to Vg. As the temperature is lowered to 250 K, the linear relationship becomes hard to resolve due to the scatter in the data points, but a linear least-squares fit gives an estimate of the dependence. For 100 K, the absolute noise magnitude is much larger as expected from previous observations and the direct proportionality between Svg and Vg vanishes. Instead, the gate-referred noise increases as gate voltage is decreased. In this regime, the correlated mobility fluctuations have been completely suppressed and what we observe is the gate voltage dependence of the carrier number fluctuation noise, or in other words the gate voltage dependence of the interface trap density. √ The calculated slopes correspond to α Cox µ SVFB. Both the mobility and the flatband-voltage noise density have a slight temperature dependence from 300 K down to 250 K. Accounting for this, it is determined that the scattering coefficient α decreases as the temperature is lowered, from

1.9 × 104 V · s/C (at 300 K) to 96 V · s/C (at 250 K). The capacitance values were obtained from

Atlas 3D simulations as mentioned in the previous section. As temperature is lowered, it is also observed that mobility increases due to reduced phonon scattering. This trend is observed upto the lowest temperature measured (around 100K). Lower temperatures were impractical due to the fact that the handle layer was not degenerately doped and therefore at low temperatures, freeze-out of the dopant atoms render the handle layer completely insulating and back-gating becomes impossible.

The temperature dependent measurements of mobility for two devices are shown in Figure 4.9.

The mobility is calculated from the measurement of the peak transconductance (extracted from numerical diﬀerentiation of the Id-Vg curve), through the following:

L g µ = m (4.4) W Cox Vds

Thus, both mobility scattering and mobility ﬂuctuation noise is suppressed in those devices as temperature is lowered.

48 Figure 4.9: Plot of mobility as a function of temperature for 2 NW devices, showing the increase in mobility as temperature is decreased due to suppressed phonon scattering.

For devices where a large number of trapping/detrapping events are involved, the superposition of multiple Lorentzian spectra (signature of a two level random telegraph signal) results in 1/f- type spectra[37]. However, for certain combinations of gate bias and temperature, only a few traps are involved in the carrier number ﬂuctuation and we are able to decompose the 1/f spectra into its constituent Lorentzian components[69][70]. Figure 4.10 explicitly shows the evolution of the 1/f spectrum at room temperature to a Lorentzian curve superimposed on a 1/f spectrum, as temperature is lowered to 120 K. The primary eﬀect of the decrease in temperature is to reduce the number of traps which are thermally accessible, resulting in a noise spectrum originating from a few

ﬂuctuators only. 1/f noise is still present for frequency values much less than 25 Hz, but the roll-oﬀ at approximately 25 Hz and the subsequent 1/f2 dependence clearly indicates a superimposed RTS power spectrum. We will investigate RTS spectra further in the next section. This decomposition of the 1/f noise into a regime where a few active traps dominate the noise power spectrum provides very strong evidence for trapping/detrapping processes as being the physical origin of 1/f noise[37].

4.4 Random Telegraph Signals

Random Telegraph Signals (RTS) are discrete transitions in the current level which represent the interactions of electrons with a single trap, of a well deﬁned energy level. A simple schematic of such

49 Figure 4.10: Evolution of the normalized noise power spectral density from room temperature (300 K) to 120 K for a NW device. At certain gate voltages and at low temperature (120 K), only a few traps are active and contribute to the noise spectrum, which consequently changes from a 1/f spectrum (with the dotted line representing a 1/f least-squares fit) to a Lorentzian superimposed on a 1/f trend, evident for the larger frequencies (with the solid line representing a Lorentzian least-squares fit with a corner frequency of 25 Hz). signals is shown in Figure 4.11. The power spectrum of RTS can be modeled through a Lorentzian as such: K Γ S = (4.5) f Γ2 + (2 π f)2 where K is usually a fitting parameter describing the amplitude of the RTS, Γ is a function of the two characteristic time constants, τ0 and τ1, representing the average time spent in the low and high current states respectively. Γ can be calculated from:

1 1 Γ = + (4.6) τ0 τ1

In the previous section, we showed how 1/f noise spectra can be decomposed into Lorentzian spectra (characteristic of RTS). Figure 4.12 shows how multiple Lorentzian spectra, from discrete single level trapping events, can be combined to give a 1/f spectrum, within a certain frequency range. For certain combinations of temperature and gate voltage, we observed clear RTS signals

50 I (A)

τ1

τ0

Time (s)

Figure 4.11: Illustration of RTS in a current-time trace, showing two discrete current levels with characteristic times τ0 and τ1, representing the low and high current states respectively.

Figure 4.12: Computed results showing how the addition of Lorentzian spectra due to discrete two-level trapping systems can and indeed does result in 1/f noise spectra for an ensemble of such traps.

Figure 4.13: A segment of drain current versus time measurement for a NW bioFET device showing the discrete two-level switching, indicating the activity of a single trap resulting in RTS. in our NW devices as can be seen from the time trace in Figure 4.13. The noise power spectra for diﬀerent gate voltages are shown in Figure 4.14 and it is obvious that the shape follows the

Lorentzian spectrum given in Equation 4.5. As the gate voltage is increased to 27 V, it is observed that the Lorentzian spectrum starts to change to a more 1/f type spectrum.

To obtain more information about the nature of the trap, we investigated the mean times spent in the low and high current states (τ0 and τ1 respectively) and their dependence on gate voltage first and secondly on temperature. The histograms in Figure 4.15 show that as gate voltage is increased, the current spends more time in the “low” state. We associate the “high” current state with a neutral trap state, since that is the condition under which coulombic scattering is minimized. As the gate voltage is increased, the Fermi level gets closer to the conduction band (for an n-channel device in this case) and the probability of a trap being occupied increases. Therefore, we conclude that the “low” current state is associated with a filled trap state and the “high” current state is associated with an empty trap. Since the trap is charged when filled and neutral when empty, we conclude that the trap is an acceptor type trap[71]. It is common and more informative to refer to the characteristic emission and capture times (τe amd τc) instead of τ0 and τ1, when characterizing

Figure 4.14: Normalized noise spectra at diﬀerent gate voltages showing the typical Lorentzian spectra associated with RTS. As the voltage is increased to 27 V, it is clearly seen that the Lorentzian spectrum is changing to a 1/f spectrum, indicating a gate voltage dependence of the RTS.

a certain trap level. The characteristic emission time (τe) refers to the average time it takes before an electron is emitted from the trap whereas the capture time refers to the average time is takes before an electron is captured into the trap. After identifying the nature of the trap (whether it is an acceptor or donor), it is straightforward to determine which of τ0 or τ1 corresponds to τe. In our case, since the trap is an acceptor, the “low” or “0” current state is associated with a filled trap and therefore, τ0 = τe and τ1 = τc. For each current time trace (such as that shown in Figure 4.13) we assign a certain threshold current value to differentiate between the two states, 0 and 1. The time spent in each state was then determined and a Poisson fit was applied to the distribution of capture and emission times to extract the characteristic τe and τc for each RTS time trace. Figure 4.16 shows the extracted characteristic times τe and τc at different gate voltages. The inset shows an example distribution of emission times along with the exponential Poisson fit which allows us to extract a characteristic emission time. From the plot in Figure 4.16, we confirm our deduction regarding the nature of the trap since τe increases and τc decreases as the gate voltage is increases, which means that the electron spends more time before being emitted as the trap occupancy increases.

53 We can further model the two-level switching as a thermally activated process between two states, where the average time (τi) spent in state i is given by an Arrhenius law[70]:

E τ = τ exp i (4.7) i 0,i k T

where Ei is the activation energy required to leave state i and 1/τ0,i corresponds to an attempt frequency which is usually on the order of the inverse phonon frequency. By varying the temperature, we are able to plot the characteristic emission and capture times in Figure 4.17. On a semilog plot, the slope allows us to determine the activation energy of the capture process (Ea, c

= Ea, 1 = 250 meV) as well as the activation energy of the emission process (Ea, e = Ea, 0 = 180 meV). The emission and capture times can be used to independently calculate the corner frequency

(fc) using Equation 4.6 where it is important to note that Γ = 2 π fc. fc can also be estimated directly from the Lorentzian spectra in the frequency domain (see Figure 4.14). The estimated corner frequencies are in good agreement with the calculated ones using Equation 4.6. It is found that fc also follows an Arrhenius law, with an activation energy of 230 meV (see Figure 4.18).

By considering the statistics of capture and emission involving the occupancy of a single trapping level, the following relationship between the capture and emission times can be derived[72]:

τ E − E c = g exp T F (4.8) τe k T

where (ET − EF) is the trap energy level relative to the Fermi level and g is the degeneracy factor which is usually considered to be one. Combining Equations 4.8 and 4.7, we deduce that:

τ0,c ET − EF = Ea,c − Ea,e + kT ln (4.9) τ0,e

The term kT ln τ0,c was calculated to be equal to 60 meV, which results in a trap level that is 10 τ0,e meV below the Fermi level. Since the measurements of the RTS were carried out in the subthreshold

54 Vg = 25 V

Vg = 26 V

Vg = 27 V

Figure 4.15: Histogram of current values showing the bimodal distribution characteristic of a two- level switching signal. The changes in trap occupancy as the gate voltage is varied can be seen as changes in the populations of the “low” and “high” current states. From the changes evident in the histograms, we conclude that the active trap in this case is an acceptor trap, that is the trap is charged when ﬁlled and neutral when empty.

55 T = 130K 90 2.8 80 -t/τ 70 ̴ e 2.6 60 2.4 τ c

50 (ms) 40 2.2 (ms) e

τ 30 2.0 20 10 1.8 24 25 26 27 Vg (volts)

Figure 4.16: Plot of the capture (τc) and emission (τe) times as a function of gate voltage at a temperature of 130 K. The inset shows the typical distribution of times which follow a Poisson distribution. An exponential or Poisson ﬁt allows us to extract the characteristic emission and capture times.

Emission Capture

Figure 4.17: Arrhenius plot of the characteristic emission time (τ0) and capture time (τ1) as a function of temperature. From the slope, the thermal activation energy of the capture and emission processes can be extracted.Ea, e = 250 meV and Ea, c = 180 meV.

56 Figure 4.18: Arrhenius plot of the corner freqency (estimated from the noise power spectra) at diﬀerent temperatures. The linear ﬁt shows that fc can be modeled by a thermally activated process with an activation energy of 230 meV. regime of the FET device, we assume that the Fermi level is close to mid-gap. This results in an acceptor trap level that is about 0.57 eV from the conduction band edge, which is consistent with deep acceptor levels that are caused by the presence of gold[73]. In our case, the source and drain contacts were formed from evaporated titanium followed by gold which might have migrated closer to the channel during the annealing step.

The relative amplitude of RTS can be modeled as[74]:

∆I 1 1 d = ± αµ (4.10) Id WL N where α is the scattering coefficient we encountered earlier in Equation 2.30 and N is the number of carriers per unit area. These devices show extremely large relative amplitudes (50 - 120%) compared to the values that have been reported in the literature[75]. The relative amplitude as a function of 1/Id is plotted in Figure 4.19. As we expect, the relative noise amplitude is linearly proportional to the inverse of the drain current (Id) with the slope of the line being related to the device dimensions as well as the effective field-effect mobility (µeff ). Since the slope does not change much in the temperature range investigated, we conclude that the changes in mobility are

1.2

1.0

0.8 ∆Ι/Ι

0.6 110K 120K 0.4 130K

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 9 -1 1/Id (x10 A )

Figure 4.19: Relative amplitude of RTS plotted as a function of the inverse of drain current (1/Id). The linear fit shows that the data agrees well with the 1/N dependence of relative RTS amplitude. The large changes in the level of the RTS noise is attributed to changes in the scattering coefficient α, resulting in different levels of mobility scattering. negligible. Therefore, any changes in the intercept are due to changes in the scattering coefficient α.

As temperature is lowered, the value of α is found to increase, resulting in more mobility scattering and thus a larger relative amplitude of the RTS. These large amplitudes of RTS present a major problem for ultra-scaled devices where the eﬀects of a few scattering centers become much more signiﬁcant. Therefore, even though gold is an inert material for electrochemical and biochemical applications, its use in the fabrication of bioFETs should be avoided for better noise performance.

4.5 Summary

In this Chapter, we have sought to apply noise analysis techniques to silicon nanowire bioFETs as a non-destructive and accurate tool to characterize the noise performance of such devices, with the goal of improving the signal-to-noise ratio. We have demonstrated the use of anisotropic wet orientation dependent etching with TMAH as a method of producing bioFETs with high-quality surfaces and, consequently, superior electrical characteristics as compared to plasma etched surfaces.

Our results lead us to conclude that, as bioFET devices are downscaled further and the surface-to- volume ratio increases, the particular etch process used will be critical in determining the density of

58 surface states and, ultimately, the noise performance. We have also characterized the temperature dependence of the LFN behavior of NW bioFETs. At room temperature the devices are shown to follow the correlated number-mobility fluctuation model with noise spectra that show a 1/f dependence even in subthreshold. As the temperature is lowered, we observe a suppression of the correlated mobility fluctuations, yielding a pure carrier number fluctuation noise. For even lower temperatures, the LFN noise is decomposed further to a few carrier number fluctuators, which give rise to a Lorentzian power spectrum instead of a 1/f spectrum. For certain combinations of gate voltage and temperature, we were able to probe the regimes where we would observe very strong RTS time traces (with relative amplitudes >100%). Using time-domain as well as frequency domain analysis techniques, we were able to extract the characteristic times and activation energies for capture and emission and also determined that the trap was due to a deep acceptor level 0.57 eV from the conduction band edge, indicative of the presence of gold. The measurements carried out in this Chapter clearly indicate that noise fluctuations can be a very significant issue for highly scaled devices and to ensure that such miniaturization can be pursued, while keeping the signal-to-noise ratio unchanged, will require a deep understanding of the noise generating mechanisms in such devices. For instance, the RTS analysis demonstrating the presence of gold clearly shows that the use of gold is a significant source of current fluctuations and therefore should be avoided in the design of bioFET sensors even though gold is a great inert material for a lot of biochemical/electrochemical applications. Furthermore, noise analysis can be used as a benchmarking tool to identify process steps that yield a lower noise figure for instance and thus, guide the fabrication and development of bioFET sensors with lower noise and consequently lower LOD.

59 Chapter 5

Signal-to-Noise Ratio as a

Performance Metric

5.1 Introduction

Noise analysis is a tool that has only recently been adopted by the nanowire research community as described in Chapter4 and only more recently been applied to the field nanowire/nanoribbon based biosensors[36][76][35] with the realization that the noise properties will drastically impact the smallest signal changes that can be measured as the detection limits are being pushed further and further. A commonly used metric in the field of biosensors is the sensitivity, defined as the relative change in the signal (∆I/I), which allows for comparisons across devices with different dimensions and transfer characteristics. Consequently, a lot of theoretical as well as experimental conclusions are based on the optimization of this performance metric[13][32]. However, as far as the limit of detection of sensors is concerned, this metric fails to account for the primary limitation which is the noise of the particular sensor system/device. As devices are scaled down to the nanometer regime, the channel current becomes more prone to fluctuations due to oxide traps and interface states and the low-frequency noise of the device becomes a very serious limitation for any DC

60 measurement as we have shown in Chapter4. Therefore, it becomes essential, in the design of better sensors with low limits of detection (LOD), to consider a performance metric which includes the signal transduction/amplification as well as the effects of noise fluctuations, in order to provide a complete physical model to understand the parameters which affect the LOD. Signal-to-noise ratio

(SNR) can be used as such a metric[77] since it involves both the device transconductance (gm) which is directly proportional to the signal generated as well as the current noise power density

(SI ) which can be modeled using the correlated ∆n-∆µ model given in Equation 2.30 for instance.

An equation for SNR was derived in Chapter 2 (see Equation 2.33) with the very simple result that the LOD (which is given by 1/SNR) is roughly equal to the amplitude of the ﬂatband voltage noise.

Therefore, using the noise measurement tools described in Chapter4, SNR can be extracted for any device, prior to sensing experiments and consequently be used to either compare devices with diﬀerent LOD or screen the devices for the lowest LOD.

5.2 Sensitivity

The sensitivity of FET biosensors is usually deﬁned as ∆I/I. This relative signal change, which is a property of the device and measurement conditions, needs to be distinguished from the sensitivity of the chemical/biological transduction layer, which turns out to be more relevant for biosensing applications. For example, when considering the pH sensitivity of a device or surface, the value is usually reported as a change in device signal per unit change in the measurand, in this case pH value of the solution. The relative signal change is a function of the bias point (Vg − Vth) as can be seen in Equation 5.1. Looking at the latter equation, it is obvious that the closer the gate voltage

(Vg) is to the threshold voltage (Vth), the larger the relative signal change (∆I/I). However, as can be seen in Figure 5.1, the larger the relative signal change, the larger the relative noise level as well. Figure 5.1 shows the same pH measurement (from pH 7.1 to 7.9) carried out at diﬀerent gate voltage bias points, resulting in diﬀerent relative signal changes as given in Equation 5.1. As mentioned earlier, using the relative signal change as a performance metric ignores the fact that

61 the amplitude of the noise also varies with the sensitivity.

∆I ∆ψ = 0 (5.1) I (Vg − Vth)

The true sensitivity remains unchanged as can be seen from Figure 5.2. The device response (∆I) scales linearly with gm, as expected. From the linear ﬁt, the change in surface potential for a unit change in pH can be extracted as 39 mV/pH. This clearly indicates that the true sensitivity is independent of the bias point that is chosen. It only aﬀects how the surface potential change is extracted from the current signal change. Figure 5.2 also highlights the fact that the measurement itself is a measurement of ∆I and since any bias point (i.e. gm values) can be used to extract the true surface sensitivity, we should focus our attention on where the device noise is minimized so that the measurement is carried out with the highest signal-to-noise ratio (SNRmeas) possible.

A similar investigation was carried out for biotin-streptavidin binding. This model system is often times used for its strong binding aﬃninity (∼ 10−14 M)[78], resulting in very clear and stable signals from the binding events. The functionalization is also more robust and straightforward for this binding system which results in more consistent and comparable sensing data. Streptavidin, being a tetrameric protein, consists of four binding pockets which can potentially bind to four biotin molecules. In the case of surfaces functionalized with biotin, the bound streptravidin molecules still contain unconjugated binding pockets which can interact with other biotin molecules in the solution bulk and therefore can be competitively desorbed if the bulk concentration is much higher than the surface concentration. This process is schematically shown in Figure 5.3. Using such a competitive desorption process allows us to re-use the same bioFET device, yielding results that are easier to compare and thus quantify. The bioFET response for streptavidin binding followed by competitive desorption using D-biotin is shown in Figure 5.4. At the pH used in this experiment (pH 7.5) the charge on each streptavidin molecule is about −2 e [79], which results in a decrease of the drain current on streptavidin binding (The devices used for this investigation are n-channel FETs). The complete restoration of the baseline current provides strong evidence that the competitive desorption

62 (a)

(b)

Figure 5.1: (a) Normalized current data for a pH change from pH 7.1 to pH 7.9 at diﬀerent bias points (diﬀerent Id levels). (b) Corresponding Id-Vg curve, where the bias points used in (a) are indicated with crosses. For measurements done closer to the threshold voltage, the resulting ∆I/I is larger as can be seen from Equation 5.1 and the experimental data in (a). The relative noise level is also larger.

63 Figure 5.2: Plot of device reponse (∆I) as a function of the transconductance (gm at different gate voltage bias) for a pH change from 7.1 to 7.9. From the linear least squares fit, the pH sensitivity of the device was extracted as 39 mV/pH. strategy works and therefore can be used to regenerate surfaces with bound streptavidin. Using this regeneration method, we carried out detection of the same concentration (20 pM) of streptavidin at different bias points, resulting in different normalized current changes (different ∆I/I) as shown in Figure 5.5. As expected, the relative signal change is larger for gate voltage values closer to the threshold voltage (see Equation 5.1). In the normalized current response plot, it is also seen that the relative noise amplitude is larger for gate voltage values closer to the threshold voltage.

The signal-to-noise ratio for this measurement can be extracted from the ratio of the response to

D-Biotin D-Biotin

Figure 5.3: Illustration of the competitive desorption process of surface bound streptavidin molecules using a high bulk concentration of D-biotin molecules. The surface bound streptavidin consists of unbound sites that are available to molecules in the bulk solution. By introducing D- biotin to the bulk, the strength of that interaction is enough to pull the streptavidin molecules away from the surface bound biotin molecules.

64 Manual Switching

D-Biotin

Streptavidin

Figure 5.4: BioFET response to streptavidin binding (20 pM) in 0.01X PBS, followed by competitive desorption using 1mM D-biotin. The initial current drop is due to the positive charge of streptavidin and the subsequent restoration of the baseline current, on addition of D-biotin, shows that the competitive desorption strategy works. The sampling rate used was 1000 Hz.

√ the current noise magnitude at f = 1Hz ∆I/ SI . The results are plotted in Figure 5.6 and it is obvious that the largest signal-to-noise ratio is obtained at the larger overdrive voltages (|Vg − Vth|) even though the relative signal change is smallest in that regime (Figure 5.5). Independently of the bias or operating regime that is chosen, the actual sensitivity of the biotin functionalized bioFET surface remains constant since that is dependent upon the particular functionalization procedure and the quality of that functional receptor layer. Figure 5.7 shows a plot of the absolute response as a function of the transcoductance at diﬀerent bias points. From a linear least squares ﬁt, the sensitivity of the biotin functionalized bioFET is found to be 100 mV for 20 pM of Streptavidin in

0.01X PBS. This value represents the detection of about 50 000 electronic charges which corresponds to a surface coverage density of approximately 5 × 1012 molecules/cm2.

65 (a)

(b)

Figure 5.5: (a) Normalized current response due to 20 pM of Streptavidin in 0.01X PBS at diﬀerent gate voltage values (bias points) for a sampling rate of 1000 samples/s. One can see that the normalized response is a function of the gate bias, as expected, and so is the relative noise level (which increases for the lower drain currents). (b) Id-Vg curve for a biotin functionalized bioFET device, indicating the bias points used for the sensing measurements in (a) using color coded crosses.

66 Figure 5.6: Plot of the measured signal-to-noise ratio (at a f = 1Hz) as a function of gate bias voltage. Even though the relative signal change is larger for small overdrive voltages as can be seen in Figure 5.5, the SNRmeas is lower.

Figure 5.7: Plot of the absolute bioFET response as a function of transconductance (gm) at diﬀerent gate voltage bias points. From the slope of the linear ﬁt to the data, the surface potential change of 100 mV can be extracted for 20pM of streptavidin binding in 0.01X PBS.

67 5.3 Optimal Operating Regime for BioFETs

It is well-known that the sensitivity (deﬁned as ∆I/I for a current based sensing experiment) is maximized in the subthreshold regime[80][81][49]. However, it is also known that the normalized

2 current noise power amplitude (SI /I ) reaches a plateau and is highest in the subthreshold regime for silicon-silicon oxide devices[47][82] and concerns have been expressed that signal-to-noise ratio

(SNR) would be impacted for measurements carried out in subthreshold[80][83]. On the other

2 hand, SI /I is lower in the linear regime but the sensitivity is also lower. In order to determine the ideal regime for optimal SNR, we carried out both I-V and noise measurements for solution gated devices. Our measurements indicate that the current noise is independent of electrolyte concentration, composition, or pH, leading us to conclude that the intrinsic electronic properties of the silicon NW bioFETs determine the optimal SNR achievable by these sensors. We also ﬁnd that

SNR is maximized in the linear regime at the point where the transconductance (gm) is largest.

We carried out measurements in phosphate buffered saline (PBS) at three different concentrations as well as measurements using a different salt system, namely potassium chloride solution (KCl 0.1

M). The concentrations were limited to those values used commonly in sensing experiments to stay close to physiological conditions. The results of the noise measurements are shown in Figure 5.8.

We observe negligible differences both in the noise spectra and the transfer characteristics, which result in similar SNR for the different concentrations and solutions investigated. This leads us to conclude that the gate response and the noise properties are mostly a function of device properties, resulting in similar SNR across different electrolyte systems and concentrations. It is true that

Debye screening is a function of buffer concentration and composition, and affects the sensitivity of the sensing experiment[84], but this variation only affects the surface potential (∆ψ0) seen at the

NW surface. From the noise proﬁle plotted in Figure 5.8(a), we can clearly see that the data follows

2 the (gm/Id) curve which indicates that the scattering coeﬃcient α is negligible in this case and the noise can be modeled using the ∆n model. The SNR was deﬁned in Equation 2.33 per unit voltage change in surface potential and is therefore independent of the actual change in surface potential

68 Figure 5.8: (a) Normalized current noise power density at f= 1Hz is plotted against drain current. The noise profile does not change significantly with changes in PBS (phosphate buffered saline) concentration or by changing the electrolyte to KCl (potassium chloride). The proportionality to 2 (gm/Id) confirms that our data are well fitted by the number fluctuation model. (b) Signal-to-noise ratio (as defined in text) is plotted against solution gate voltage to highlight the regime at which SNR is maximized. (c) Transconductance values extracted from I-V measurements are also plotted against solution gate voltage to point out that maximum SNR occurs close to the point of peak transconductance. and is intrinsic to the device as our results indicate, which means that we can safely define and use this figure-of-merit to predict the detection limit of these bioFET sensors. We also observe that

SNR for our devices is maximized in the linear regime, close to the peak transconductance (gm, peak), which is contrary to what was observed in other works[77][35], where SNR was determined to be maximum in subthreshold. The difference in the operating regime at which maximum SNR occurs can be explained by different mobility fluctuation noise regimes[85] (potentially caused by different material systems used, by different gate configurations, or by contact resistance dominated regimes).

We also carried out measurements of the SNR at diﬀerent pH values of the electrolyte solution.

The data is shown in Figure 5.9 and we can again see that the peak SNR coincides with the peak transconductance. It is also observed that the peak SNR values are unchanged for the diﬀerent pH

69 solutions used, even though the threshold voltage shifts with changes in pH as indicated by the shifts in both the peak SNR and peak gm. These results show that the charge state of the surface

(which is a function of the solution pH) has no effect on the noise properties of the bioFET sensors, and further supports the claim that sources of 1/f noise, closer to the silicon nanowire channel, dominate the total noise of the NW sensor as opposed to charge fluctuations originating at the biofunctional layer. √ The limit of detection (LOD) is given by 1/SNR and in this case LOD = SV . The drain current √ noise (SI ) can be converted to a gate voltage referred noise (SV ) by applying Equation 2.29. SV as a function of the solution gate voltage is plotted in Figure 5.10, with a minimum which corresponds to the point of peak SNR and peak gm. This plot clearly proves that the scattering coefficient, α, in the ∆n-∆µ model is negligible since we do not see a linear relationship between SV and Vg. From √ the minimum gate voltage noise amplitude, we determine the LOD to be roughly 0.1 mV/ Hz at f = 1 Hz. For a realistic bandwidth, the minimum detectable voltage is 0.3 mV for a signal of the same size as noise amplitude (SNRmeas = 1). For the NW dimensions in question, we extract a top-oxide capacitance of 2 × 10−15, which results in a charge detection limit of about 4 electronic charges (4e). This of course does not consider screening or any surface chemistry which would reduce the effective charge that can be detected or affect the surface potential produced by such a charge. However, this represents the best case scenario of the minimum number of charges that can be detected by this bioFET sensor, given the intrinsic device SNR.

In order to probe the validity of using SNR to predict the LOD, we carried out very careful pH sensing measurements in order to compare the measured SNR and hence the theoretical LOD with an actual detection limit. Figure 5.11 shows the dependence of SNR on the solution gate voltage for a device 10 µm in length and 1 µm wide as well the variation of gm with gate voltage.

As observed previously, the SNR is maximized close to the region of peak transconductance. To extract a LOD in terms of pH, we need to determine the pH sensitivity of the device, that is the pH sensitivity of the APTES functionalized silicon oxide top-gate. The current-time trace data for a pH sensing calibration measurement is shown in Figure 5.12. Combining the current response

70 (a)

(b)

Figure 5.9: (a) Signal-to-noise ratio (as deﬁned in text) is plotted against solution gate voltage to highlight the regime at which SNR is maximized. The pH of the solution is varied showing the independence of the peak SNR value on pH, except for the location of the peak which shifts as the threshold voltage shifts with pH. (b) Transconductance values extracted from I-V measurements are also plotted against solution gate voltage to point out that maximum SNR occurs close to the point of peak gm. Peak gm also shifts with gate voltage due to changes in Vth caused by the diﬀerent pH.

71 √ Figure 5.10: The gate voltage noise ﬂuctuations ( SV ) are plotted against solution gate voltage (limited to the linear regime of operation). The absence of a linear dependence indicates that number ﬂuctuations are the dominant cause of the noise of these bioFET√ devices. The dip in the data also highlights the region of maximum signal-to-noise ratio (1/ SV ), which is again shown to occur around the region of peak transconductance.

12000 350 SNR 300 10000 gm 250 ) 8000 gm (nA/V) -1 200 V 6000 150 SNR ( 100 4000 50 2000 0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 Vsg (V)

Figure 5.11: Plot of the signal-to-noise ratio (SNR) and the device transconductance (gm) as a function of solution gate voltage, highlighting the observation that SNR is maximum at the point of peak transconductance. The maximum SNR for this device is 11 000 which translates to a minimum detectable pH change of 0.01.

with the Id-Vg characterization, we can extract an average pH sensitivity of 24.9 mV/pH for the

APTES functionalized oxide surface. The peak SNR value of 11,000 from Figure 5.11 translates to a minimum detectable voltage of ≈ 270 µV (for a typical sensing measurement, the sampling √ rate is around 10 Hz and the measurement takes about 30 minutes, which gives BW ≈ 3), and with an extracted pH sensitivity of 24.9 mV/pH for that device (Figure 5.12), we deduce a limit of detection in terms of pH of 0.01. The pH sensitivity of the oxide surface varies with the quality of the surface modiﬁcation and is usually found to be in the range 20 - 40 mV/pH. Figure 5.13 shows a successful detection of a pH change of 0.07 with a signal-to-noise ratio of about 3.5, for a measured LOD of 0.02 pH, which agrees well with the theoretical LOD (0.01 pH) we expect from the I-V and noise characterization in Figure 5.11. This shows that we can use the SNR as a reliable and quantitative way to predict the performance of a bioFET sensor, before the actual sensing experiment and before any extensive and time consuming biofunctionalization steps. More importantly, understanding what aﬀects the SNR from the device standpoint and how to optimize it, would ultimately lead to the design of sensors with better limits of detection (LOD).

73 pH 8.2 24.9 mV/pH

pH 6.05 pH 6.05

pH 4.03 pH 4.03

pH 2.23 pH 2.23

Figure 5.12: Current vs time data showing the device response at diﬀerent pH values. From the Id-Vg curve and the pH response curve, the sensitivity is determined to be 24.9 mV/pH.

pH 5.13

pH 5.06 pH 5.06

Figure 5.13: pH sensing experiment to investigate the limit of detection (LOD) of the bioFET sensor, showing the successful detection of a change in 0.07 pH with a measured signal-to-noise ratio of ≈ 3.5.

74 5.4 Inﬂuence of surface functionalization

The effect of surface functionalization on device performance and noise has been reported previously[86][87]. However, the effect of the surface passivation/functionalization has not been studied in the context of the SNR. Considerations of noise and device parameters such as mobility and subthreshold slope, separately, are not very useful in predicting the real sensitivity and limit of detection of a bioFET sensor, as we have shown earlier. Moreover, the effect of APTES functionalization on the noise properties has not been previously studied. APTES functionalization is a common first step to bio-molecular functionalization of a bioFET sensor surface as well as being a widely used pH sensitive layer, known to improve the pH sensitivity of silicon oxide surfaces[88][14].

Figure 5.14(a) shows the normalized current noise power density plotted as a function of drain current for two sets of devices, of exactly the same dimensions, but one set functionalized with

APTES while the top oxide of the other set of devices remained un-functionalized (bare oxide devices). The results indicate that functionalization with APTES results in reduced current

ﬂuctuations which is most likely due to the passivation of surface states, which eﬀectively reduces

Not in Equation 2.28. Figure 5.14(b) shows the peak SNR that was extracted from the same sets of devices, clearly demonstrating the improved signal-to-noise ratio that accompanies the reduction in current noise power density. The APTES functionalized devices, on average, show an increase of about 3x in the SNR which can be converted to a reduction of about 9x in the value for Not.

This represents almost an order of magnitude decrease in the trap density, for the surface modiﬁed bioFETs and highlights both the impact of surface states on the measured device characteristics for nano-scale thickness devices as well the possibility of modifying/reducing these surface states by chemical modiﬁcation of the oxide surface.

Amine functionalization can also be conferred onto a silicon oxide surface using a polymer backbone through the use of Poly-L Lysine (PLL)[89]. The latter consisting of a high density of amine groups (−NH2) are positively charged at near neutral pH (pKa≈9-10) whereas the silicon oxide surface is negatively charged (pI≈2-3), resulting in a strong electrostatic attraction and subsequent

(a) 1E-5

1E-6 Bare SiO2

1E-7

1E-8 APTES Funct.

(at f=1Hz) (1/Hz) 1E-9 2 D /I I S 1E-10 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5

Drain Current, ID (A) (b) 300000 APTES Funct. Bare SiO2 250000

) 200000 -1 V (

150000 100000 SNR 50000

Figure 5.14: (a) Comparison of the normalized current noise power as a function of drain current, for APTES functionalized devices vs. un-functionalized bioFETs (bare oxide surface). The APTES functionalization results in a signiﬁcant reduction in the current noise power density. (b) The extracted SNR compared for the functionalized and bare oxide devices, showing the improvement that results from bioFET surfaces chemically modiﬁed with APTES.

76 surface assembly. Due to the high density of positive charge groups, one can in principle achieve a higher functionalization density when using PLL as the functional amine layer, which in turn results in larger signal-to-noise ratio[90]. However, the stability of the layer is a concern due to the electrostatic nature of the binding[91] as opposed to the covalent bonding of silane molecules during APTES functionalization. In addition to the stability of the amine layer, the improvement in SNR that was observed for APTES functionalized devices compared to bare oxide devices, is not seen in the case of PLL functionalized devices. As can be seen from Figure 5.15, the noise proﬁle remains completely unchanged after PLL is electrostatically bound to the silicon oxide surface. Our hypothesis here is that during the covalent bonding of APTES molecules, there is a certain amount of charge transfer that occurs to neutralize traps in the oxide and eﬀectively reduce the trap density (Not) in Equation 2.28. During the electrostatic binding of PLL to the negative oxide surface however, no such reaction involving charge transfer occurs and Not remains unchanged. In the case of APTES functionalization of the surface, using Equation 2.28, we extracted a trap density of 2.4 × 1018 eV−1 cm−3 for the bare oxide devices as compared to a trap density of

2.7 × 1017 eV−1 cm−3 for the APTES functionalized ones.

With a multiplexed approach to functionalization utilizing four PDMS micro-channels as shown in

Figure 5.16, we are able to compare the additional noise contributions and/or SNR degradation from additional bio-functional layers. All devices were functionalized with APTES first and using the multiplexed functionalization technique, the device surfaces were modified with either NHS-Biotin or NHS-PEG. A channel was left with no additional layer above the APTES. The results of the SNR as a function of solution gate bias for some of the devices are shown in Figure 5.17. It is obvious that the difference in the SNR values are very small for the different functionalization schemes, indicating that further functional layers do not either degrade or improve the SNR of the bioFETs.

The fact that the additional biofunctional layers do not contribute to additional noise confirms our previous obervations that different buffer concentration and composition do not significantly influence the device noise, which is still dominated by trapping/detrapping processes between the oxide and silicon. The effective trap density (Not) is only reduced by the first functionalization step

77 Figure 5.15: Normalized noise proﬁle for a bare oxide device compared to the same device after poly-L Lysine (PLL) functionalization. The noise proﬁle is unchanged, which is consistent with the electrostatic interaction of the positively charged PLL with the negative silicon oxide surface.

(APTES) where Si−O−Si bonds are formed, aﬀecting the interface/oxide states close to the top surface of the silicon oxide layer.

5.5 Gate Coupling

√ According to Equation 2.28, the SNR (which is equal to 1/ SVFB) should also improve if the gate capacitance per unit area is increased. This makes sense if one considers that a fixed amount of oxide charge yields a smaller voltage noise if the capacitance is increased. Along the same line of reasoning, a common amplification strategy for dual-gated biosensors is to measure the back- gate response due to a surface potential change at the top-gate. The ratio of the capacitance of the top-gate to that of the back-gate (CTG/CBG) provides the voltage amplification[24][92]. In our devices, this ratio is roughly equal to 6 and as can be seen from Table 5.1, the ratio of gm was measured to be about 5 for the two gating schemes applied to the same set of devices (W

= 2µm and L = 10µm). Looking back at Equation 2.1, gm should be proportional to the oxide capacitance, which is what we observe since the ratio of gm agrees well with the ratio of oxide

78 Figure 5.16: Optical image of a device showing the PDMS microﬂuidic channels functionalized with FITC (green) and channels functionalized with TAMRA (yellow). There is no leakage of ﬂuorophors between channels as evidenced by the high contrast of the image.

4 x 10 6 APTS1 APTS2 5 PEG1 PEG2 4 Biotin ) -1 3 SNR (V SNR 2

0 -0.8 -0.6 -0.4 -0.2 0 Gate Voltage (V)

Figure 5.17: SNR plotted as a function of solution gate bias for different surface functionalization schemes, demonstrating that the SNR varies minimally for the different types of surface modifications after the first step of APTES functionalization.

79 capacitance. Table 5.1 also clearly shows that the SNR is degraded when the back-gating scheme is employed. The SNR is reduced by a factor of 10, which cannot be solely explained by a smaller capacitance (factor of 5), which would only result in a 5-fold reduction in SNR. We believe that the additional reduction in SNR is due to the diﬀerent oxide trap densities involved when the top-gate oxide is used as opposed to the back-gate oxide. The back-gate oxide is the buried oxide (BOX) from the Smart-Cut process[93] whereas the top-gate oxide is formed from the dry oxidation of the active silicon layer. The BOX has a slightly higher oxide trap density (roughly

4x higher) which results in the additional reduction in SNR when the measurement is carried out using the back-gate. We calculated the oxide trap densities involved in each gating scheme and the results are presented in Table 5.1. Even though measuring using the back-gate yields a larger voltage change due to the smaller capacitance, any fluctuations in the BOX charge will also couple to the channel and produce larger voltage fluctuations[36]. Thus, voltage amplification using the back-gate is canceled out by an equivalent voltage noise increase (Even though SNR as defined in

Equation 2.33 decreases, it is defined per unit volt change in surface potential and therefore does not factor in the voltage amplification. The measured signal-to-noise ratio, SNRmeas remains constant with or without such voltage amplification). However, if the BOX has a higher trap density than the top-oxide (TOX), such as in the case of our devices, the voltage noise increases by a larger amount than the amplification of the signal and back-gated measurements consequently become less sensitive than top-gated ones. Table 5.1 also presents the results for devices with atomic layer deposition (ALD) Al2O3 as the gate dielectric. Looking back at Equation 2.28, we expect the SNR to increase as the gate capacitance per unit area increases. However, we observe a decrease in the peak SNR, which leads us to conclude that the trap density(Not) at the interface of the silicon and aluminum oxide layer is much larger than for the silicon oxide gate devices. Using Equation 2.28, the trap density for the Al2O3 devices can be determined (Table 5.1), which indicates the need for further optmization of the ALD process in order to minimize the trap density. It is important to note here that the SiO2 devices were APTES functionalized and then measured, whereas the

Al2O3 devices were measured without any surface modiﬁcations. Nonetheless, these results show

80 Oxide Thickness Peak gm Peak SNR Trap Density Gating Scheme (nm) (nA/V) (V−1) (eV−1cm−3) 17 Top Gated SiO2 20 380 66 000 2.1 × 10 17 Back Gated SiO2 120 80 6 900 7.6 × 10 18 Top Gated Al2O3 20 600 18 400 7.2 × 10 Table 5.1: Table showing the average values of the measured SNR and extracted trap densities for measurements carried out using the top gate silicon oxide, back gate silicon oxide and top gate aluminum oxide dielectrics.

that even though the Al2O3 layer shows the ideal Nernstian pH sensitivity (≈ 60 mV/pH), without surface modiﬁcations the improvement in signal will be canceled by the worse noise performance due to the much larger Not.

5.6 Device Scaling

The argument for scaling down FET biosensors to the nanometer regime comes from a consideration of the relative change in conductance in a cylindrical wire as a result of a change in the surface charge density (∆σs). The relative conductance change be written as a function of the radius

(R)[32]: ∆G ∆σ 2 = s (5.2) G0 n0 e R

where G0 and n0 are the initial conductance and carrier density respectively. From Equation 5.2, it is clear that if one wants to maximize ∆G/G one must scale the devices down to lower values of R. It also follows from Equation 5.2 that the doping density of the nanowire sensor should be kept low for larger relative signal changes. However, this relative signal change does not account for the fact that the relative noise amplitude increases as devices are scaled to the nanometer regime.

The current signal generated by a sensor, for a particular change in surface potential, is directly proportional the device transconductance (gm) which is given by:

W g = µ C V (5.3) m L ox ds

14000 12000 10000 8000 (nA/V)

m 6000 g 4000 2000 0 0 2 4 6 8 10 W/L

Figure 5.18: Measured peak transconductance (gm) plotted for diﬀerent device dimensions, showing 2 that gm scales with the ratio W/L as predicted by Equation 5.3. The R value of the linear least squares ﬁt is 0.9947.

where µ is the effective mobility of charge carriers, Vds is the drain-to-source voltage, Cox is the oxide capacitance per unit area, W and L are the width and length of the sensor respectively. Figure 5.18 shows the linear dependence of gm on the ratio W/L, verifying that Equation 5.3 holds for the devices used in this investigation. The transconductance was extracted by numerical differentiation of the Id-Vg curve and the peak gm values were extracted and subsequently plotted. The SNR is p defined as the ratio of gm and the drain current noise amplitude given by SI(f = 1Hz). Therefore, it is important to de-couple the effects of transconductance and noise. Re-casting the SNR in terms of voltage fluctuations such as in Equation 2.33 gets rid of the dependence on gm and allows us to focus on what truly limits the minimum detectable voltage, namely, the gate-voltage referred noise (SVFB). Equation 2.28 predicts that the SNR is directly proportional to the square root of the device area. The devices measured were all from the same wafer, with a silicon oxide top-gate dielectric of thickness 20 nm, resulting in a constant Cox for all measured devices. Figure 5.19 indeed √ shows a linear relationship between SNR and WL, validating the use of Equation 2.28 in better understanding and engineering devices with lower limits of detection. The data also demonstrates

4.5x105 4.0x105

) 5 -1 3.5x10 3.0x105 2.5x105 5 2.0x10 1.5x105

Peak SNR (V 1.0x105 5.0x104 0.0 0 5 10 15 20 25 30 35 √(WL) (µm)

Figure 5.19: Peak√ SNR is extracted and plotted for diﬀerent device dimensions, showing that peak SNR scales with WL as expected from Equation. The R2 value of the linear least squares ﬁt is 0.9988. that increasing the device area results in larger SNR and therefore more sensitive bioFET sensors, which is in direct contrast with the common scaling argument that smaller devices result in larger relative signal change, and therefore will behave as more sensitive biosensors[59]. The use of the relative signal change (∆I/I or ∆G/G) as a metric has the fundamental limitation that it does not consider how the noise also scales with device dimensions. Here, we need to point out, that the

SNR scales with p(area) in so far as the surface potential changes over a constant proportion of the whole device area. This is generally true for pH sensing experiments, where the surface potential changes over the whole device area. We set up a 2D simulation grid (in Matlab) to model the nanoribbon surface, where the size of each cell could be considered to be equivalent to the pitch of the receptor molecules attached to the surface[94]. Each cell is assigned a certain arbitrary noise level SR and if a binding event occurs in one of the cells, the resistance of the cell changes by an arbitrary amount, ∆R. Here, we assume that the device is operating in accumulation mode, as is the case with most of our sensing experiments. The total noise as well as initial and ﬁnal conductance, are determined by assuming that rows of cells are independent. Figure 5.20 shows

83 Figure 5.20: Results from a 2D simulation of the SNR of 2 bioFETs, both with a 50% surface coverage of bound analyte molecules. The length of the device is increased from 30 to 50 a.u., resulting in an increase in the device area and consequently an increase in the SNR from 4.7 to 6.1 a.u., which correlates very well with our experimental results. two devices of diﬀerent areas, both with a 50% surface coverage of bound molecules (cells with bound molecules are colored white). The extracted SNR is higher in the case of the larger area as we expected from our earlier experimental results. Carrying out the calculations for various sizes of devices and keeping the surface coverage ﬁxed at 50%, we obtain the results shown in Figure 5.21.

The linear dependence of SNR on the p(area) from the simulation results is independent of the percentage of surface coverage (as long as the percent coverage is fixed) and again confirms our previous experimental observations. The scaling of the SNR with p(area) for planar devices can be physically understood by realizing that the signal change scales with the area (for a fixed percent coverage, in the case of sufficient analyte molecules), whereas the current noise level (δi) scales with p (area) since the noise power (SI ) is proportional to the trap density, Not, and therefore SI is √ p the quantity that is proportional to the area. δi ∝ SI and consequently scales with (area).

Our simulations results also show that the SNR varies minimally for diﬀerent conﬁgurations having

84 Figure 5.21: Simulation results for the SNR calculated at 50% surface coverage of bound analyte molecules, for different device areas. The simulation confirms our experimental findings that SNR is linearly proportional to p(area). the same area. Thus, we conclude that it is not the layout of the device that is most important, but rather the total area available for binding. Figure 5.22 shows the simulated SNR values for various configurations of number of rows and columns, while keeping the area constant at 900 a.u., showing that different layouts of width and length sizes have a negligible effect on the SNR that is measured. Changing the total area however results in much larger changes in SNR as we showed in Figure 5.21.

The situation can be very diﬀerent when considering low numbers of analyte molecules and a much larger binding aﬃnity, for which, the percent surface coverage is not necessarily constant, since the number of available molecules is not enough to bind to the available receptors, and hence the surface area of the device must be optimized, depending on the size of the molecule or cell and the target concentration. If such optimization is not carried out, the signal will be derived from an area much smaller than the device area, whereas the noise will still be generated from the whole device area, resulting in a degradation of the signal-to-noise ratio. Such limitations are related to the binding kinetics of the analyte-receptor system in question and will be considered in detail in

85 4.725

4.72

4.715

4.71 SNR 4.705

4.7

4.695 0 100 200 300 400 Column Index n

Figure 5.22: SNR as a function of different number of rows and columns, keeping area constant at 900 a.u. The small differences in SNR show that the layout is not as significant as the total surface area available for binding. the next Chapter. The previous measurements were carried out on optically defined nanoribbons

(W > 1µm) and it that regime, it would seem that the aggressive scaling down of bioFET sensors results in degradation of the SNR and consequently the LOD. A compelling argument, however, for the reduction in size is the ability to exploit advantages that might result from quantum confinement effects. For instance, a phenomenon called volume inversion was observed for gate-all-around(GAA) silicon nanowire FETs, below a diameter of 10 nm[95]. At such a size scale, due to quantum confinement, the charge carriers are concentrated in the middle of the channel instead of being concentrated at the edges, closer to the surface. Thus, surface scattering is reduced and the charge carriers are less likely to interact with interface traps. Volume inversion results in a reduction of the effective trap density Not and therefore improves the noise performance as the diameter is reduced further below 10 nm. To investigate a smaller size regime, we carried out SNR measurements on e- beam defined nanowires with device widths ranging from 60 nm to 2 µm. The active layer thickness was the same as before (40 nm) and the measurements were carried out using the back-gate. The results are shown in Figure 5.23. There is considerable scatter in the data points and no clear trend can be extracted. This large and random variability is probably due to the variations in the trap

86 Figure 5.23: Peak SNR extracted for measurements carried out on nanowire bioFETs fabricated using e-beam lithography, of diﬀerent widths ranging from 60 nm to 2 µm. density as a result of the electron beam process, which is also a major consideration in the reliable and reproducible fabrication of ultra-scaled FET devices.

5.7 Summary

In this Chapter, we combine noise measurements with the I-V characterization of bioFETs resulting √ in signal-to-noise ratio (SNR) as a performance metric. SNR is defined simply as the ratio gm/ SI which can be extracted from I-V and noise characterization for different gate voltages. Defined as such, the SNR is given per unit change in surface potential (ψ0) and is purely a device dependent quantity. More specifically, SNR can be formulated as 1/SVFB, that is the SNR can be written in terms of the flatband voltage noise, which is a function of device parameters such as dimensions, gate capacitance and interface/trap density. To relate this definition of SNR to an actual signal-to-noise ratio (SNRmeas), we need to merge the intrinsic device characteristics with the sensitivity of the sensing surface. We have shown that the true sensitivity is defined not as a relative signal change

87 (∆ I/I), but rather in terms of the surface potential change per unit change in the concentration of the analyte to be measured. By combining SNR measurements with pH calibration curves, we have demonstrated the relevance of SNR as a metric to predict the actual LOD of a particular pH sensing experiment (measured LOD of 0.02 pH compared to a theoretical LOD of 0.01 pH). This same procedure can be used to predict the results of biosensing experiments once the appropriate calibration curves are known. Using SNR as a performance metric allows us to accurately place a lower bound on the limit of detection of a bioFET device in an actual sensing experiment. Thus, this metric not only enables us to screen devices that have the desired sensitivity but also aids in the design of sensors with lower detection limits. The effect of APTES functionalization was quantified as approximately a 3-fold enhancement in the SNR, and consequently almost an order of magnitude decrease in the trap density for APTES functionalized surfaces compared to bare silicon oxide surfaces. SNR is also shown to increase as p(area) , which means that aggressive scaling is not always the best solution and that careful sizing of the device, based on the experimental requirements is very important in order to optimize the SNR while keeping the device density per chip, high. The effect of oxide capacitance on the measured SNR is quantified and we extract a trap density of 7.6 × 1017 eV−1 cm−3 for the buried oxide (BOX) as compared to a trap density of 2.1 × 1017 eV−1 cm−3 for the top oxide (TOX). In this case, voltage amplification by back-gate measurements will result in lower measured SNR as compared to top-gated measurements, since the noise is amplified along with the signal and the noise is intrinsically higher for the back-gate compared to the top-gated case (due to a larger Not in the BOX). Our measurements of the

SNR for e-beam deﬁned nanowire devices (with widths as low as 60 nm and as large as 2 µm) showed considerable scatter which we attribute to the variability of the e-beam fabrication process, resulting in diﬀerent values of Not. Our results clearly show that we are on the right path by focusing on nanoribbon devices (W > 1 µm) which have a lower LOD and more uniform electrical characteristics, as compared to the smaller nanowire devices.

88 Chapter 6

Binding Aﬃnity Considerations

6.1 Introduction

The binding between receptor and analyte molecules is not an instantaneous event. The response

(both time and magnitude) of a bioFET sensor is dictated by (1) the mass-transport of the analyte to the surface of the sensor where the binding reaction can happen and (2) the aﬃnity of that particular receptor-analyte system. Issues related to the transport/diﬀusion of target molecules to the surface of a bioFET has been addressed theoretically[96][97][98] and will not be discussed in this

Chapter. These issues inﬂuence the time it takes for a certain number of molecules to bind to the sensor surface, and in the current Chapter we will consider the equilibrium state at the end-point of detection only. Therefore, to discuss detection limits of bioFETs in the context of binding kinetics, we will assume, for the most part, that the sensor response is reaction-limited and we will focus on the binding equilibrium between receptor molecules and target molecules at the end-point of detection. The basic conjugation reaction between an analyte (A) and a receptor molecule (R), assuming one-to-one binding, is given by:

kon A + R )−−−−−−* AR (6.1) koff

89 kon is the association rate and koﬀ is the dissociation rate, which are used in Equation 2.21 and

Equation 2.22. The equilibrium dissociation constant (KD) of an analyte-receptor system is given by koﬀ /kon and KD in turn determines the equilibrium number of bound analyte molecules (A) for a given areal density of receptor molecules (R) as was derived in Equation 2.24. The plot of number of bound molecules as a function of concentration as given by Equation 2.24 is named the

Langmuir isotherm[99], with KD being temperature dependent and determining the shape of the curve. Therefore, KD places an upper limit on the number of bound charges at equilibrium for a given bulk analyte concentration. Figure 6.1 very clearly shows the eﬀect of the value of the KD on the minimum detectable concentration of analyte (ρ0). For the sake of simplicity, let us assume that the analytes are similarly charged. Therefore, the dashed line in Figure 6.1 represents a certain detection limit based on the noise limitations of the device, which consequently limits the number of bound charges than can be detected. For a certain surface density of receptors, let us say that 40% of the receptors need to be conjugated to reach the minimum detectable charge level due to factors such as the intrinsic device noise levels, the amount of charge per target molecule, steric hindrance due to other bound molecules and screening limitations imposed by the choice of the electrolyte.

In such a case, it is evident from Figure 6.1 that the lower the KD of the system, the smaller is the minimum concentration that can be detected (intersection of the dashed line and the Langmuir isotherm). This is an often understated and under-discussed area in the biosensor community: the

KD determines the occupancy of the receptor sites at a certain bulk analyte concentration. As shown in Figure 6.1, if the minimum required surface coverage of a bioFET is given by the dashed line, the detection limit would be approx. 70fM, 70pM and 70nM for values of KD corresponding to

100fM, 100pM and 100nM repectively. It is clear that the aﬃnity of the receptor molecules to the analyte of interest plays a huge role in determining the detection limit (as an analyte concentration value) of that particular functionalized bioFET.

90 1

0.9

0.8

0.7

0.6

0.5

0.4 Surface Coverage Surface 0.3

K = 100fM 0.2 D K = 100pM 0.1 D K = 100nM D 0 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 10 10 10 10 10 10 10 10 10 10 10 10 Analyte Concentration, ρ (M) 0

Figure 6.1: Langmuir isotherm plotted on a semi-log scale for analyte-receptor systems of diﬀerent

KD values. The dashed line indicates a certain detection limit which occurs, for a particular charge per analyte (Z), at a surface coverage of 40%. The detection limit in terms of concentration is then obviously dependent upon the binding equilibria of the analyte-receptor system.

91 6.2 BioFET as an aﬃnity sensor

The ability to accurately and reliably characterize protein interactions has tremendous value in understanding cellular function in medicine and biology. Furthermore, affinity sensors can be used to characterize the strength of interactions between analyte and receptor pairs, with the goal of designing receptors with higher binding affinities than conventional antibodies. To improve the binding efficiency and hence the detection limit, a lot of effort has gone into engineering proteins[100][101] and DNA/RNA aptamers[102][103], which bind to the target of interest with a higher affinity (lower KD) and better chemical stability than the conventional monoclonal antibodies. However, the popularity and availability[104] of various kinds of antibodies mean that they remain the receptors of choice when designing affinity sensors. The gold standard, currently, in the field of affinity biosensors, is surface plasmon resonance (SPR). However, SPR suffers from two major limitations, namely: (1) it cannot resolve the binding of small molecules (<2000 g mol−1) and

(2) it requires optical components which increase the cost of the setup and make high-throughput measurements much less likely. Since BioFET sensors rely on charge detection, they are not limited by the size of the molecule as long as the charges on the molecule are suﬃcient to overcome the

LOD. In fact, smaller molecules are more desirable for the bioFET platform, since the small size ensures that all of the analyte molecule remains close to the sensor surface and therefore within the

Debye layer (λD). Since BioFETs are manufactured using Integrated Circuit (IC) technology, they can easily be scaled up and thereby be used as a platform to achieve high-throughput measurements of binding kinetics.

The solution to Equation 2.21, for the association phase and in the particular case of fast mixing such that ρs = ρ0 at all times, is given by:

h i −t (konρ0+koff ) N(t) = Neq × 1 − e (6.2)

where Neq was deﬁned earlier in Equation 2.23. The change in surface potential (∆ψ0) can be easily extracted from the current signal by normalizing using the transconductance. Such

92 normalized binding curves are shown in Figure 6.2. The data represents the real time response of diﬀerent concentrations of DNA binding to HMGB1 (high mobility group box 1) protein, which was immobilized onto the bioFET surface. The association part of the reaction can be clearly seen as the slow increase of the normalized current until the signal reaches equilibrium. Subsequently, on introduction of pure buﬀer solution, the signal decreases due to dissociation of the bound DNA molecules. To solve for the dissociation phase, one simply assumes that koff > kon which results in:

N(t) = e−koff N t (6.3)

Equations 6.2 and 6.3 were then fitted to the data to extract the values of kon and koff . The latter can be readily extracted from the exponential decay fitting suggested by Equation 6.3. To extract kon, one must plot the fitting parameter konρ0 + koff as a function of ρ0. The slope of the resulting plot then gives the value of kon. The plot showing the linear dependence of the fitting parameter on concentration is shown in Figure 6.3. With the values of kon and koff , the KD can be determined. An alternative way of determining the KD of a particular system is to consider only the end point of detection. The real-time sensing data can be used to plot Langmuir isotherms such as the theoretical ones plotted in Figure 6.1. The Langmuir isotherm for the binding of DNA to HMGB1 is shown in Figure 6.4. Referring to Equation 2.24, the equilibrium number of bound molecules is solely a function of the bulk analyte concentration (ρ0) for a given dissociation constant and surface receptor density. Thus, by fitting an equation of the form given in Equation 2.24, one can very easily extract values for KD. This technique is useful when binding kinetic curves are hard to extract due to mass transport limitations or when the fluid delivery is not well controlled.

6.3 Binding Kinetics Simulator and SNR

As we have seen in the previous sections, the binding between an analyte and receptor molecule can be described by Equations 2.21 and 2.22. So far, we have focused on a simpler problem by assuming fast mixing, that is km is very large such that ρs is always equal to ρ0 at all time t. In most realistic

93 Figure 6.2: Real-time sensor responses of HMGB1-DNA binding. Each curve represents the measurement of a different DNA concentration from multiple devices, and sensor responses are normalized by the transconductance and offset such that all traces start at zero. The dashed lines represent the linear least squares fit to the data using Equations 6.2 and 6.3 from which values for kon and koff are estimated.

94 Figure 6.3: Plot of the ﬁtting parameter konρ0 + koff as a function of DNA concentration. The linear ﬁt indicates good agreement of the data with our binding model and the from the slope of the line, we can extract the value for kon (i.e. k1).

Figure 6.4: Langmuir isotherm plotted using the data obtained from the real time current traces of DNA binding to HMGB1. The isotherm is used to extract a value for the KD of 105 nM using Equation 2.24.

95 Simulation Parameters Value 12 Number of receptors, N0 A × 1 × 10 Reaction volume, V (µL) 100

km 0 10 kon 10 −5 koff 10 23 Avogadro’s number, Na 6 × 10 −12 Bulk concentration, ρ0 (M) 10 Initial number of conjugated receptors, N(t = 0) 0

Initial concentration, ρs(t = 0) ρ0

Table 6.1: Table showing the parameters and their typical values for the binding kinetics simulations using Matlab’s ODE solver. The area of the bioFET device is given by A, in units of cm2. cases however, the binding process is not reaction limited and analyte diffusion to the surface of the biosensor affects the final signal that is measured. In order to account for the diffusion of analyte molecules, the two-compartment model (Equation 2.22) was developed. The first compartment is a reaction volume within which the analyte molecules are close enough to the surface so as not to be limited in their transport to the sensor surface. The second compartment represents the bulk of the solution beyond the reaction volume. The concentration of analyte molecules in the second compartment (bulk solution) is always fixed at ρ0 and km determines the ability of these molecules to diffuse into the reaction zone where they can subsequently be captured by the receptor molecules on the sensor surface. An analytical solution to Equations 2.21 and 2.22 is not possible. However using numerical solvers (e.g. Matlab’s ODE solvers), it is possible to obtain solutions to various initial conditions. To understand the binding limitations at low analyte concentrations, we carry out such numerical simulations. Typical parameters used in our simulations are given in Table 6.1.

From the simulation parameters presented in Table 6.1, we can calculate values for N (the number of bound analyte molecules) for any user-deﬁned array of time values. The binding kinetic curves for diﬀerent device areas (A) are given in Figure 6.5. As expected, as the area increases so does the number of analyte molecules bound to the sensor surface. Since in this example, we used an

−12 −15 analyte concentration (ρ0 = 10 M) much higher than the KD (10 M), we obtain a number of bound molecules which equals the number of receptor sitres at the end-point of detection, as we

96 5 x 10 10 10 to 106 receptors 8

2 Number of bound molecules of Number

0 0 200 400 600 800 1000 Time (s)

Figure 6.5: Simulation results based on the parameters given in Table 6.1, showing the binding kinetics for different device areas (and therefore different numbers of receptor sites) in the case where the analyte concentration (ρ0) is much larger than the KD expect from Equation 2.24. This confirms the validity of our numerical model and allows us to further use the coverage ratio obtained from the simulation results (coverage ratio is defined as the ratio of number of bound molecules to the number of receptor sites, Neq/N0) in extracting the SNR for different device areas. The 2D simulation grid to calculate the SNR for different coverage ratios was introduced in Section 5.6. To summarize, each cell in the 2D grid represents a binding site and for a certain coverage ratio, occupied cells are randomly assigned. Upon binding to a cell, the cell conductance changes whereas the noise of that particular cell is assumed to be minimally affected.

In Section 5.6, we have shown that for a ﬁxed percentage coverage the extracted SNR scales with p(area). In the next sections we will explore the conditions under which the coverage ratio is constant and conditions under which the coverage varies with area. Finally, we will demonstrate the eﬀects on the SNR and the p(area) scaling rule, due to a coverage ratio which varies with the device area.

97 1 10 to 106 receptors 0.8

0.6

0.4

0.2 Number of bound molecules of Number

0 0 200 400 600 800 1000 Time (s)

Figure 6.6: Simulation results for binding curves corresponding to diﬀerent device areas and thus diﬀerent numbers of receptors. Here, we consider a high KD system of 1 nM and an initial bulk analyte concentration of 1 fM, yielding a very low occupation probability and thus, low numbers of bound molecules at the end-point of detection.

6.4 High KD Case

We have seen that as the sensor area increases, so does the number of bound molecules such that the coverage ratio, as determined by Equation 2.24, remains constant. The implicit assumption here is that there are enough analyte molecules in the reaction volume to continue populating the additional surface receptors, such that ρ0 is a constant. However, if we wish to consider the case of limited analyte, we have to apply the two-compartment model and in the case of fixed number of analyte molecules, we consider the case of km = 0, such that there is no diffusion of additional molecules into the reaction volume. The reaction volume we consider is one we typically use in our experiments where the fluidic cell holds 100 µL of liquid. In such a reaction volume, even a low analyte concentration such as 1 fM consists of 6 × 104 molecules. We consider a low binding affinity system with KD = 1 nM and the simulation results of the binding curves from the two- compartment model is shown in Figure 6.6. From the simulation data, we arrive at the conclusion

98 -6 x 10 1.1

1.05

1 Coverage ratio

0.95

0.9 0 2 4 6 8 10 Number of receptors 5 x 10

Figure 6.7: Coverage ratio extracted as from the binding curves in Figure 6.6 and plotted as a function of number of receptor sites. Coverage ratio remains constant at 10−6 since there are always enough molecules in the reaction volume to populate the increasing number of sites on the surface. that at 1 fM and at equilibrium conditions, the occupation propability of the surface sites is so low that Equation 2.24 correctly gives a very low number of bound molecules, as can be seen in

Figure 6.6, and also a low coverage ratio of 10−6. In fact, the coverage ratio for each of the binding curves can be extracted from the ﬁnal equilibrium number of bound molecules, Neq. Such data is plotted as a function of the number of receptors in Figure 6.7. The numerically determined coverage ratio is also 10−6, conﬁrming the value obtained analytically. Such a low coverage ratio essentially ensures that there are always enough molecules in the reaction volume to populate the increasing number of receptor sites as the sensor area is increased. In this regime, Equation 2.24 applies very well since the concentration in the reaction volume does not appreciably change due to surface conjugation of only a small number of molecules.

Typically good surface functionalization results in surface densities of about 1012 cm−2. Typically, devices are less than 10−6 cm2 in area and thus the maximum number of receptor sites is around

6 10 , which is what we consider in our simulations. It is therefore clear that for high KD binding

99 systems, there are always enough molecules in solution to bind to the surface receptors, which is why Equation 2.24 can be conﬁdently used to ﬁt to the data as we have shown in the case of HMGB1-DNA binding (Figure 6.4) where the KD was even higher (100 nM) and the smallest concentration measured in that case was 3 nM (which corresponds to a coverage ratio of 3%). For such systems, decreasing the device area does not alter the coverage ratio (since coverage ratio is

ﬁxed at 3%), but instead degrades the measured SNR as we showed from our experimental data in

Figure 5.19 and from our SNR simulation results in Figure 5.21.

6.5 Low KD Case

The question remains: Are there cases for which the coverage ratio depends on the device area such that the SNR scales diﬀerently with device size? In the case of a low KD, the occupation probability is higher at low analyte concentrations and we consequently enter a regime where the number of molecules in the bulk might not be suﬃcient to conjugate to the increasing number of receptors as the device area is increased. Considering the same bulk analyte concentration as before (ρ0 = 1 fM), in the same reaction volume of 100 µL, we have 6 × 104 molecules. For the sake of discussion, let us assume that KD = 1 fM. This means that the coverage ratio predicted by Equation 2.24 is 50%.

It is immediately evident that this represents a number of bound molecules that can potentially exceed the number of molecules available in the bulk solution. Using the same simulation conditions as before, with KD = 1 fM, we can simulate the binding kinetics and from the equillibrium number of bound molecules, at the end-point of detection, we can extract the coverage ratio for a certain number of receptor sites. Figure 6.8 shows the coverage ratio plotted as a function of the number of receptor sites. Unlike Figure 6.7, the coverage ratio in this case varies with the number of receptors or equivalently, the device area. More speciﬁcally, the coverage ratio decreases very quickly from the analytical solution of 50% coverage to almost 1% as the number of receptors is increased to 106.

This can be understood from the fact that the number of analyte molecules available in solution quickly gets depleted as the number of receptors is increased and thus, not all the receptor sites

100 0.5

0.4

0.3

0.2 Coverage ratio

0.1

0 2 4 6 8 10 Number of receptors 5 x 10

Figure 6.8: Coverage ratio extracted from the simulated binding curves for a high KD system (1 fM) and plotted as a function of number of receptor sites. The coverage ratio is no longer a constant quantity and instead decreases with increasing the surface area, since the number of molecules in the bulk are limited and is smaller than that required for conjugation to the increasing number of receptors. can be populated as predicted by Equation 2.24. This leads to a signiﬁcant drop in the coverage ratio as the device area is increased.

For a non-constant coverage ratio, the increase of SNR with p(area) no longer applies. Using the SNR 2D simulation, combined with the results of the binding kinetics, one can determine the coverage ratio for each device area and subsequently determine the SNR for that device area and coverage ratio. The process is then repeated for a diﬀerent device area and the results are displayed in Figure 6.9. The plot looks very diﬀerent from what we obtained for the case of constant surface coverage (Figure 5.21). Instead of being proportional to p(area), the SNR in this case decreases after a certain optimal device area. The latter optimum also depends on the analyte concentration as can be seen from Figure 6.9. Since the coverage ratio decreases as the device area is increased, beyond a certain area, the signal generated no longer scales as fast as the increase in noise due to the larger device area. Thus, for a larger device area, the SNR begins to decrease. This special case highlights a regime where a smaller sized device would be better for the optimization of the SNR in a certain concentration range. However, from the simulation results, it seems that the SNR has

101 8

SNR 4

3 ρ = 1fM 0 2 ρ = 0.5 fM 0 1 0 0.5 1 1.5 2 -8 Device Area (cm ) x 10

Figure 6.9: SNR as a function of device area, for the case of a low KD (1 fM) and limited analyte molecules such that the coverage ratio is no longer constant (see Figure 6.8). This results in a SNR that does not increase with p(area) but instead is maximized at some intermediate device area. The results are shown for two diﬀerent analyte concentration showing that the optimal device size depends on the target concentration of analyte. a weak dependence on the device area beyond the optimal point.

This case is similar to that of the strong binding system of biotin-streptavidin (KD on the order of

≈ 10 fM). Using our numerical model, we are also able to investigate the dependence of the coverage ratio on concentration for a particular device area (number of receptors). Figure 6.10 shows the equilibrium coverage ratio as a function of the analyte concentration in the case of the low KD system (1 fM) under study for number of receptors set at 106 and 105. As the number of receptors is decreased, or equivalently as the device area is decreased, it is observed that the simulated curve approaches the Langmuir isotherm given by Equation 2.24. This is because for a smaller number of receptor sites, there will be enough analyte molecules in the bulk solution to occupy the surface and the conjugation will not be limited by the bulk concentration, ρ0. For a large number of receptor sites (consider the case of 106 receptors), it is obvious from Figure 6.10 that the LOD in terms of analyte concentration becomes worse as compared to the case of the ideal Langmuir isotherm.

This conﬁrms what we observed in Figure 6.9, that reducing the device area (and thus lowering the

102 1

0.8

0.6

0.4 Coverage Ratio 0.2 106 receptors 105 receptors 0 -18 -16 -14 -12 -10 10 10 10 10 10 ρ (M) 0

Figure 6.10: Coverage ratio as a function of the analyte concentration in the regime of low KD (1 fM) and limited number of analyte molecules. As the number of receptors is increased (that is device area is decreased), the 106 receptors curve approaches the Langmuir isotherm given by Equation 2.24. number of receptors) results in a smaller LOD or in other words a higher SNR.

6.6 Summary

In this Chapter, we focus on demonstrating how the bioFET platform can be used to reliably and accurately extract binding kinetics data and we also focus on how the binding affinity of an analyte- receptor system affects the LOD. We successfully measured and extracted the KD of a low binding affinity system, namely HMGB1 protein-DNA, showing that the platform is both a quantitative and accurate tool for studying biomolecular interactions. This is very promising for the bioFET platform as a potentially cheaper and higher throughput alternative to surface plasmon resonance

(SPR). We also discuss the binding aﬃnity (KD value) of a receptor-analyte pair as a limitation to the smallest measurable concentration and therefore how the LOD is determined by the KD of the analyte-receptor pair. As we have seen in Chapter5, the SNR as a performance metric is deﬁned in terms of a unit change in surface potential (∆ψ0 = 1 V). The real SNR of the measurement depends on the reactions happening in the bio-sensitive layer which in turn determine the change

103 in the surface potential. In Chapter5 we considered the case of a surface potential that scales with the device area (coverage ratio being constant) which is relevant in the case of pH detection and as we have seen in the current Chapter, this is also relevant for high KD systems, where the number of analyte molecules available in the bulk solution is always enough to conjugate to the necessary number of surface receptors given by Equation 2.24. In the latter case, the coverage ratio is constant for diﬀerent device area and the SNR scales with p(area) as we have found in Chapter5. In this

Chapter we also considered the case of a low KD, and we showed that the coverage ratio is no longer a constant as the device area is varied. Instead, the coverage ratio decreases very rapidly as the device area is increased due to the fact that the number of analytes available in the bulk solution is too low to populate the surface receptors to the degree required by Equation 2.24. Thus, the binding isotherm deviates from the ideal Langmuir isotherm and the detection limit worsens.

We also showed that when the coverage ratio decreases with device area, the SNR first peaks at an optimal value of the area and then slowly decreases as the area is increased further. Moreover, the optimal area is different for different analyte concentrations (ρ0) and would require careful optimization depending on the target concentration. It is important to note that in our simulations we focused on a reaction volume of 100 µL, since this matches our experimental conditions. Of course, the regime of limited analyte molecules can also be achieved at a higher KD, if one uses a smaller reaction volume and the same device surface area. The goal of this Chapter is to highlight the possibility of such a regime and the conditions under which this would occur, and the results that follow from operating in such a regime. It is evidently clear that a careful consideration of the experimental variables, in determining the regime of operation, is critical to interpreting the results of sensing experiments and eventually optimizing the device size in order to maximize the signal-to-noise ratio.

104 Chapter 7

Reference Electrode

7.1 Introduction

A good reference electrode, for biosensing or pH sensing applications, is one whose interfacial potential does not change signiﬁcantly compared to the surface potential of a bioFET and is stable over time. Looking back at Figure 2.2, it is clear that if the potential at the electrode (φs1) changes, the potential distribution will be aﬀected and the signal recorded by the bioFET device will not be due to surface reactions or conjugations. Such reference eletrodes are hard to miniaturize and integrate onto a chip, resulting in reduced stability and lifetime[105]. The alternative then became the use of pseudo reference electrodes such as bare metal electrodes (Pt, Ag or Ag), Ag/AgCl wires

(without the KCl ﬁlling solution) or even silicon oxide surfaces. These electrodes can maintain a reasonably stable potential given the right conditions, even though they are not as stable as the actual reference electrode. The main diﬀerence is that the value of that quasi-stable interfacial potential is not a priori known in various electrolyte environments and changes based on the ionic content and sometimes pH of the solution. This poses an immediate problem for pH sensing applications where the changes that one is trying to detect involve changes in the bulk pH of a solution. In terms of charge (biomolecular) sensing applications, the use of a pseudo reference electrode, implies that one must be careful in controlling the ionic species as well as the pH of

105 the buﬀer solution in order to ensure the correct interpretation of the sensing results. In this

Chapter, we will consider the requirements and conditions for accurate and sensitive measurements of pH response as well as charge sensing applications. Bio-fouling or the adsorption of biological molecules to a reference electrode is also a very important issue in the design of biosensors for long term operation, especially when such surface adsorption results in erroneous signals due to changes in the electrode interfacial potential. It has been observed previously[106] that protein adsorption on a platinum electrode can result in shifts of the electrode potential of up to 40 mV, which can significantly affect the bioFET signal and lead to unreliable and inaccurate results. A further requirement for the reference electrode which has not been previously considered is the additional noise generated in the drain current (Ids) of a bioFET due to fluctuations in the interfacial potential of the reference electrode. A potential with minimal drift but which has a large voltage noise will adversely affect the LOD of the measurement and therefore, in this Chapter, we will also consider the noise contribution of different electrodes.

7.2 Electrode requirements for pH sensing

For the sensitive detection of small pH changes, one requires that the electrode potential not drift and not change as the concentration of H+ ions is varied. This is not the case for bare metal electrodes such as platinum (Pt), as can be seen in Figure 7.1. Even though the drift in the data is small, the sign of the current change is incorrect. For a p-type bioFET device, we expect the current to increase as the pH is raised since the surface of the device becomes more negative, which leads to more charge carriers (holes) induced in the channel. The “opposite” signal leads us to conclude that the potential change at the reference electrode is much larger than and therefore counteracts the potential change at the oxide surface. The spikes in the current-time trace are due to the manual switching of the two buﬀers and it is obvious that for a bioFET biased in strong accumulation (larger current and larger gm) the size of the switching spike is larger than for the device biased closer to the threshold voltage (Vth). The magnitude of the spike is also indicative

106 7.45 7.45

7.95

7.45 7.45

7.95

Figure 7.1: pH response of a bioFET device using a Pt wire as the solution gate electrode (pseudo reference electrode) at two diﬀerent bias points. The change in the current does not correspond to changes in the surface charge of the bioFET (TRIS buﬀer used at pH 7.45 and pH 7.95), but rather is a measurement artifact due to the interfacial potential at the reference electrode itself changing with pH.

107 Figure 7.2: Current response (∆I) at different bias points plotted as a function of the corresponding transconductance (gm), showing that the potential change involved in the switching of the two well controlled buffers is consistent and repeatable. The slope of the linear fit line gives a “pH response” of 39 mV/pH. of the ability of the reference electrode to pick-up noise from the environment, which is larger in the case of the bare metal electrodes. Despite the “opposite” sign of the signal change, for a well controlled set of buffers, the response due to pH changes is quite repeatable as can be seen in

Figure 7.1. By repeating the same experiment over different operating regimes (bias points), we show in Figure 7.2 that there is a consistent potential change due to the change in pH. The linear dependence of the current response with the gm at the different bias points shows that the potential change is repeatable for this well controlled set of 2 buffer solutions. In this case, the potential change as extracted from the slope of the linear fit was 19.5 mV for the change in pH of 0.5.

Another pseudo reference electrode that is commonly used is the Ag/AgCl electrode, which is essentially a silver (Ag) wire that is electrochemically or chemically oxidized to silver chloride

(AgCl). A complete Ag/AgCl reference electrode consists of the Ag/AgCl wire immersed in a

3M KCl solution. To maintain a liquid-liquid junction (between the test solution and the internal

ﬁlling solution of the reference electrode) while minimizing the diﬀusion of Cl– ions, a porous frit

108 is usually employed. Since the complete reference electrode involves a bulky design, the use of only the Ag/AgCl wire has become very popular and there have been attempts at integrating the Ag/AgCl electrode on-chip[107]. However issues of long term stability and lifetime of such on-chip electrodes remain. Using the Ag/AgCl electrode has the obvious advantage of a smaller interfacial potential, as can be seen in Figure 7.3. The smaller interfacial potential results in a smaller operating voltage due to the lower Vth. We also observe that the potential is more stable and less immune to external noise sources when the Ag/AgCl electrode is employed as can be seen from the pH sensing measurements in Figure 7.4. More importantly, for both buﬀer solutions used, namely TRIS and HEPES, the change in the drain current has the correct sign. For a larger pH the surface of the device becomes more negatively charged and the p-type bioFET device responds by an increase in Id. However, the magnitude of the surface potential change is clearly dependent on the ionic composition of the solutions under test. Figure 7.4(a) shows the reponse of a device in

HEPES buffer yielding a pH sensitivity of 12.2 mV/pH. Figure 7.4(b) shows a similar pH sensing experiment carried out with TRIS buffer, resulting in a sensitivity of 24.6 mV/pH. We are led to conclude that the buffer has an effect on the potential changes occuring at the reference electrode and this becomes more evident when considering that the pH of HEPES is usually adjusted using sodium hydroxide whereas the pH of TRIS is adjusted using HCl, which results in a difference in the chloride ion concentration, [Cl–]. Since the potential established at the interface of Ag/AgCl and solution depends upon [Cl–], there is an additional response due to the pseudo reference electrode when using TRIS as a buffer solution. The best way to carry out pH sensing measurements when using the Ag/AgCl pseudo reference electrode is to make sure that the [Cl–] is constant by adding in NaCl or KCl to the buffers that are used.

Alternatively, back-gating is often used to supply the operating bias point of the bioFET. The potential thus drops across the buried oxide (BOX) instead of the top oxide (TOX) and this leads to an ampliﬁcation of the signal by the ratio of the capacitances, CTOX /CBOX as described in

Section 5.5. Using the back-gate (BG) as a pseudo reference electrode for pH sensing is possible as can be seen from the I-V curves in Figure 7.5. The direction of the change (more negative Vth

109

300 250 Ag/AgCl 250 Ag/AgCl 200 Pt Pt 200 150

150 Id (nA) Id (nA) 100 100

50 50

0 0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Solution Gate Voltage (V) Solution Gate Voltage (V)

Figure 7.3: Id-Vg curves for two bioFET devices, demonstrating the diﬀerence in the interfacial potential of the Pt electrode as compared to that of the Ag/AgCl electrode. The larger interfacial potential of the Pt electrodes translates into a more negative threshold voltage when the transfer characteristics are measured.

HEPES (a) TRIS (b)

9.9 8.92 7.5 7.04

Figure 7.4: (a) pH response of a bioFET using Ag/AgCl as a pseudo reference electrode and 10mM HEPES as the pH buffer solution. The extracted pH sensitivity is 12.2 mV/pH (b) pH response of a bioFET using Ag/AgCl and 10mM TRIS as the buffer solution with an extracted sensitivity of 24.6 mV/pH. This shows the influence of the buffer on the potential changes that are measured due to the response of the pseudo reference electrode itself to [Cl–].

110

1E-6 pH5.8 pH 7.3 pH 8.5 1E-7

(A) D I 1E-8

1E-9 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 Back Gate Voltage (V)

Figure 7.5: Id-Vg curves of bioFET sensors for different pH values of the PBS buffer solution, showing the expected negative Vth shift for smaller pH values. for lower pH) is correct and the pH sensitivity of the measurement can be extracted by taking into account the amplification factor (CTOX /CBOX ) which roughly gives 15 mV/pH. In our experience, however, the response of the bioFET when using the BG electrode varies quite unpredictably. The sensing data in Figure 7.6 shows absolutely no change in the drain current as the pH is changed drastically from 6.05 to 2.24, which indicates that the response of the BG electrode completely offsets the response of the bioFET device. This same device showed a pH response of 50 mV/pH when using the Ag/AgCl reference electrode, which confirms that the top-surface of the bioFET is indeed pH responsive. This kind of cancellation of the change in potential has been reported in the literature[108], without a thorough explanation as to its origins. The authors speculate that the change in potential on the surface of the oxide covering the gate electrode (BG) has the same magnitude but opposite polarity to the change in potential at the top oxide surface. Variations in this observation probably has to do with the quaility of the two oxide surfaces under consideration.

If the density of chemically reactive groups is quite diﬀerent, the changes in interfacial potential will not cancel each other out.

Our results therefore indicate that the Ag/AgCl pseudo reference electrodes are much more reliable

111 -8 x 10 10 pH 6.05 pH 2.24

Current (A) 4

0 2 4 6 8 10 12 Time (min)

Figure 7.6: Current-time trace for a bioFET device using the back-gate (BG) as a pseudo reference electrode, showing the lack of response due to the potential change at the electrode cancelling the change at the device surface. than bare metal electrodes such as Pt or silicon oxide gate electrodes. However, the chloride concentration in the buﬀer solutions used should be well controlled to minimize artifacts in the bioFET signal due to changes in the reference electrode potential. It is also clear that Ag/AgCl electrodes are less sensitive to external noise sources such as manual or electro-magnetic switching of ﬂuidic valves as can be seen by comparing the switching spikes in Figures 7.1 and 7.4. The back gated approach results in non-reproducible results as well as noisier results (see Section 5.5), even though it provides a simple way of biasing the bioFET when the integration of reference electrodes is tricky.

7.3 Electrode noise and its eﬀects on SNR

The choice of the reference or pseudo reference electrode has a profound effect on the LOD of the particular measurement since any fluctuations or noise pickup at the reference electrode will be translated into current fluctuations and consequently add on to the intrinsic device noise, reducing

112 Figure 7.7: SNR as a function of solution gate voltage for a Pt electrode (red) compared to Ag/AgCl electrode (black). the SNR and degrading the LOD. In order to investigate the influence of the solution gate electrode on the total noise, we carry out measurements of the SNR as a function of the gate voltage such as those in Chapter 5, for the Pt electrode and Ag/AgCl pseudo reference electrode. The results in Figure 7.7 show that the peak SNR is slightly degraded in the case of the Pt electrode (The shift in the position of the peak SNR is due to the larger interfacial potential of the Pt electrode as we observed in Figure 7.3). This confirms our previous observations that the Pt electrode is more susceptible to picking up noise fluctuations from the surrounding environment as we saw with the fluidic switching peaks. The difference is nonetheless a small one, which means that a well isolated Pt electrode would perform just as well as an isolated Ag/AgCl reference electrode since the main source of noise in our system, as we have shown in Chapter 5, is the intrinsic 1/f noise of the bioFETs themselves.

A lot of measurements, however, cannot be performed in complete isolation. Either the device itself needs to be continuously exposed to the environment, if the application involves environmental monitoring, or the device needs to operate under flow conditions so that different analytes can be introduced at different times. Under fluid flow conditions, the reference electrode can experience the

113 effects of a streaming potential which could potentially result in additional voltage fluctuations at the solution gate electrode. We have observed that under fluid flow conditions, the signal measured by the bioFET becomes more stable since the injection of a new solution is now part of a continuous process instead of being a process that disrupts the static equilibrium. The pH sensing results shown in Figure 7.8 were carried out using an Ag/AgCl electrode, under solution flow at 50 µL/min and the switching spikes that are seen are due to the solenoid valves switching on and off. Under solution

flow, the transients becomes smoother and the reponse in general more repeatable. However, since the whole system is now in a quasi-equilibrium state the reference electrode potential becomes more vulnerable to increased voltage fluctuations. The effect of the flow on the drain current noise power spectrum of the bioFET is shown in Figure 7.9. As can be seen from the latter figure, both the Pt and the Ag/AgCl electrodes show an increase in the noise level as the flow is switched on to 50 µL/min, even though the Ag/AgCl shows a smaller increase in noise around f = 1 Hz. The noise spectrum for the Pt electrode is very ”noisy” at the large frequencies (f > 10 Hz), illustrating the more significant noise pickup of the Pt electrode, as we expected from the switching spikes we observed from the earlier current time traces. These results further confirm the advantages of an

Ag/AgCl electrode over a Pt electrode, even though the latter is easier to integrate in a micro- fabrication ﬂow process.

We also carried out similar flow dependent measurements using a miniature Ag/AgCl reference electrode (Harvard Apparatus Inc.). This electrode consists of a Ag wire in contact with a gel electrolyte composed of 3M KCl, within a Teflon tube, with a conductive polymer at the tip for electrical contact with the solution under test. The results of this reference electrode contrasted with the Pt pseudo reference electrode are shown in Figure 7.10. It is very clear that the potential at the full Ag/AgCl electrode has very low noise even under flow conditions. There is a significant difference in how the Pt electrode responds to the switching on of the flow whereas the miniature reference electrode shows barely any change at all. This measurement also highlights the fact that the potential at the bioFET surface does not pick up additonal noise due to the movement of electrolyte ions. There is of course a shift in the drain current as the flow is switched on due to

114 pH 8.05 pH 8.05

pH 6.59 pH 6.59

Figure 7.8: pH sensing results for the Ag/AgCl electrode under fluid flow conditions of 50 µL/min. The switching spikes correspond to the switching on/off of the electronic solenoid valves.

Pt Ag/AgCl

Figure 7.9: 1/f noise spectra for the bioFET biased in strong accumulation, comparing the spectra of the Pt electrode to the spectra of the Ag/AgCl electrode under no flow conditions as well as 50 µL/min fluid flow. The spectra for the Pt electrode is noisier for high frequencies and the noise power increases by a larger amount than the noise power of the Ag/AgCl electrode, when the flow is switched on as we expected from earlier measurements.

115 Figure 7.10: 1/f spectra for a bioFET biased in strong accumulation, comparing the noise of the Pt electrode to that of a miniature Ag/AgCl reference electrode, under no flow and 50 µL/min fluid flow conditions. the establishement of a new quasi-equilibrium. In the case of both the Pt and Ag/AgCl pseudo reference electrodes, in addition to the current shift, the noise level also increases. For the miniature

Ag/AgCl reference electrode, the drain current shifts but the noise level remains unchanged, which is what we want for very sensitive detection under ﬂow conditions. From the 1/f noise spectra, it is obvious that the reference electrode displays fewer spikes in the high frequency region (f > 10 Hz), which indicates that the miniature reference electrode is less susceptible to noise pickup from the environment. The LOD in terms of pH sensing was carried out using the miniature reference electrode (see Figure 5.13) and the stability as well as reproducibility of the response, under ﬂow conditions (100 - 300 µL/min), can be clearly seen in Figure 5.12.

7.4 Inﬂuence of the reference electrode on charge sensing

From the previous section, it has been demonstrated that for sensing experiments involving pH changes, the choice of the solution electrode is critical in avoiding erroneous and random results, due to measurement artifacts resulting from an unstable solution electrode potential. It is not clear however, whether charge sensing (biomolecular sensing) is aﬀected by the choice of the solution gate

116 V

+ - Ag/AgCl Test Electrode Reference

Figure 7.11: Schematic of the experimental setup used to examine the changes in interfacial potential occuring for various test electrodes upon addition of charged biomolecules, by meauring the changes in the open circuit potential. electrode. One of the major concerns is biofouling of the reference electrode, that is, the non-specific binding of proteins or other biomolecules to the surface of the solution electrode leading to electrode voltage drift and eventually to electrode failure. This problem would seem to be universal across all different types of electrodes since it is a result of surface adsorption. However, the effect of such protein adsorption has been reported to be much lower in the case of a full reference electrode as compared to a Pt pseudo reference[106]. In this section we carry out open circuit measurements to determine the change in voltages at the electrode-electrolyte interface for various combinations of electrodes using the experimental setup depicted in Figure 7.11. To investigate the effects of protein binding to the test reference electrodes, we used 1 mg/mL of poly-L-lysine (PLL) in 0.1X

PBS (phosphate buﬀered saline). The results of the platinum electrode compared to the silver- silver chloride electrode are shown in Figure 7.12. As expected, the Pt electrode displays a larger open circuit potential (≈ 500 mV) compared to the Ag/AgCl wire (≈ 130 mV). More relevant to the case of biomolecular sensing is that the Ag/AgCl wire shows a much smaller change of potential as compared to the Pt wire, demonstrating that it might be possible to accurately use the Ag/AgCl pseudo reference electrode for charged based sensing as the potential is minimally aﬀected by protein adsorption. To ensure that the full reference electrode is not experiencing a

117 0.5 0.1322

0.48 Pt 0.132 Ag/AgCl 0.1318 0.46 0.1 mV 80 mV 0.1316 (V) 0.44 (V) oc oc

V V 0.1314 0.42 0.1312

0.4 0.131

0.38 0.1308 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 Time (min) Time (min)

Figure 7.12: Open circuit potential (Voc) of the Pt and Ag/AgCl electrodes measured against a full Ag/AgCl reference electrode, showing the transients and voltage shifts upon addition of 1 mg/mL of PLL. corresponding change in its interfacial potential and to have a baseline for comparison, we carry out the same measurement using a second Ag/AgCl true reference electrode. The results are shown in Figure 7.13. Firstly, we note that the open circuit potential is very small (≈ 3 mV) as expected for a full reference electrode. Second, there is still a small potential change upon addition of the

PLL and it is somewhat encouraging to see that the change in open circuit potential is the same as in the case of the Ag/AgCl pseudo reference electrode.

7.5 Outlook on integration of on-chip reference electrode

From the previous sections, it becomes clear than an on-chip Ag/AgCl pseudo reference electrode is a viable alternative to the full reference electrode. It is also evident that the on-chip Ag/AgCl supplies a more robust electrode potential than the Pt, both in the case of pH and biomolecular sensing. However, the fabrication on an on-chip Ag/AgCl electrode is tricky because of the need to form the AgCl layer after the deposition of Ag and the subsequent potential erosion of the AgCl layer as a result of long term usage. To create the AgCl layer, two methods exist: (1) electrochemical oxidation of the Ag, by applying +3V for 15 mins to the Ag with a Pt electrode used as the ground.

(2) Chemical oxidation of the Ag by immersing in 10% household bleach solution. Method (2) is a

118 -3 x 10 -2.9

-3 0.1 mV -3.1

(V) -3.2 oc V -3.3

-3.4

-3.5 0 1 2 3 4 5 Time (min)

Figure 7.13: Open circuit potential (Voc) measurement for two full Ag/AgCl reference electrodes upon addition of 1 mg/mL of Poly-L-Lysine (PLL). The transient is due to the manual addition of PLL and the voltage change is 0.1 mV. slower process and therefore allows more control in the case of thin layers of Ag and our experience shows that the quality of the resulting Ag/AgCl electrode is the same as that obtained from Method

(1). A test wafer for on-chip electrode characterization is shown in Figure 7.14, before and after the chlorination process using household bleach. The open-circuit potential of the on-chip electrodes was found to change from 200mV, in the case of bare Ag, to 36 mV for the Ag/AgCl electrode.

We carried out some initial characterization of the on-chip Ag/AgCl test structures to examine the stability of the open-circuit potential (measured w.r.t the Ag/AgCl reference electrode) as a function of time, pH and ionic composition. The drift of the on-chip electrode as a function of time is shown in Figure 7.15, demonstrating its relative stability over a time span of two hours. The on-chip Ag/AgCl electrodes were also tested for their stability to changes in pH. Upon the addition of concentrated sodium hydroxide (NaOH, 1N), barely any change in the open circuit potential was observed as can be seen in Figure 7.16(a). This is very encouraging as it demonstatrates that the on-chip electrode can accurately be used for pH sensing as long as the chloride concentration

([Cl–]) is held constant since the electrode potential depends on the equilibrium between the solid

119 Bleach

Voc ≈ 200 mV Voc ≈ 36 mV

Figure 7.14: The optical micrograph on the left shows patterned Ag metal deposited by e-beam evaporation on to a silicon substrate. After the treatment with bleach, a thin layer of AgCl is formed resulting in a darker color. The open circuit potential can be used to conﬁrm the successful conversion of Ag to AgCl as the potential changes from 200 mV to 36 mV.

45 Potential Difference (mV) 40 0.0 0.5 0.9 1.4 1.9 2.3 Time (Hours)

Figure 7.15: Open circuit potential (Voc) measured w.r.t a Ag/AgCl reference electrode as a function of time, demonstrating the small amount of drift for the on-chip Ag/AgCl pseudo reference electrode.

120

70 0 (a) (b) 3 M KCl -20 65 -40

60 -60 55 30mM KCl NaOH added -80 Potential Difference (mV) Potential Difference (mV) 50 -100 0.0 2.8 5.6 8.3 11.1 13.9 16.7 0.0 6.9 13.9 20.8 27.8 Time (min) Time (min)

Figure 7.16: (a) Response of the open circuit potential of the on-chip Ag/AgCl pseudo electrode (measured w.r.t a reference Ag/AgCl electrode) upon addition of sodium hydroxide (NaOH), showing that pH changes do not aﬀect the electrode potential as long as [Cl–] remains constant. (b) Response of the on-chip Ag/AgCl electrode upon an increase in [Cl–], showing that the electrode potential is indeed responsive to changes in the chloride concentration.

AgCl and the chloride ions in the electrolyte. Figure 7.16(b) shows the response of the electrode to a change in the chloride concentration, showing that the electrode is indeed responsive to Cl– ions and that the larger the [Cl–], the smaller the potential diﬀerence since the interfacial potential becomes similar to the full reference electrode (ﬁlling solution of 3M KCl).

7.6 Summary

The choice of the solution gate electrode (reference electrode) is critical to the correct interpretation of sensing results, since any change in the electrode interfacial potential results in a change of the device current which can easily be mistaken for a real signal. A complete reference electrode (such as a full Ag/AgCl single liquid junction electrode) involves the solid phase (AgCl) in contact with a ﬁlling solution (3M KCl) which keeps the interfacial potential constant irrespective of the sample solution that is being investigated. A pseudo reference electrode however, has an interfacial potential that depends on the potential determining species in the test solution. Therefore, the composition as well as the pH of the solution under test should be carefully controlled for the accurate interpretation of results when using a pseudo reference electrode. Our results show that using a Pt electrode results in inconsistent pH sensing results and that the Ag/AgCl electrode can be used for pH sensing

121 provided that the chloride concentration is well regulated. From our noise measurements using different electrodes, we conclude that under static conditions the performance of all electrodes is very similar, especially at low frequencies. The Ag/AgCl electrodes display a slightly higher peak SNR which translates into a slighlty lower LOD. Under fluid flow conditions, however, both the Pt and

AgCl pseudo reference electrodes fare significantly worse than a full Ag/AgCl reference electrode due to an increased level of the low frequency noise which in turn affects the LOD. The increase in noise of the Ag/AgCl electrode is less than that of the Pt electrode however, which is consistent with our observations of switching spikes which are more significant for Pt than Ag/AgCl. The full reference electrode (Harvard Apparatus Inc.) exhibits a very stable interfacial potential that does not pick up additional noise from the fluid flow of the surrounding medium. We have also characterized the performance of the different electrodes for charge sensing applications by considering changes in the open circuit potential upon the addition of a high concentration of biomolecules. Our results again highlight the potential stability issues of the Pt electrode as compared to the Ag/AgCl pseudo reference electrode which is found to be as robust as the full reference electrode.This led us to consider an on-chip Ag/AgCl electrode configuration, which requires an additional chemical oxidation step (using household bleach) to create a layer of AgCl on top of the deposited Ag. This layer was found to be result in a fairly stable potential over time, with a relatively small interfacial potential (30-60 mV w.r.t Ag/AgCl reference). We also ensured that the on-chip Ag/AgCl electrode maintained a constant interfacial potential even as the pH of the solution was changed, even though as we demonstrated in this Chapter, the chloride concentration should still be carefully controlled as Cl– is the potential determining species for the Ag/AgCl electrode. The preliminary electrode characterization results of this Chapter clearly show that an on-chip Ag/AgCl electrode is a viable option and will result in much better reproducibility and accuracy than the Pt electrode. In situations where the LOD of the setup becomes an important consideration, such as sensing small analyte concentrations under flow conditions, a full reference electrode still yields a higher peak

SNR and therefore a smaller LOD, than either one of the pseudo reference electrodes.

122 Chapter 8

Conclusions

The work of previous graduate students provided the foundation for the work presented in this thesis. My experiments and investigations build upon the standardization of the fabrication process as well as the functionalization and measurement procedure resulting in enhanced reliability and accuracy of sensing results. At the time when I started my thesis work, there were a variety of publications claiming very sensitive detection (down to attomolar levels) but these measurements were either inconsistent with each other or with the large time scale that was theoretically required for such low concentrations. Moreover, a lot of theoretical work focused on parameters that affect the “sensitivity” or in other words, the relative signal change (∆I/I), which justified the aggressive scaling down of biosensors. It became very clear to me that the noise performance, which was being overlooked, also varied with these parameters and that it is the noise level of a particular sensor which determines the smallest measurable signal, i.e. the limit of detection (LOD). This led to the realization that noise characterization, which was a standard procedure in the study of electronic devices and more specifically MOSFETs, could easily be applied to our bioFET sensors and would result in a better understanding of the physical parameters which determine the noise level and consequently the LOD. Hence, the bulk of this thesis is in the application of noise characterization and modeling tools to the problem of biosensing using field effect transistors, with the general goal

123 of understanding the noise mechanisms and parameters which aﬀect the limit of detection. To improve the LOD of these bioFET sensors, additional work needs to be carried out in the following areas:

1. Intrinsic device noise level, especially for ultra-scaled devices or when the use of high-k

dielectric stacks are involved.

2. Debye screening, to allow for measurements in physiological conditions or whole blood without

any extensive sample preparation/ﬁltration.

3. Binding kinetics/equilibria, to improve the detection signal as well as reduce the time needed

for a particular measurement.

In this thesis, we focus on items 1 & 3. Firstly, the fabrication process was optimized further to include a top-gate dielectric layer formed by thermal oxidation of silicon or by atomic layer deposition of aluminum oxide (Al2O3), resulting in much better device lifetime and stability. An

8-channel measurement setup was also designed and custom built to allow for the concurrent measurement of drain current from 8 devices, thereby increasing the throughput and allowing for statistical analysis of the sensing data. The multiplexed detection setup was also made more compact and hence more portable by combining the device DIP holder and readout as well as the ampliﬁcation stage on a single PCB.

We then focus on Item 1, which is the intrinsic low frequency noise of the FET device itself and which relates to the fundamental limit of the FET sensor. We utilize various noise models to characterize our devices and found that they compare very favorably with current bottom-up nanowire systems when the Hooge’s parameter is extracted and compared. Hooge’s parameter is used to provide a quantitative justification for the use of TMAH in etching the nanowire/nanoribbon channels, resulting in bioFETs with better noise performance. To model the subthreshold as well as the linear regime of the transfer characteristics, we make use of the number fluctuation model as well as the correlated number-mobility fluctuation model. By carrying out temperature dependent measurements, we show the transition from the correlated number-mobility fluctuation model to

124 a purely number fluctuation model and finally we investigate the influence of only a few, discrete

ﬂuctuators giving rise to two-level swtiching signals called random telegraph signals (RTS). These

RTS become dominant for certain combinations of temperature and gate voltages and our results demonstrate the decomposition of 1/f noise as a superposition of singe trap dynamics. Our RTS analysis led to the conclusion that deep acceptor traps due to gold were a major source of drain current ﬂuctuations for the nanowire devices. Consequently, the use of aluminum for the source- drain contacts is recommended.

Next, we focus on the limit of detection of these FET biosensors, by combining noise measurements with I-V characterization in order to gain insight into the physical parameters that determine the LOD on the sensor side. We show that the real sensitivity (that is the change in surface potential for a unit change in the measurand) is independent of the operating point of the device and therefore independent of the relative signal change, which is maximum in the subthreshold regime. Consequently, we devise an alternative performance metric that we name SNR, defined as the ratio of the transconductance and the drain current noise amplitude at f=1Hz. Using the latter as a metric, we were able to show that the optimal regime for operation is the linear regime, close to the point of peak transconductance. Our measurements of the SNR also allow us to extract values for the trap density and quantify the effects of surface modification on the surface states of the bioFET device as well as compare the quality of the back gate to the thermally grown top gate oxide/dielectric. APTES functionalization is shown to passivate oxide traps and result in almost a ten-fold reduction in Not. The trap density of the back-gate is found to be larger than that of the top-gate oxide, rendering any back-gated measurements noisier than solution gated ones. It is also found that the SNR increases with p(device area), which is contrary to the common scaling argument where smaller devices result in larger relative signal changes.

We also carry out measurements of binding kinetics (association and dissociation phases) to show the applicability of the bioFET platform in the case of such measurements, as a potential replacement for surface plasmon resonance (SPR). This is the ﬁrst time that such measurements have been reliably and accurately carried out on a nanowire system, highlighting the quality of top-down

125 fabricated devices and the accuracy in determing the equilibrium constants for both high and low

KD systems. This thesis then proceeds to discuss the limitations imposed by the binding equilibria of the analyte-receptor system, namely the value of the equilibrium dissociation constant (KD). By combining the binding kinetics considerations with the noise or SNR limitations, we highlight the p high KD regime where SNR scales with (device area) as well as the low KD regime where, in some cases, the device area has to be optimized for maximum SNR.

Finally, we also investigate the influence of the solution gate electrode on the measurement accuracy, stability and noise. It is found that using Pt as a pseudo reference electrode results in anomalous pH response signals and higher noise levels under fluid flow conditions. The ideal solution would involve the use of a complete reference electrode such as the Ag/AgCl reference but this renders miniaturization of the measurement setup intractable. We show here that a pseudo reference consisting of Ag/AgCl can be used to yield accurate as well as consistent results with a smaller amount of noise pick-up than a metal solution gate electrode. We show very encouraging results on the potential integration of an on-chip Ag/AgCl pseudo reference electrode.

The work presented in this thesis considers the factors which influence the smallest analyte concentration that can be reliably measured. We approach this problem by looking at the low frequency noise of the nanowire/nanoribbon bioFETs, which is the dominant noise source for such field-effect transistor platforms. Combining noise measurements with I-V characterization, we come up with a performance metric that allows us to answer, in a quantitative manner, questions regarding the optimal bias regime, optimal gate dielectric stack and fabrication etch processes.

SNR as a performance metric (diﬀerent from SNRmeas) is more relevant than the relative signal change (∆I/I) in predicting the limit of detection of the sensor, due to the direct relationship

LOD = 1/SNR. SNR is also very easily extracted prior to any surface modiﬁcation and sensing experiment. Focusing on the noise performance and the SNR results in a more honest approach to the design of better bioFET sensors, which would eventually lead the technology closer to commercial applications. For instance, considering Equation 2.28, a larger area (obtained either by increasing W or increasing L) results in a lower LOD, upto the point where the instrumentation noise

126 dominates the device noise and SNR no longer follows Equation 2.28. Also, larger devices mean fewer devices per die. Therefore, there has to be an engineering trade-off between the requirements of small LOD and high bioFET device density. At a first glance, it would seem that increasing Cox would improve the LOD. However, increasing Cox also reduces the surface potential change for a given bound analyte charge, with a net result of the LOD being unchanged. The dielectric layer is important for other reasons however, namely that the density of functional groups can be different depending on the material and the stability of the layer to electrolyte ion diffusion also varies with the choice of dielectric material. However, as we have shown in this thesis, a lot of work needs to be done in reducing the interface trap densities associated with dielectric stacks other than silicon oxide.

Undoubtedly, certain technical challenges remain. Additional work in the area of micro-ﬂuidic integration would allow one to use the full potential of the bioFET platform in terms of high throughput analysis and the ability to study small sample volumes. Another area, which relates to the binding kinetics of the analyte-receptor system, is the reproducibility of high functionalization density on top of the bioFET surface which is the main cause of variability of results and even anomalous results in the ﬁeld currently. The signal generated from the conjugation of analyte moelcules to receptors is directly proportional to the density of receptor sites as well as to the

KD, and a lot of research is currently underway to replace the unstable monoclonal antibodies with antibody fragments or synthetic recognition molecules, which are not only more stable over time but also exhibit a higher binding aﬃnity. It is only by combining the low variability and low noise of CMOS fabrication with more robust and consistent bio-molecular functionalization that the promising technology of bioFET sensors can be brought closer to commercialization.

127 References

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