Ultrasensitive Quartz Crystal Microbalance

Home , Q factor

The Pennsylvania State University

The Graduate School

Department of Electrical Engineering

ULTRASENSITIVE QUARTZ CRYSTAL MICROBALANCE

INTEGRATED WITH CARBON NANOTUBES

A Thesis in

Electrical Engineering

Abhijat Goyal

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2006 ii

The thesis of Abhijat Goyal was reviewed and approved* by the following:

Srinivas Tadigadapa Associate Professor of Electrical Engineering Thesis Advisor Chair of Committee

Peter Eklund Professor of Physics Professor of Materials Science and Engineering

Joan Redwing Professor of Electrical Engineering Professor of Materials Science and Engineering

Charles L. Croskey Professor of Electrical Engineering

David Allara Professor of Chemistry Professor of Materials Science and Engineering

W. Kenneth Jenkins Professor of Electrical Engineering Head of the Department of Electrical Engineering

*Signatures are on file in the Graduate School iii

ABSTRACT

In this thesis, an ultrasensitive Quartz Crystal Microbalance (QCM) which can be configured as a versatile (bio)chemical sensor is presented. The high sensitivity of the

QCM was achieved via miniaturization using micromachining techniques. The absolute mass sensitivity of sensor was increased by decreasing the thickness and the area of the electrodes of the resonators. Through optimal design, microfabrication, and miniaturization the mass sensitivity of the sensors was increased by more than four orders of magnitude to less than 1 pg/Hz; as compared to 17 ng/Hz for commercially available 5

MHz bulk resonators. Miniaturization of the resonators enables their fabrication in an array format with each pixel of the array being individually addressed. This enables true spatial and temporal mass sensing capabilities. The fabricated resonators were tested for operation in air and water and high quality factors of 7500 and ~2000 were obtained respectively.

A dielectric etch process was developed to achieve the miniaturization of the sensors. The optimization of the dielectric etch process was achieved using statistical techniques such as Design of Experiment (DOE). An etch rate of 0.5 μm/min at rms surface roughness of less than 2 nm was achieved after the optimization process. The process parameters, namely the ICP power, the substrate power, the flow rate of gases, the operating pressure of the etch tool, distance of substrate holder from the source, and the temperature of substrate holder, were quantitatively related to the etch rate and rms surface roughness using least square fit to the etch data. iv

The QCMs were integrated with carbon nanotubes using a simple spray-on technique. It was found that the addition of carbon nanotubes onto the electroded surface of the resonator increased its Q-factor by as much as 100%. It was proposed that the carbon nanotubes due to their high stiffness suppress the out-of-plane flexural vibrations in the

QCMs thereby suppressing an energy loss channel and hence causing an increase in the

Q-factor. Measurement of out-of-plane vibrations of the quartz crystals using a laser based optical vibrometer revealed that the out-of-plane vibrations of QCM increase from

13 pm to 26 pm when carbon nanotubes are removed from the surface of the resonator – directly confirming the suppression of the out-of-plane motion on the resonator surface by carbon nanotubes.

Additionally, the QCMs were used to study the gas adsorption and desorption behavior of nominally “open-ended” isolated and nominally “close-ended” bundled SWNTs. Using the ultrasensitive QCM, we were able to probe gas storage properties of carbon nanotubes. It was found that carbon nanotubes can adsorb large amount of gas molecules not only in the cylindrical pore that they enclose, but also on their external surface. Four different gases were tested, namely Helium, Nitrogen, Argon, and SF6. It was found that the change in resonance frequency and quality factor for the “fill in” and “evacuation” of gases from carbon nanotubes exhibited a characteristic ~ MW relationship, where MW is the atomic/molecular weight of gas species adsorbed. Such a behavior was consistently observed both for change in resonance frequency and Q-factor during the events of “fill in” and “evacuation” in the case of bare quartz with gold electrode, gold electrode covered with nominally isolated “open-ended” SWNTs, and gold electrode with nominally bundled “close-ended” SWNTs. In the case of bare quartz with gold electrode, v

the observed change in resonance frequency and Q-factor and their characteristic

~ MW relationship can be explained on the basis of the viscous dissipation arising due to gas ambient through the Gordon-Kanazawa equation. In the case of QCM with carbon nanotubes, the change in Q-factor and its characteristic ~ MW relationship could be explained on the basis of enhanced viscous dissipation arising due to surface roughness or modified Gordon Kanazawa equation. However, for the case of frequency change in the presence of carbon nanotubes, the characteristic ~ MW relationship and the

observed change in magnitude of resonance frequency was explained in terms of physical

adsorption of gas molecules near the inside and outside walls of carbon nanotubes, in

regions where the potential due to the carbon atoms for gas atoms and molecules is

attractive.

TABLE OF CONTENTS

LIST OF FIGURES LIST OF TABLES ACKNOWLEDGEMENTS

1. Introduction……………………………………………………………………. 1 1.1. Resonators and Resonance…………………………………………………. 2 1.1.1. Piezoelectricity and crystal oscillator……………………………….. 4 1.1.2. Quartz Crystal……………………………………………………….. 4 1.2. Quartz Crystal Microbalance……………………………………………….. 10 1.2.1. Why miniaturize QCMs?...... 13 1.2.2. Radial dependence of mass sensitivity of QCM…………………….. 14 1.2.3. Quality (Q-) factor of a QCM……………………………………….. 17 1.2.4. Noise analysis of AT-cut quartz resonator…………………………... 21 1.3. Review of resonator based mass sensors…………………………………… 25 1.3.1. Cantilever based mass sensors………………………………………. 26 1.3.2. SAW based mass sensors……………………………………………. 27 1.3.3. Flexural plane wave sensor………………………………………….. 30 1.3.4. Thin rod sensors……………………………………………………... 32 1.3.5. FBAR mass sensors………………………………………………….. 34 1.3.6. Thin film PZT based sensors………………………………………… 36 1.3.7. Carbon nanotube based mass sensors………………………………... 36 1.3.8. Comb drive actuator…………………………………………………. 38 1.3.9. Comparison with QCM……………………………………………… 39 1.4. Applications of QCM……………………………………………………….. 40 1.4.1. QCM as a immunosensor……………………………………………. 42 1.4.2. DNA biosensors……………………………………………………... 43 1.4.3. Drug analysis………………………………………………………… 43 1.4.4. Vapor phase chemical sensor………………………………………… 43 1.4.5. Protein adsorption…………………………………………………… 44 1.4.6. Cell adhesion and cell function……………………………………… 46 1.5. Optical techniques and comparison with QCM…………………………….. 47 1.6. Thesis Organization………………………………………………………… 49

2. Etching for miniaturization……………………………………………………. 52 2.1 Introduction…………………………………………………………………. 52 2.2 Literature Review…………………………………………………………… 55 2.2.1 Micromachining using wet etching techniques……………………… 56 2.2.2 Micromachining using controlled dissolution of quartz blanks……… 60 2.2.3 Modeling of chemical wet etching processes………………………... 62 2.2.4 Dry etching techniques for micromachining………………………… 64 2.2.4.1 What is plasma?...... 65 2.2.4.2 Ions and radicals in plasma………………………………………. 66 2.2.5 Evolution of plasma etching equipment……………………………... 67 vii

2.3 ICP source used in current experiments……………………………………... 76 2.4 Experimental Procedure……………………………………………………... 79 2.5 Results and discussion……………………………………………………….. 81 2.5.1 Design of Experiment (DOE)………………………………………... 81 2.5.2 Effect of variation of process parameters……………………………. 92 2.5.2.1 Effect of operating pressure……………………………………… 93 2.5.2.2 Effect of ICP power and substrate power………………………... 95 2.5.2.3 Effect of flow rate of gases………………………………………. 97 2.5.2.4 Effect of substrate temperature…………………………………... 102 2.5.2.5 Effect of distance of substrate holder from the ICP source……… 103 2.5.3 Quantification of etching process…………………………………… 104 2.6 Conclusion…………………………………………………………………… 110

3. Design, fabrication and characterization of QCM…………………………… 112 3.1 Introduction………………………………………………………………….. 112 3.2 Design of quartz microbalance array………………………………………… 112 3.2.1 Energy trapping and spurious modes………………………………… 113 3.2.2 Inverted mesa and energy trapping…………………………………... 127 3.2.3 Choice of materials for QCM electrode……………………………… 128 3.3 Fabrication of quartz microbalance array……………………………………. 131 3.4 Measurement of resonance parameters of QCM…………………………….. 141 3.5 Operation of the device in liquid ambient…………………………………… 144 3.6 Mass calibration experiments of the QCM…………………………………... 145 3.7 Conclusion…………………………………………………………………… 146

4. Use of carbon nanotubes to increase the Q-factor of QCM………………….. 147 4.1 Introduction…………………………………………………………………... 147 4.2 Carbon nanotubes for functionalization of QCM……………………………. 147 4.2.1 Introduction…………………………………………………………... 147 4.2.2 Structure of carbon nanotubes……………………………………….. 149 4.2.3 Growth of carbon nanotubes…………………………………………. 152 4.2.4 Modulus of carbon nanotubes………………………………………... 152 4.3 Equivalent circuit parameters of QCM………………………………………. 153 4.4 Importance of quality factor…………………………………………………. 164 4.5 Experimental methodology…………………………………………………... 166 4.5.1 Preparation of carbon nanotubes……………………………………... 166 4.5.2 Coating the quartz resonator with carbon nanotubes………………… 167 4.6 Results and discussion……………………………………………………….. 168 4.7 Existence and suppression of flexural vibrations in quartz resonators………. 174 4.8 Experimental proof of suppression of flexural vibrations in QCM………….. 184 4.8.1 Principle of laser Doppler Vibrometry………………………………. 184 4.8.2 Results and discussion……………………………………………….. 188 4.9 Conclusion…………………………………………………………………… 189

5. Weighing molecules using QCM integrated with carbon nanotubes……….. 192 5.1 Interaction of gases with carbon nanotubes………………………………….. 192 viii

5.1.1 Gas uptake by carbon nanotube……………………………………… 192 5.1.2 Interaction processes of gas molecules with carbon nanotubes……… 194 5.2 Experimental Details…………………………………………………………. 195 5.3 Results and discussion……………………………………………………….. 201 5.3.1 Bare gold coated quartz surface……………………………………… 201 5.3.2 Addition of carbon nanotubes to bare gold coated quartz surface…… 213 5.3.3 Coating with bundled close ended SWNTs………………………….. 222 5.3.4 Adsorption of gases in carbon nanotubes……………………………. 223 5.4 Conclusions…………………………………………………………………... 233

6. Conclusions and future work…………………………………………………... 235 6.1 Conclusions…………………………………………………………………... 235 6.2 Future work…………………………………………………………………... 241 6.2.1 Quartz calorimeter…………………………………………………… 241 6.2.2 Functionalization using self assembled monolayers………………… 248 6.2.3 Preliminary data……………………………………………………… 252 6.3 Automatic Gain Control Oscillator Circuit……………………………….…..254 6.3.1 Introduction…………………………………………………………... 254 6.3.2 Conventional circuits without dynamic feedback……………………. 256 6.3.3 Proposed circuit with dynamic feedback…………………………….. 258

APPENDIX A……………………………………………………………………….. 261 References…………………………………………………………………………… 263 ix

LIST OF FIGURES

Figure 1.1: Schematic depiction of a grown quartz crystal. Also shown is the crystallographic orientation for the AT cut of quartz crystal along with other cuts. AT-cut is the most popular cut of quartz crystal in use [4]…………………..……………………5

Figure 1.2: Different modes of vibrations of the quartz crystals [5] ….…………………6

Figure 1.3: (a) Variation in resonance frequency of quartz resonator for different cuts. As can be seen from the figure, the minimum variation in frequency with temperature at ambient room temperature is exhibited by AT and GT cuts. (b)Variation of frequency (y- axis) of an AT-cut quartz crystal with respect to temperature (x-axis) as a function of different cut angles with respect to the AT-cut [5]…..……………………………………7

Figure 1.4: (a) A 3D schematic diagram of the micromachined quartz resonator, (b) Cross-sectional view of the resonator along the dashed line shown in (a)..……………..10

Figure 1.5: Amplitude variation across the surface of a quartz crystal for a Bessel function distribution and a Gaussian distribution. The mismatch between the two curves is at the electrode edges. While Bessel function goes to zero at the edges, the Gaussian function shows nonzero amplitude outside of the edges of the electrodes.……………...16

Figure 1.6: The resonance curves for the quadrature component as represented in equation 1.21, for A=1, Q=1000, and f0 = 50 MHz. The shape of the curve is symmetric only for phase angles of o and 180 degrees, which means that the resonance frequency is equal to the frequency at which the maximum amplitude occurs only for these two curves...... ….18

Figure 1.7: Overview of the different kinds of resonators that can be used as mass sensors………………………………………………………………………………...….25

Figure 1.8: (a) Schematic of optical readout technique commonly used in cantilevers, (b) SEM image of an array of microfabricated cantilevers [31]….………………………….26

Figure 1.9: Typical electrode configuration of a Surface Acoustic Wave Resonator (SAW)……………………………………………………………………………………28

Figure 1.10: Schematic illustration of a flexural plate wave (FPW) sensor, employing a piezoelectric ZnO film and interdigitated electrodes to excite flexural waves in a thin membrane. ……………………………………………………………………………….29

Figure 1.11: Schematic diagram of (a) Electrode Layout, (b) Cross Sectional View, (c) Cross Sectional view in operation, for a magnetically actuated flexural plane wave sensor…………………………………………………………………………………….31 x

Figure 1.12: Schematic illustration of the thin rod sensors. Mechanical resonance is induced in the thin fiber using piezoelectric transducer through glass horns……………32

Figure 1.13: Cross sectional view of a FBAR used for mass sensing in: (a) vapor, (b) liquid. (c) Front side photo, (d) Back side photo of a completed FBAR, (e) resonance frequency shifts at the fundamental and second harmonic resonance frequencies due to Al added to an FBAR surface [43]……………………………………………..…………...34

Figure 1.14: (a) Schematic view of a resonant Piezo layer, (b) Frequency shift vs. mass load for Piezo layers with different thickness [46]..……………………………………..35

Figure 1.15: (a) Cantilevered and (b) bridged nanotube resonator with attached mass. (c) Fundamental resonance frequency of cantilevered carbon nanotube resonator as a function of attached mass, (d) Fundamental Resonance frequency of bridged carbon nanotube resonator as a function of attached mass [47]..………………………………..37

Figure 1.17: The quartz crystal microbalance is essentially a non-specific platform. By use of different sensing functionalization layers, the QCM can be used for a large number of applications, few of which are depicted schematically in this figure……………………………………………………………………..………………41

Figure 1.18: Schematic representation of the device principles of different optical label free techniques. (a) Surface Plasmon Resonance Spectroscopy (SPR), (b) resonance mirror (RM), (c) Grating coupler, (d) reflectometric interferometric spectroscopy (RIFS)……………………………………………………………………………………47

Figure 2.1: (a) High surface roughness that results when the surface of the quartz resonator is mechanically polished. (b) However, after subjecting the rough surface to chemical etching, due to diffusion limited etching, planar smooth surface results…...…57

Figure 2.2: Dissolution rate at different temperature of AT-plates plotted against the removal depth in a NaOH.H2O solution [128].…………………………………………..60

Figure 2.3: 2D Wulff Jacodine plots…………………………………………………….63

Figure 2.4: Schematic illustration of (a) Barrel RIE system, (b) Downstream etching system [133]..……………………….…………………………………………………....68

Figure 2.5: Schematic illustration of different geometries for capacitively coupled RIE systems. (a) Capacitively coupled rf diode system, (b) Capacitively coupled planar single frequency triode system [133]………….………………………………………………..70 xi

Figure 2.6: Electrode geometries for ICP power supplies, (a) Pancake or stove top, (b) Planar, (c) Cylindrical, (d) Hemispherical and (e) Helical [133]………………………..72

Figure 2.7: Different geometries for the Electron Cyclotron Resonance based RIE system [133]……………………………………………………………………………………...74

Figure 2.8: Etching equipment using microwave excited non-equilibrium atmospheric plasma [134]……………………………………………...………………………………75

Figure 2.9: Schematic illustrating the ICP RIE set up used in this work. The vertical position of the substrate holder which is backside cooled using He can be adjusted with respect to the ICP source. Also, the diffusion chamber is lined with magnets to increase the density of the plasma. ………………………………………………………………..78

Figure 2.11: Surface plots of (i-vi) rms Surface Roughness (nm) and (vii-xii) Etch Rate (µm/min) as a function of flow rates of SF6, Ar, and ICP and substrate power…………84

Figure 2.12: Surface plots of (i-iii) rms Surface Roughness (nm) and (iv-vi) Etch Rate (µm/min) as a function of flow rates of O2, SF6 and C4F8………………………………85

Figure 2.13: Surface plots of (i-iii) rms Surface Roughness (nm) and (iv-vi) Etch Rate (µm/min) as a function of flow rates of SF6, C4F8, and CH4………………………….…87

Figure 2.14: Surface plots of (a) rms Surface Roughness and (b) Etch Rate (µm/min) as a function of ICP and substrate power……………………………………………………..89

Figure 2.15: (a) Image of the etched surface generated after etching for one hour using the process conditions as given as Table 1. An rms surface roughness of 1.4 nm is obtained in this case. (b) Side view of the etched feature showing almost vertical sidewalls and a flat bottom. The figure in the inset shows the image of the sidewall generated using Scanning Electron Microscopy (SEM). No attempt was made to characterize, quantify or optimize the roughness of the sidewalls……………………....90

Figure 2.16: Variation of rms surface roughness and etch rate as a function of variation in operating pressure inside the chamber during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in Table 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis……..………………………….…94 xii

Figure 2.17: Variation of rms surface roughness and etch rate as a function of variation in ICP power during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis ……………………………………………………………...…96

Figure 2.19: Variation of rms surface roughness and etch rate as a function of variation in flow rates of (a) Ar and (b) SF6 gases during etching for SF6/Ar based chemistry. All other parameters are kept at their optimum value as in Table 2.2. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis....100

Figure 2.20: Variation of rms surface roughness and etch rate as a function of variation in flow rates of (a) C4F8, (b) SF6 (c) Ar and (d) O2 gases during etching for SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis ………………...………………………………….100

Figure 2.21: Variation of rms surface roughness and etch rate as a function of variation in distance of substrate holder from ICP source during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in Table 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis ………………...……103

Figure 2.22: Plot of (a) natural logarithms of etch rate number and the etch rate, and (b) natural logarithms of rms surface roughness number and the rms surface roughness. A linear relationship is obtained with a slope of 1………………………………………..107

Figure 2.23: Plot of (a) natural logarithms of etch rate number and the etch rate, and (b) natural logarithms of rms surface roughness number and the rms surface roughness. A linear relationship is obtained in both the cases with a slope of 1……………………...109

Figure 3.1: Schematic illustration of partially electroded AT-quartz wafer of infinite extent [164]……………………………………………………………………………. 113

Figure 3.2: Schematic illustration of the principle of energy trapping [164]…...……..115 xiii

Figure 3.3: Schematic illustration of plate with energy trapped structure……………..115

Figure 3.4: Presence of spurious modes in the resonance spectrum of the resonator with 2a/b of 15. A maximum ratio of 10 could be used according to the design criteria……125

Figure 3.5: Absence of spurious modes in the spectrum of a resonator with 2a/b of 5.5……………………………………………………………………………………….125

Figure 3.6: Graphical representation of allowed values of thickness of gold electrode as per the Bechmann’s condition for resonator whose thickness is 34 microns (resonance frequency ~50 MHz), and having an electrode diameter of 1 mm. As can be seen from the figure, electrode thickness near or more than 28 nm would result in spurious modes. The shaded region represents the allowed design space as per the Bechmann’s criteria. The horizontal line represents the value of 2a/b…………………………………………….126

Figure 3.8: Generalized process flow for fabrication of quartz resonators……………133

Figure 3.9: Mask designs for (a) Etching inverted mesa structure, (b) Top electrode for the un-etched side, (c) mask for bottom electrode on the etched side. The process is a three mask process. Each mask results in four chips, each having three by three arrays of resonators on it. Out of these four chips, two chips have electrode diameter of 100 μm, one chip has electrode diameter of 250 μm, and the remaining chip has electrode diameter of 500 μm……………………………………………………………………………….134

Figure 3.10(a): Schematic illustration of the patterned gold and chrome as seed layer for deposition of Nickel…………………………………………………………………….135

Figure 3.10(b): Schematic illustration of electroplated nickel on the patterned seed layer of chrome and gold……………………………………………………………………..137

Figure 3.10(c): Schematic illustration of inverted mesa structures formed in the quartz wafer after the etching step……………………………………………………………..139

Figure 3.10(d): Schematic illustration of the three by three resonator array formed after the etching step…………………………………………………………………………139

Figure 3.11: Optical picture of the fabricated array of three by three quartz crystal resonators. Also shown in the inset is the zoomed in view of the single pixel, showing an electrode diameter of 500 μm and the diameter of the inverted mesa structure to be 1 mm……………………………………………………………………………………...140 xiv

Figure 3.12: Optical picture of a packages resonator array. We can see in (b) that the un- etched side is on the top. Also visible is the GE silicone used to create a water tight reaction chamber using the walls of the hole drilled using water jet cutting through the package…………………………………………………………………………………142

Figure 3.13: Output of the Mathematica based curve fitting program showing the resonance curve in black and the fitted curve in red. Excellent fits can be achieved by use of this program………………………………………………………………………….143

Figure 3.14: Resonance curves for quartz resonator in water (red) curve and subsequent curves obtained when the water was evaporating from the surface. The last curve is in vacuum, wherein highest Q factor with positive frequency shift is obtained…………..144

Figure 3.15: Frequency shift obtained upon mass loading as compared to the theoretical value…………………………………………………………………………………….145

Figure 4.1: (a) Bonding structures of graphite, nanotube and fullerenes. When a graphite sheet is rolled over to form a nanotube, the sp2 hybrid orbital is deformed for rehybridization of sp2 towards sp3 orbital or σ-π bond mixing. (b) Picture of a Multiwalled Carbon Nanotube showing several coaxial nanotubes…………………....149

Figure 4.2: (a) The unrolled honeycomb lattice of a nanotube. When the lattice sites O and A, and sites B and B’ are connected, an (n,m) = (4,2) nanotube can be constructed. (b) STM image of a SWNT exposed at the surface of a rope. A portion of a 2D graphene sheet is overlaid to highlight the atomic structure [175]….……………………………150

Figure 4.3: A 2-D graphene sheet showing the indexing used for carbon nanotubes. The large dots denote metallic tubes while smaller dots denote semiconducting tubes [175]…………………………………………………………………………………….151

Figure 4.4: The electrical equivalent circuit of a resonating QCM. This circuit is called Butterworth Van Dyke equivalent circuit, and represents the resonating crystal in terms of discrete impedance elements. The capacitance Cq represents the mechanical elasticity of quartz, the inductance Lq the initial mass, the resistance Rq the energy loss arising from viscous effects, internal friction, and damping induced by the crystal holder. The static capacitance C0 determines the admittance away from resonance, while the motional components dominate near resonance………………………………………………….154

Figure 4.5: Simulated impedance spectrum from the BVD-equivalent circuit with marked resonance frequencies fZmin, fs, fp, and fZmax for the case of Rq > 0 [194]…..….163

Figure 4.6: The quality factor of the resonator increases with sequential loading of SWNTs. A direct evidence for the deposition of SWNTs is indicated from the decrease in the resonance frequency as more and more SWNTs are added on the surface. When the coated resonators are subject to vacuum (~6.5e-4 mbar), the Q-factor increases further due to desorption of physisorbed, chemisorbed, and trapped gas and solvent molecules in xv

the SWNTs. Correspondingly, the resonance frequency increases in vacuum because of desorption of mass (gas and solvent) molecules from its surface……………………....170

Figure 4.7: The Q-factor of the resonator coated with SWNTs increases when kept in a vacuum of ~6.5E-4 mbar over several hours. The increase follows a characteristic 1/x law indicating the desorption process of gases from the SWNTs on the surface of the resonator is probabilistic. When the vacuum is released and the resonator operated in air, some of the gases are readsorbed causing the resonator Q-factor to decrease………....171

Figure 4.8: Q-factor of the resonator as a function of the motional resistance of the resonator shows the expected 1/x dependence for both air and vacuum ambients as seen by the curve fits………………………………………………………………………....173

Figure 4.9: Schematic representation of the frame of reference, dimensions of the crystal and the electrode………………………………………………………………………..176

Figure 4.10: Variation of Q as a result of variation of energy in escaping flexural waves as ratio of diameter of electrodes to that of thickness of the AT-cut quartz plate. The periodicity shown in this figure can be disrupted if existence of face shear, extensional, and other vibrations modes of vibrations of the quartz plate are taken into account [209]…………………………………………………………………………………….182

Figure 4.11: (a) Simple schematic illustration of basic set up for Laser Doppler Vibrometry.(b) Detailed set up of laser Vibrometry…………………………………....186

Figure 4.12: Schematic illustration of the set up used for measuring out of plane flexural vibrations of QCM using Laser Doppler Vibrometry…………………………………..188

Figure 5.1: (a) Optical image of the microfabricated AT-cut Quartz Crystal Microbalance Array showing 3 by 3 electrode configurations with bond pads. (b) Zoomed in image of a single pixel. The thickness of the diaphragms is ~ 56.7 micron. SWNTs are deposited on one of the electrodes. AFM image of a representative nanotube on surface is as shown in (c). (d) Schematic illustration of the inverted MESA configuration quartz resonator used in this work…………………………………….....196

Figure 5.2: Schematic illustration of the valves and the chamber for the processes of “fill in” and “evacuation” as described in the text…………………………………………..198 xvi

Figure 5.3: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for bare quartz surface without any nanotubes. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question………………………………………………....203

Figure 5.4: Change in resonance frequency and quality factor plotted as function of molecular (or atomic) weight of the adsorbate. The dashed lines are fit to the data and show a characteristic ~MW0.5 relationship for change in resonance frequency and quality factor as a function of molecular weight (or atomic weight) of the adsorbate………....205

Figure 5.5: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for quartz coated with partially open ended isolated SWNTs. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question………………………………..216

Figure 5.6: Change in resonance frequency and quality factor plotted as function of molecular (or atomic) weight of the adsorbate for the QCM coated with partially open isolated SWNTs. The dashed lines are fit to the data and show a characteristic ~MW0.5 relationship for change in resonance frequency and quality factor as a function of molecular weight (or atomic weight) of the adsorbate………………………………....217

Figure 5.7: Scaling function for randomly rough surfaces. The solid line is the result of the exact solution of equations proposed by Daikhin and coworkers in their paper. The dashed and dotted lines, respectively, are long and short range asymptotes. As can be viewed from the graph, the equation describing the asymptotic behavior are excellent estimates of the exact solution except when l ≈ δ [240]…...…………………………...218

Figure 5.9: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for quartz coated with bundled close ended SWNTs. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question……………………………………………...225 xvii

Figure 5.10: Change in resonance frequency and quality factor plotted as function of molecular (or atomic) weight of the adsorbate for the QCM coated with close ended bundled SWNTs. The dashed lines are fit to the data and show a characteristic ~m0.5 relationship for change in resonance frequency and quality factor as a function of molecular weight (or atomic weight) of the adsorbate………………………………....226

Figure 5.11: Schematic illustration of (a) front view, and (b) side view of adsorption of gas molecules inside and outside the carbon nanotube. The red dots represent gas molecules while the black dots represent carbon atoms comprising a carbon nanotube………………………………………………………………………………...228

Figure 5.12: Schematic diagram of potential experienced by adsorbates inside and outside of the nanotube as a function of distance from the center of the nanotube. The nanotube was assumed to have a diameter of 0.7 nm…………………………………..229

Figure 5.13: Schematic diagram of longitudinal density of adsorbates ((a) Helium, (b) Nitrogen, (c) Argon, and (d) SF6) along the inside and outside surface of carbon nanotubes as a function of distance from the center of the nanotube. The nanotube was assumed to have a diameter of 0.7 nm………………………………………………….229

Figure 5.14: Data showing the experimental obtained change in resonance frequency, and the theoretically expected change in resonance frequency as given by using the barometric formula and by using a simple “filling” theory…………………………….231

Figure 6.1: Average electrode temperature increase for different membrane diameter and thickness for hydrolysis of 1M urea…………………………………………………….243

Figure 6.2: Calibration curve for first, third and fifth overtone modes of Y-cut quartz calorimeter. As can be seen from the graph, the temperature sensitivity of the device is linear at room………………………………………………………………………..….245

Figure 6.4: Non-specific adsorption of lysine on gold electrode of the QCM. Due to enhanced sensitivity of the QCM, we could resolve lysine solutions varying in concentration by 20 μM………………………………………………………………...252

Figure 6.5: Specific adsorption of protein Human Serum Albumin (HAS) on SAM of hexadecanethiol………………………………………………………………………....253

Figure 6.6: Schematic depicting the basic feedback topology of an oscillator……..….255 xviii

Figure 6.7: A generalized circuit diagram showing the principle of operation of oscillator circuits with feedback…………………………………………………………………..256

Figure 6.8: Schematic diagram of the oscillator circuit with feedback for maintaining constant amplitude of the signal from the quartz crystal. The buffer circuit provides the necessary current to drive the quartz crystal. The gain of the operational amplifier is adjusted using the signal coming off from the averaging circuit. The half wave rectifier feeds the averaging circuit. The frequency of the oscillator circuit is determined primarily by the quartz crystal [after 302]...... ………………………………………………..…..258

Figure 6.9: (a) Photograph of the set up used to monitor the resonance frequency of the oscillator circuit with dynamic feedback, (b) the circuit realized on an evaluation board…………………………………………………………………………………....260 xix

LIST OF TABLES

Table 1.1: A comparison of the theoretical mass sensitivity of proposed QCM with respect to the conventional QCM. The sensitivity improves by six orders of magnitude with miniaturization ...... ……………………………………………………………...13

Table 1.2: Comparison of various mass sensing techniques ………………………...... 39

Table 2.1: Process design parameters for optimizing the etch parameters, namely rms Surface Roughness and Etch rate………………………………………………………...82

Table 2.2: Optimum process variables for maximum etch rate of 0.536 µm/min, at an rms surface roughness of 1.97 nm……………………………………………………….90

Table 2.3: Optimum process conditions for the etching process………………………..91

Table 2.4: Variation of etch rate and rms surface roughness of etched samples, as a function of temperature of substrate holder, for both the gas chemistries……………...102

Table 4.1: Q-factor of the as fabricated quartz resonator and upon the deposition of SWNT’s in air and vacuum ambient. For all the three resonators a ~100% improvement in the Q-factor is observed for SWNT coated resonator in vacuum…………………....171

Table 5.1: Table depicting the value of δ for the four gases being investigated in the current experiments……………………………………………………………………..204

Table 5.2: Listing of calculated change in resonance frequency as given by the

− f 0 ωρη 2 Kanazawa equation ( Δf 0 = ). THe value of Rq in this expression is given as πRq 6 -2 -1 Rq = μq ρq = 8.83×10 kg m s . There is a small difference between the calculated and experimentally obtained values of resonance frequency which can be attributed to the non zero surface roughness of gold electrode and also to the physisorption of gases on gold at room temperature……………………………………………………………...... 210

Table 5.3: Listing of calculated change in quality factor and the experimentally observed change in quality factor for bare quartz surface with gold electrode…………………...210

Table 5.4: Listing of change in resonance frequency and quality factor obtained experimentally for partially open ended isolated SWNTs when compared with calcualted values of resonance frequency and quality factor. As can be seen, the values of quality factor obtained from experiment and from theory match within experimental errors. However, the change in resonance frequency due to surface roughness created on surface of QCM by presence of SWNTs is much less than experimentally obtained value of change in resonance frequency. This suggests that the remaining change in resonance xx frequency is due to physisorption on carbon nanotubes, which does not cause change in the quality factor of the QCM…………………………………………………………..218

Table 5.5: Listing of change in resonance frequency and quality factor obtained experimentally for close ended bundled SWNTs when compared with calcualted values of resonance frequency and quality factor. As can be seen, the values of quality factor obtained from experiment and from theory match within experimental errors. However, the change in resonance frequency due to surface roughness created on surface of QCM by presence of SWNTs is much less than experimentally obtained value of change in resonance frequency. This suggests that the remaining change in resonance frequency is due to physisorption on carbon nanotubes, which does not cause change in the quality factor of the QCM……………………………………………………………………....226

Table 5.6: Listing of values of radii where the potential is most attractive inside (r0int) and outside of the nanotube (r0ext). The values of rm, which is a measure of nearest neighbor distance for gas molecules for different gases are also listed………………...228

Table 5.7: Table listing of the density of adsorbates, at the points of maximum attractive potential at the inside and outside surface of SWNTs. For SF6, a very high value of adsorption is obtained inside the nanotube, which is probably wrong …………………………….………………...... 231 xxi

ACKNOWLEDGEMENTS

First and foremost I want to thank my parents. Without their love, values, virtues, and guidance my PhD would had not been possible. I also own my little sister a lot who has always been smarter than me and has been a source of inspiration and support.

I would also like to thank my colleagues, in the order in which I have come to know them, Steven Gross, Yuyan Zhang, Han Guen Yu, Prasoon Joshi, Nicholas Duarte, Saliya

Subasinghe, and the people at the other labs that I have worked at, Ping Kao at Dr.

Allara’s lab, Awnish Gupta, Jane, and Jian Wu at Dr. Eklund’s lab, Imme Arcibal and

Mike Santillo at Dr. Ewing’s lab, Bo Bai and Lisong Zhou at Dr. Jackson’s lab, and last but not the least, David Sarge and Fawn Houtz who have made life easier for graduate students in the clean room. Also, I would like to acknowledge the undergrad students I have worked with, Rakesh Reddy for developing the Labview program for data acquisition, Timo Mechler for devoting numerous hours towards designing and optimizing the automatic gain circuit using off the shelf components, Vincent Hood for those long hours in front of the etching machine running one sample after another, and

Jay Mathews for diligently and intelligently generating tons of data for protein adsorption on Self Assembled Monolayers of thiol molecules on the gold electrode of the QCM.

I would also like to thank Dr. Srinivas Tadigadapa for financial support along with Dr.

Peter Eklund, Dr. David Allara, for guiding me during my PhD research. I would also like to thank Dr. Milton Cole for the numerous wonderful and insightful discussions about the gas adsorption in carbon nanotubes. I would like to thank Dr. Andrew Ewing for allowing me to use his lab facilities for cell culture experiments, Dr. Tom Jackson for xxii teaching me semiconductor physics in a manner that no one else can in this world, and

Dr. Carlo Pantano for encouraging me during my etching work.

Finally, I would like to thank GOD for his blessings and providing me plenty of good luck, and a knack for serendipity which is very useful during a scientific pursuit. I pray for his continued blessings not only for me, but for whole of the world.

Chapter 1

INTRODUCTION

Measuring mass or weight has been central to human’s curiosity from the beginning

of time. Earliest mass measurement techniques involved use of gravity to balance two

weights at the ends of a stick which was suspended from its center. This method is

still widely used to measure mass. With the advent of time, more sophisticated and

indirect techniques have been used, for example, extension of a spring under the

influence of mass, etc. Such techniques allowed for additional accuracy, precision,

and resolution in the measurement of mass. With the advent of the modern age, man’s

hunger for more resolution, accuracy and precision have led to use of cyclotrons, etc.

for mass measurement. Use of resonators to measure mass has also given man the

ability to measure mass with unprecedented accuracy, precision and resolution.

Resonators based on bulk acoustic waves are one of the more versatile and rugged

methods of mass measurement available. But they suffer from resolution in terms of

the minimum mass that can be measured. However, miniaturization of bulk acoustic

wave (BAW) resonators can be used to create high sensitivity gravimetric sensors, allowing measurement of a few atoms or molecules in laboratory condition. In this thesis, the design, fabrication, and applications of a quartz BAW resonator based mass sensor commonly known as Quartz Crystal Microbalance (QCM) is presented.

An ultrasensitive micromachined miniaturized Quartz Crystal Microbalance (QCM) fabricated monolithically in an array format is presented. The chapter begins with a discussion on the fundamental concepts on resonance and resonators. This is followed 2

by a description of piezoelectric quartz crystals as resonators, in particular AT-cut

quartz crystals. Section 1.2 discusses the operation of the QCM, section 1.3 outlines

other mass sensing techniques based on resonators other than quartz crystals, various

applications of QCM showing its versatility (section 1.4), and comparison of QCM

with optical techniques for detection (1.5). The chapter ends with discussion on the

aims and motivation of this thesis (section 1.6).

1.1 Resonators and Resonance

Resonance occurs in physical systems due to motion of individual entities comprising the system or of the whole system itself around an equilibrium point. Such a motion is often termed by physicists as Simple Harmonic Motion (SHM). The motion of

particles or an ensemble of particles around the equilibrium point occurs due to the

presence of a restoring force, the magnitude of which is such that it becomes

progressively larger as the displacement of the particle from the equilibrium point

increases. This large restoring force then brings the particle or its ensemble back to its

equilibrium position, at which point the restoring force is zero but due to its

momentum, the particle or an ensemble of it continues to move past the equilibrium

point, at which point the restoring force develops in the directions opposite to the

motion of the particle (or its ensemble) forcing it back to equilibrium. This motion of

the body (comprising a single particle or an ensemble of them) continues indefinitely

in an ideal system with no damping losses, and is commonly referred to as the 3

“natural resonance”. However, in the real world, there are damping forces (for

example, friction, viscous drag, etc) which cause loss of energy from the system into

the environment. Hence, unless the lost energy is supplied to the system, the

oscillations or vibrations of the system around the equilibrium point ultimately die

down. This condition is known as “damped resonance”, and even though the

amplitude of oscillations dies down with time, their resonance frequency does not

change. If the amount of external compensating energy supplied to the system is

equal to the energy loss, the vibrations or oscillations are sustained indefinitely. In

case the vibrations or oscillations of the system are a result of external force causing

the system to resonate with the same frequency as that of the external force, then we

have what is called as “forced resonance”. In the case of forced resonance, there can

be damping or the damping can be absent. In the absence of damping, resonance

occurs when the frequency of the external force is the same as the natural frequency

of the system. When such a situation occurs, the external force always acts in the

same direction as the motion of the oscillating object, with the result that the

amplitude of the oscillation increases indefinitely. When there is a damping force

present, resonance occurs at a slightly different frequency and, though the amplitude does increase rapidly, the damping force prevents the increase from being infinite.

1.1.1 Piezoelectricity and Crystal Oscillators

When an alternating electric field is applied to the quartz crystal, it resonates at the

frequency of the applied field due to the phenomena of converse piezoelectric effect.

The direct piezoelectric effect is defined as the phenomena wherein an electric field is

generated in the crystal due to the applied mechanical strain. In the case of the

converse piezoelectric effect, as used in quartz oscillators, the alternating electric

field applied to the crystal results in generation of mechanical vibrations in the

crystal. The theory of piezoelectric effect and materials exhibiting it is rich in history

and detailed work exists on this subject, and is outside the scope of this chapter.

Reader is suggested to refer to the excellent books and review articles listed for a

comprehensive overview of the subject [1-3].

1.1.2 Quartz Crystal

Quartz is composed of two elements, silicon and oxygen (chemical formula: SiO2) and is one of the most widely available compounds on earth. In its crystalline form, it has trigonal-trapezohedral crystal symmetry resulting from its hexagonal prism structure with six cap faces at each end which are shown as in Figure 1.1. The prism faces are called as m-faces and the cap faces are designated as R- and r-faces. The R- faces are called as major rhomb faces and the r-faces are called as minor rhomb faces.

As depicted in Figure 1.1(a), there are three of each faces on the two ends of the quartz crystal. Crystalline quartz occurs in natural form but is expensive and difficult 5 to find. Hence quartz crystals are grown commercially in the laboratory and subjected to several processes such as annealing, and electrical sweeping to reduce the number of defects and impurities present in the grown quartz crystal. Figure 1.1 [4] also depicts various quartz crystal cuts with respect to the crystal orientation. Also depicted is the so called AT-cut, which has been used in this thesis. The principle or the z-axis in the quartz is the axis of three fold symmetry in quartz. This means that all the physical properties repeat each 120° as the crystal is rotated about the Z-axis.

R R r r s

m x m

m r x s r r R R

Flexure Mode Extensional Mode Face Shear Mode

Thickness Shear Fundamental Mode Mode Thickness Shear Third Overtone Thickness Shear

Figure 1.2: Different modes of vibrations of the quartz crystals [5]. . 7

(a)

Tinf

(b)

Figure 1.3: (a) Variation in resonance frequency of quartz resonator for different cuts. As can be seen from the figure, the minimum variation in frequency with temperature at ambient room temperature is exhibited by AT and GT cuts. (b)Variation of frequency (y-axis) of an AT-cut quartz crystal with respect to temperature (x-axis) as a function of different cut angles with respect to the AT-cut [5]. 8

Quartz crystal is piezoelectric, which means that applications of stress on the crystal

causes generation of an electric field. Due to non-linear nature of the Si-O bonds,

there is a net dipole moment in the quartz. Under the application of an electric field,

the opposite ends of the dipole tend to be pushed in opposite directions and the dipoles tend to rotate themselves to align in the direction of the field. The resulting

displacements results in a net strain (very small in magnitude). Hence, when an AC

field is applied across the thickness of a quartz crystal, the displacement of dipoles

also varies with the electric field resulting in the mechanical vibrations in the quartz crystal. The frequency of these vibrations is approximately equal to the frequency of the applied alternating field. There are different modes of oscillations of the quartz resonator that can be induced, which are depicted in Figure 1.2 [5]. Different cuts of

quartz crystal have different properties which can be used for different applications.

AT-cut of the quartz crystal, which is described in Figure 1.1, is obtained by shearing the quartz crystal at an angle of 35 º from the z-axis, and is one of the most widely used cuts of the quartz crystals for applications in which the resonating crystal acts as a reference frequency source. The main reason for the prolific use of AT-cut quartz crystal is their exceptional frequency stability, and high quality (Q-) factor. The material properties of single-crystal AT-cut quartz are extremely stable with time, temperature, and other environmental changes, as well as highly repeatable from one specimen to another. The acoustic loss or internal friction of quartz is very low, leading directly to one of the key properties of a quartz resonator, its extremely high

Q factor. The second key property of the AT-cut quartz resonator is its stability with

respect to temperature variation. Figure 1.3(a) [5] shows the variation in resonance 9

frequency with temperature for different cuts of quartz. The AT cut exhibit minimum

variation in resonance frequency as a function of temperature at room temperature.

Figure 1.3 (b) shows the variation in resonance frequency of AT-cut quartz angles as

a function of temperature. As can be seen from the figure, a relatively stable

frequency (under 10 ppm/ºC) can be generated over a wide range of temperature. The

temperature dependence of frequency of a quartz crystal can be expressed as the

following equation

Δf 0 2 3 = a()()()T − Tinf + b T − Tinf + c T − Tinf (1.1) f 0

where, Δf0 is the change in frequency due to change in temperature, f0 is the resonance

frequency, a, b, and c are the first, second and third order temperature coefficients of frequency, T is the ambient temperature and Tinf is the inflection temperature. Also

shown in Figure 1.3 is the inflection temperature of the quartz resonator, which is

around room temperature of 25ºC. For the temperature insensitive AT-cut quartz, the

first and second order temperature coefficients of frequency cancel each other,

resulting primarily in third order variation of resonance frequency with temperature.

This is the main reason for the temperature independent frequency characteristics

around the inflection point. The third essential characteristic of the quartz resonator is

related to the stability of its mechanical properties. Short and long term stabilities

manifested in frequency drifts of only a few parts per million per year are readily

available from commercial units. Precision crystal units manufactured under closely

controlled conditions are second only to atomic clocks in the frequency stability and

precision achieved. 10

Resonator Area

Top Electrode b

Bottom Electrode Figure 1.4: (a) A 3D schematic diagram of the micromachined quartz resonator, (b) Cross- sectional view of the resonator along the dashed line shown in (a). 1.2 Quartz Crystal Microbalance

AT-cut quartz crystal in a disc shape with overlapping metal electrodes on its two faces is commonly used as a quartz crystal microbalance (QCM). Figure 1.4 shows the schematic of a QCM. When an AC field of appropriate frequency is applied on the electrodes of the QCM, it resonates at its resonance frequency, which is given by

μ q ρ q f 0 = (1.2) 2tq

where, f0 is the resonance frequency of the resonating crystal, µq is the shear modulus

11 -1 -2 of the quartz crystal (2.947×10 g cm s ), ρq is the density of the quartz crystal

-3 (2.648 g cm ) and tq is the thickness of the quartz crystal blank. The resonance frequency of a QCM changes when the mass on one of its electrodes changes. In 11

1959, Sauerbrey derived a directly proportional relationship between the change in frequency and the change in attached mass[6] as

Δm Δf = −S (1.3) c A

where, A is the area of the overlapping electrodes of the QCM, Δf is the change in the

resonance frequency of the resonator with deposition of mass on one of its electrode,

Sc is the Sauerbrey constant and Δm is the change in the mass on top of the electrode of the QCM. The negative sign in equation (1.3) indicates that the resonance

frequency decreases as mass is added on the electrodes of the QCM. The Sauerbrey

equation can be derived as follows:

If we define mq to be the mass per unit area and Mq to be the total mass of the quartz

crystal, then we have

M m = q = t ρ (1.4) q A q q where the terms in the equation have already been defined. Now combining equation

1.2 and equation 1.4, we get

μq ρq f0 = (1.5) 2mq

The addition of mass per unit area on the top of the resonator (Δmq) causes a change in the resonance frequency of the oscillating crystal (Δfo). This implies that equation

(1.5) can be written as

μq ρq f0 + Δf0 = (1.6) 2(mq + Δmq ) 12

Substituting for f0 in equation (1.6) we get

μq ρq μq ρq Δf0 = − (1.7) 2(mq + Δmq ) 2mq or,

μq ρq (−Δmq ) Δf0 = (1.8) 2 Δmq 2mq (1+ ) mq

μq ρ q Substituting = f 0 in the above equation, we get 2mq

f 0 (−ΔM q ) Δf 0 = (1.9) ΔM q M q (1+ ) M q

For a thin deposit, wherein Δmq << mq, we get

f0 (−Δmq ) Δf0 = (1.10) mq or,

f 0 (−Δmq ) Δf 0 = (1.11) tq ρ q

Further substituting for tq from equation 1.2 in the above equation, we get

2 2 f 0 (−Δmq ) Δf 0 = (1.12) μq ρ q or, 13

2 2 f 0 Δm Δm Δf 0 = − = −Sc (1.13) μq ρ q A A

where Δm is total mass deposited on top of the electrodes of the QCM. Equation

(1.13) is called as the Sauerbrey equation.

1.2.1 Why miniaturize QCMs

Plugging in the material constants for quartz in equation 1.13, we get

2 f 2 (−Δm) f 2 f 2 Δf = 0 = 2.264×10−6 0 (−Δm) = S 0 (−Δm) (1.14) 0 A*883383 A c A

-6 -1 2 Here, Sc is called the Sauerbrey constant and is equal to 2.264x10 g cm s. The

Sauerbrey constant depends only on the material properties of quartz. According to

equation 1.14, the change in frequency of the resonator for a unit mass deposited on

its electrode is directly proportional to the square of resonance frequency of the QCM

and inversely proportional to the electroded area (A) of the QCM. Hence,

theoretically it is possible to increase the change in resonance frequency for unit mass

deposition by increasing the resonance frequency of the QCM and by decreasing its

electroded area. According to equation (1.2), the resonance frequency of the QCM is

inversely proportional to the thickness of the quartz crystal. Hence in order to achieve

high mass sensitivities, it is desirable that the thickness of the quartz crystal be

Table 1.1: A comparison of the theoretical mass sensitivity of proposed QCM with respect to the conventional QCM. The sensitivity improves by six orders of magnitude with miniaturization.

Thickness Resonance Mass A (cm2) (μm) Frequency (MHz) Sensitivity Proposed QCM 16.68 100 10-4 (100x100 μm) 4 fg/Hz Conventional QCM 333.6 5 1 (1x1 cm) 17 ng/Hz

14 reduced to a minimum along with a reduction in the electroded area of the resonator.

Commercially available QCM’s have a typical thickness of 300 µm and a diameter of

10mm. Table 1.1 indicates the theoretical mass sensitivities that can be achieved by reduction in thickness and electroded area of the QCM, and compares it with the mass sensitivity values for the conventional commercial QCM. As can be seen from the table, the theoretical mass sensitivity improves by at least 6 orders of magnitude with miniaturization.

1.2.2 Radial dependence of mass sensitivity of QCM

According to the Sauerbrey equation the mass sensitivity per unit area, scales as square of the resonance frequency of the QCM. Table 1.1 depicts that the absolute mass sensitivity of the QCM can be increased by six orders of magnitude using miniaturization. However, the increase in mass sensitivity per unit area is only 20 times 20 or 400 as per Table 1.1. Hence one can argue that if we can detect a femtogram using the miniaturized QCM, then it should be possible to detect 400 femtograms using the commercial QCM. However, such is not the case. The problem lies in the fact that the mass sensitivity of the QCM depends on the radial distance of the deposited mass from the centre of the electrode. This means that for 400 fg to be detected accurately, the phenomena responsible for 400 fg of mass change (for example, desorption of gases, deposition of metal film, or self assembled monolayer) should occur over a large percentage of area of the electrode, so that the effect of radial mass sensitivity averages and there is little difference from one reading of mass change to another. The point can be illustrated using an example. A mass change of

400 fg at the center of the electrode would yield a frequency change which is twice 15 the frequency change when the same event occurs near the periphery of the electrode.

Considering a practical situation, for the study of release of vesicles from a population of neurons grown on the electrode of the QCM, the commercial sized

QCM would function well. But if we want to study the release of vesicles at a single synaptic junction between neurons, we need QCM which are miniaturized and have an absolute mass sensitivity which is higher than that of commercial QCM to detect the event of release of vesicles at the single synaptic junction between neurons.

In order to derive this radial dependence of mass sensitivity, the wave equation for a quartz crystal can be written as [7]

∂2u ∂u = v2∇2u − b + F(t) (1.15) ∂t 2 ∂t where u is the particle displacement in the quartz plate, t is the time, v is the wave velocity in quartz, b is the damping coefficient, and F(t) is the forcing function (for example, the electric field). Assuming no anisotropy, zero displacement at circular electrode boundaries, no loss and forcing terms, we get

∂2u = v2∇2u (1.16) ∂t 2

Solving the above equation by separation of variable for a circular electrode, we obtain

⎛ r ⎞ ⎛ nπz ⎞ u(r, z, t) = ∑ An J m ⎜ χ mk ⎟ sin⎜ ⎟ sin()ωnmk t (1.17) ⎝ R ⎠ ⎝ L ⎠

th where Jm is a Bessel Function of the first kind of order m, χmk is the k root of Jm, R is the electrode radius, L is the plate thickness, ω is the resonant frequency, and An is a 16

1.2

Bessel Function 1

Gaussian with a=2 0.8

0.6

0.4

0.2

0 -1.5 -1 -0.5 0 0.5 1 1.5

-0.2

at depends on the velocity profile at t=0. The variables r and z are the radial and vertical positions measured from the center of the plate. By oscillating the crystal in the lowest frequency mode, only the first term of the solution is needed

⎛ 2.41r ⎞ ⎛ πz ⎞ u(r, z,t) = AJ ⎜ ⎟sin⎜ ⎟sin()ωt (1.18) 0 ⎝ R ⎠ ⎝ L ⎠

Considering only the motion on the surface of the crystal, then z = L/2 and the above equation becomes

⎛ 2.41r ⎞ u(r,l / 2,t) = AJ ⎜ ⎟sin()ωt (1.19) 0 ⎝ R ⎠

The surface amplitude as represented by the Bessel function in the above equation is depicted in the Figure 1.5. In the figure, the boundary conditions are assumed such 17 that there is no vibration outside of the edges of the electrodes. In reality, there is always some amplitude outside away from the edges of the electrode. A Gaussian amplitude distribution, also shown in Figure 1.5, includes motion near the electrode edge and has been found experimentally for oscillation of crystals in air. The form of the Gaussian distribution solution is

2 2 A(r) = Amax exp(− ar R ) (1.19) where a is a dimensionless constant that determines the broadness of the peak. The

Gaussian distribution function has been found experimentally using different techniques, such as using a 75 µm thick tungsten wire probe [7], Scanning Electron

Microscope [8-12], x-ray topography [13], neutron diffraction [14], holography [15], and interferometry techniques [16, 17], etc.

1.2.3 Quality (Q-) factor of a QCM

As mentioned in previous sections, with increasing resonance frequency of a QCM, the change in frequency per unit mass deposited on its electrode increases quadratically. Hence it is desirable to operate the crystal at higher resonance frequency for better mass sensitivity. Central to this idea of increased mass sensitivity with increasing resonance frequency is the concept of frequency stability or frequency noise of the resonator, which in turn is determined by a dimensionless quantity known as the Quality Factor (Q-factor) of the resonator. Simply stating, the quality factor of a resonator is the ratio of energy input into the resonator, divided by energy lost in the resonator per oscillation cycle. However, it is useful to define the

Q-factor in terms of the shape of the resonance curve. The signal from the quartz 18

1 φ=0° φ=45° φ=90° φ=135° φ=180° φ=225° 0.5 φ=270° φ=315°

ψ 0

-0.5

-1 4.98E+7 4.985E+7 4.99E+7 4.995E+7 5E+7 5.005E+7 5.01E+7 5.015E+7 5.02E+7 Frequency (Hz)

resonator looks like a Lorentzian with some arbitrary phase shift and may be written

as [18]

2 ( f f0 )+ (1− ( f f0 ) )Qi i()ωt+φ s S(t) = A0 e (1.20) 2 2 2 2 ()f f0 + ()1− ()f f0 Q

where A0 is a dimensionless constant, f is the frequency, f0 is the resonance

frequency, Q is the quality factor, and φs is the phase angle of the resonance signal

with respect to the reference (which can be the input signal in this case). If the phase

difference between the input and the output signal is small, then the quadrature

component of the output is expected to have less crosstalk (noise) since the signal 19 amplitude depends on sine of the phase angle between the input and the output.

Hence the quadrature component of the signal is used for measurement purposes. If we define the phase angle (φs) to be equal to φ = π/2 - φs, then the quadrature part of the resonance (ψ) can be written as

2 ( f f0 )cosφ + (1− ( f f0 ) )Qsinφ ψ ( f ) = A0 (1.21) 2 2 2 2 ()f f0 + ()1− ()f f0 Q

The function is plotted in Figure 1.6 for different values of φ . If φ is taken to be zero, then for sufficiently high Q (>100), the function in above equation will appear as a symmetric peak with its maximum at the centre frequency, i.e,

( f f0 ) ψ 0 ( f ) = A0 (1.22) 2 2 2 2 ()f f0 + ()1− ()f f0 Q

Let us define new parameters, ΔfFWHM, which is the full width at half maximum of the quadrature component of signal from the quartz. The maximum amplitude of the

resonance curve occurs near f0 and not exactly at f0. Expressing f/f0 as g and ψ 0 A0 as

ψˆ 0 , then we can rewrite the above equation as

g ψˆ0 = 2 (1.23) g 2 + ()1− g 2 Q2 and hence,

2 2 2 2 3 2 dψˆ 0 g + ()1− g Q − g(2g + (− 4g + 4g)Q ) = . (1.24) 2 2 dg ()g 2 + ()1− g 2 Q 2 20

dψˆ In order to find the maximum of ψ A or ψˆ , we set 0 = 0 , which yields 0 0 0 dg

1+ (2 +1 Q 2 )g 2 − 3g 4 = 0. (1.25)

For large Q, this equation is nearly satisfied by g=1, which is equivalent to saying f = f0. One can then approximate with

ψ max ≅ψ = A0 (1.26) f = f0

The half maximum points will hence occur at ψ 0 = A0 / 2 , and hence we can write the equation for frequencies at these points

( f f0 ) A0 A0 = (1.27) 2 2 2 2 2 ()f f0 + ()1− ()f f0 Q or, expressing the above equation in terms of parameter g,

2 g 2 + (1− g 2 ) Q2 = 2g (1.28) or,

1/ 2 2g − g 2 Q = (1.29) 1− g 2

2 Multiplying the numerator and denominator by f0 , we get

3 2 2 1/ 2 2 ff 0 − f f 0 Q = (1.30) 2 2 f 0 − f 21

If the peak is nearly symmetric (which is true in the current case), then the

frequencies at the half maximum points can be approximated as f = f0 ± fFWHM / 2 .

Substituting this in the above equation, we get

2 1/ 2 ⎛ fFWHM ⎞ 3 ⎛ fFWHM ⎞ 2 2⎜ f0 ± ⎟ f0 − ⎜ f0 ± ⎟ f0 ⎝ 2 ⎠ ⎝ 2 ⎠ Q = (1.31) 2 2 ⎛ fFWHM ⎞ f0 − ⎜ f0 ± ⎟ ⎝ 2 ⎠

Simplifying, we get

2 1/ 2 4 ⎛ fFWHM ⎞ 2 f0 − ⎜ ⎟ f0 ⎝ 2 ⎠ Q = . (1.32) 2 ⎛ f FWHM ⎞ m fFWHM f0 − ⎜ ⎟ ⎝ 2 ⎠

Since, f ≅ f0 >> fFWHM if Q>> 1, we can discard the higher order terms in fFWHM to obtain

4 1/ 2 f0 f Q = = 0 . (1.33) fFWHM f0 fFWHM

Hence, the quality factor (Q) can be expressed as a ratio of the resonance frequency and the full width at half maximum of the quadrature component of resonance spectrum of quartz.

1.2.4 Noise analysis of AT-cut quartz resonator

The instantaneous output voltage (V(t)) provided by the oscillator can usually be modeled, as per Pardo et al. [19] as 22

V (t) = A0 sin(2πf 0t + φ(t)) (1.34)

where A0 is the nominal amplitude, f0 is the nominal frequency, and φ(t) the instantaneous phase fluctuations around the nominal value or phase noise. The instantaneous frequency can be expressed as

f (t) = f 0 + Δf (t) (1.35) where Δf(t) represents the instantaneous frequency fluctuation, or frequency noise, of the signal. The instantaneous relative frequency variation, y(t) can be defined as

Δf (t) y(t) = . (1.36) f 0

This variable is very useful to compare the performances of oscillators with different nominal frequencies. The frequency stability can be characterized in the frequency domain or the time domain. The time domain characterization is usually used because it can be used to determine the stability of oscillator in a given time interval (τ), which is the usually the quantity of interest during QCM measurements. The commercial frequency measurement instruments, such as frequency counter, do not provide instantaneous value of the frequency, but provide an estimate of the average calculated on a time interval (τ), starting from the instant tk,

1 tk +τ yk (t) = y(t)dt . (1.37) τ ∫tk

The frequency stability is defined as a measure of variation of yk over different intervals of time. Using the two-sample variance as proposed in the pioneering work of Allan et al. [20], the variance is defined as 23

1 2 σ 2 (τ ) = (y − y ) . (1.38) y 2 k +1 k

The oscillator detection limit, i.e. the smallest frequency deviation that can be detected in the presence of noise is equal to

Δf (τ ) = σ y (τ ) f 0 . (1.39)

The resolution can be obtained by the relationship between the detection limit and the sensitivity, which is given by

Δf (τ ) resolution = 2 (1.40) Sc f0

where Sc is the Sauerbrey constant and has been defined as in equation 1.13. Vig and

Walls [21, 22] have proposed an empirical relationship between the smallest level of noise generated by an oscillator and the quality factor of the resonator, Q, which is given as

1×10−7 σ (τ ) = . (1.41) y min Q

Thus the minimum frequency noise attainable increases when the quality factor Q of the resonator decreases. Herein lies the importance for maintaining the high Q of the resonator. The higher the Q, the lower the noise and hence greater is the frequency resolution or the mass sensitivity. At the same time, these authors indicate that the maximum quality factor achievable for quartz manufactured in the best condition is inversely proportional to the frequency. For an AT cut resonator, the product Qmax time f0 is 24

13 Qmax f 0 = 1.6×10 Hz . (1.42)

Therefore the minimum noise, assuming a constant maximum achievable Q factor, increases with frequency according to the expression

−21 σ y (τ ) min = (6×10 )f 0 . (1.43)

In this way, the oscillator detection limit will be

−21 2 Δf min = (6×10 )f 0 (1.44) and the expression for resolution limit will be

Δfmin 2 resolution = 2 = 2.7 fg / cm . (1.45) Sc f0

Therefore, the resolution limit of a microbalance oscillator using an AT cut resonator does not depend upon frequency, it value being about 2.7 fg/cm2. One more conclusion that can be drawn from the above equation 1.45 is that by reducing the area of the resonator, much higher fundamental limits of mass resolution can be achieved. Coming back to the discussion on frequency stability, if we increase the resonance frequency of the crystal by a factor of 3, then the mass sensitivity will improve quadratically by a factor of 9. However, this is contingent upon the fact that the frequency stability (which determines the frequency resolution) is essentially constant. In case the frequency stability degrades by a factor of 4.5 along with increase in frequency by a factor of 3, then the mass sensitivity will only increase by a factor of 2 rather than 9. Hence, while increasing the mass sensitivity of the devices by miniaturization, it is imperative that the Q factor of the resonator is maintained at a 25 reasonable high level. In this section, quantitative equations expressing frequency stability as a function of Q factor have been developed.

1.3 Review of Resonator based mass sensors

As already discussed, the QCM operates in thickness shear mode, with the resonance frequency of the oscillations changing with the deposition of mass on the electrodes.

Mass sensing can be achieved using resonators operating in several other modes. This section provides a review and basic concepts of some of these resonators used for mass sensing. Figure 1.7 schematically shows the various types of resonant mass sensors that can be used.

MICROSCALE cantilevers, comb drives, thin rod. FLEXURAL DEVICES NANOSCALE carbon nanotubes

RESONANTORS as MASS SENSORS

SURFACE WAVE SAW, flexural

CRYSTAL DEVICES BULK WAVE quartz crystal microbalance, FBAR

Figure 1.7: Overview of the different kinds of resonators that can be used as mass sensors. 26

1.3.1 Cantilever based mass sensors

Micromachined cantilevers are very useful and versatile as gravimetric sensors for applications in (bio) chemical sensing. The natural resonance frequency of the cantilever changes when the mass on them changes. Very sensitive mass detection, in the sub femtogram range has been achieved by use of these mass sensors. The cantilever resonances can be induced in multiple ways. One way, for example, is electrostatic actuation in which the cantilever acts as one of the electrodes. Periodic voltage applied between the cantilever and the electrode on the substrate causes the cantilever to resonate [23, 24]. Resonances can also be induced by placing the cantilevers on PZT bocks which in turn are driven by external frequency generators

[25]. Detection of the resonance frequency and its changes thereof can be achieved similarly in multiple ways. The most popular way is to use optical detection techniques in which a laser is focused on a gold spot on top of the cantilever [26]. By measuring the displacement of this light dot on top gold spot, the resonance frequency

(b) (a)

Figure 1.8: (a) Schematic of optical readout technique commonly used in cantilevers, (b) SEM image of an array of microfabricated cantilevers [31]. 27 of the cantilever can be measured and monitored. However, the optical system is expensive and bulky. Another detection method is to integrate or attach a stress sensitive resistor on the surface of the resonator, so the deflection of the cantilever is monitored by measuring the resistance change [27-29]. This method not only complicates the fabrication process, but also might affect the cantilever mechanical performance. Recently, a new method has been devised to monitor the resonance frequency of the cantilever, by measuring the third harmonic of the actuating current

[30]. Figure 1.8 [31] shows the typical set up for resonant cantilever based mass sensors.

1.3.2 SAW based mass sensors

Surface acoustic waves (SAW) are generated on the surface of a piezoelectric substrate using an interdigitated electrode [32]. The electrodes are planar defined on the surface of the substrate using standard lithographic methods. Unlike bulk wave devices, the resonance frequency of the SAW devices is determined not by the thickness of the substrate, but by the spacing of the interdigitated electrodes, as follows

v f = (1.46) λ where, v is the velocity of propagation of SAW waves, λ is the periodicity of the interdigitated electrodes. Changes in surface mass result in changes in wave propagation velocity, given by

Δv = −cm f 0 ρ s (1.47) v0 28

-6 2 where cm is a substrate dependent constant (1.29x10 cm s/g for ST-cut quartz), ρs is the density of the surface mass deposited and f0 is the resonance frequency. The fractional changes in propagation velocity are equivalent to fractional changes in the

Δv Δf resonance frequency, i.e. = , and hence v0 f0

2 Δf = −cm f 0 ρ s (1.48) where Δf is the change in resonance frequency. There are other mechanisms, besides mass loading, that can trigger a response from the sensor in terms of change in the resonance frequency. These events include changes in the viscoelastic properties of the material on the surface of the resonator, and modulation of electrical conductivity of mass on the surface of the resonator.

The SAW device typically also has a reflector array along with interdigitated

Reflection Input Output Reflection Grating Transducer Transducer Grating

Propagating Wave

PIEZOELECTRIC SUBSTRATE

Figure 1.9: Typical electrode configuration of a Surface Acoustic Wave Resonator (SAW). 29 electrodes [33], as shown in Figure 1.9. The electrodes are positioned in a resonant cavity formed by two distributed SAW reflector arrays patterned on the substrate.

These reflector arrays consist of half-wavelength wide meal strips or grooves; when the surface wave in incident on these periodic structures, the small amount of wave energy reflected from each discontinuity adds constructively to give nearly complete reflection. The high Q and low insertion loss that results allows for high frequency stability at relatively high frequencies (100 MHz) thereby allowing lower mass resolution and hence detection limits.

SAW devices have been fabricated on silicon, using piezoelectric ZnO and AlN films

[34-37]. Alternatively, a piezoelectric substrate such as GaAs can be used, thus alleviating the need for the piezoelectric film. One advantage of fabricating these

(a) Membrane Outline

Transducer (b)

ZnO SiN Si

Figure 1.10: Schematic illustration of a flexural plate wave (FPW) sensor, employing a piezoelectric ZnO film and interdigitated electrodes to excite flexural waves in a thin membrane. 30 devices on semiconductor substrates is that this enables them to be integrated with electronic circuitry to operate the device as a sensor.

1.3.3 Flexural plane wave sensor

The concept of flexural wave devices was first shown by Wenzel and White in 1988

[38, 39]. The device consists of a thin multilayer membrane, of which one layer is a piezoelectric material such as ZnO. Flexural waves are excited and detected using interdigitated electrodes, as shown in Figure 1.10. However, the wave velocity in the membrane is much less than in a solid substrate, and the operating frequency is much lower (for a given transducer periodicity) than in the surface acoustic wave (SAW) device. Also, since the device is fabricated on a semiconductor substrate, it can be integrated with on chip electronics. The principle of operation of the device is rather simple. The velocity of propagation of the flexural plane wave changes with deposition of mass on the surface, and is given by

Δv ρ = − s (1.49) v0 2M

where, v0 is the velocity of propagation of SAW waves, Δv is the change in the velocity due to deposited mass, ρs is the density of the mass deposited on the surface of the resonator, and M is the mass per unit area of the flexural plane wave device membrane. The confinement of acoustic energy in the thin membrane results in a very high mass sensitivity. The backside of the suspended membrane can be used for mass detection purposes, thus isolating the electronics from the analyte being detected. 31

jωt (a) I0e MEMBRANE OUTLINE

MEANDER LINE TRANSDUCER

MAGNETIC FIELD (b)

SiN Silicon

Force Force

(c)

Force Force

Figure 1.11: Schematic diagram of (a) Electrode Layout, (b) Cross Sectional View, (c) Cross Sectional view in operation, for a magnetically actuated flexural plane wave sensor.

The flexural modes in the thin membrane can be also induced magnetically. For example, a FPW device being investigated at Sandia national labs, a thin insulating

Silicon Nitride (SiN) film is suspended in a crystalline silicon frame. A metal meander line electrode is patterned on the surface of SiN as shown in Figure 1.11. 32

Alternating current flowing in the transducer interacts with a static in plane magnetic field to generate time varying Lorentz force which deform the membrane and exciting in into a resonant mode. To efficiently excite the mode, the current lines of the transducer must be positioned along the lines of maximum amplitude. This requires a critical alignment between the top electrodes and the bottom etch features. The device exhibits a high Q of 8000 in vacuum and 1000 in air. The magnetic excitation requires an externally applied magnetic field, but eliminates the need for a piezoelectric layer which frequently contains elements such as lead and zinc that are not compatible with IC fabrication techniques.

1.3.4 Thin Rod sensors

Several studies have been done on the applicability of thin rod resonators for mass sensing in (bio) chemical applications [40-42]. For example, Veins et al. [40] have excited and detected acoustic waves in 25 µm diameter metallic fibers and used these

FLEXURAL ACOUSTIC WAVE

FIXED END WITH THIN GOLD WIRE FIXED END WITH ABSORBER (21 μm) ABSORBER

GLASS HORN

PIEZOELECTRIC TRANSDUCER

Figure 1.12: Schematic illustration of the thin rod sensors. Mechanical resonance is induced in the thin fiber using piezoelectric transducer through glass horns. 33 fibers as gravimetric gas and vapor sensors. The rods in the form of thin fibers are made of Cu and Au and are coated with chemically sensitive film. Waves are excited in the fiber using a 2 MHz PZT compressional wave transducer, with energy coupled into and out of the fiber using hollow glass horns (Figure 1.12). Either extensional or flexural waves can be excited in the fiber, depending upon the orientation of horn with respect to the fiber. The principle of operation of the sensor is simple. The resonance frequency changes if there is a mass deposited on the resonating fiber. The relationship is given by

Δv ρ = − s (1.50) v0 Tρ1a

where, v0 is the velocity of propagation of waves in the fiber, Δv is the change in the velocity due to deposited mass, ρs is the density of the mass deposited on the surface of the fiber, T = 1 for extensional waves and 2 for flexural waves and ρ1 and a are the density and diameter of the fiber.

By confining the acoustic energy in a waveguide of extremely small cross sectional area, the thin rod sensor is extremely sensitive to surface mass perturbations, and mass sensitivities of 95 cm2/gram or an absolute mass sensitivity of 168 fg (for a 25 micron wire) have been achieved. Moreover, these high sensitivities are achieved at low operating frequencies, thereby allowing integration with electronics easier.

However, these devices are inherently non-planar and achieving consistency and reliability in coating the circular fiber resonator with chemical selective layer is relatively difficult.

(e)

1.3.5 FBAR Mass Sensor

Film bulk acoustic resonator (FBAR) mass sensors operate on a similar principle as a

QCM. Their resonance frequency changes when a mass is deposited on the surface of

the resonator. These are high frequency devices, with thickness and dimensions

smaller than QCM, and its fabrication process is compatible with current Integrated 35

(a)

(b)

Figure 1.14: (a) Schematic view of a resonant Piezo layer, (b) Frequency shift vs. mass load for Piezo layers with different thickness [46].

Circuit (IC) batch fabrication processes. FBAR sensors essentially consist of a thin

piezoelectric layer sandwiched between two electrodes, just like in a QCM. Bulk

longitudinal standing waves are generated in the piezoelectric layer when an AC field

in applied on the electrodes. Recently, Kim et al. [43] have developed a high

frequency (a few GHz) FBAR sensor with Aluminum electrodes sandwiching a ZnO

layer, for sensitivity in the picogram range which is shown pictorially in Figure 1.13

[43]. Lakin et al. have demonstrated a similar FBAR based on AlN piezoelectric layer 36 rather than a ZnO layer. High Q factors of 68000 were obtained at high resonance frequencies of 1.6 GHz [44].

1.3.6 Thin film PZT based sensors

In this technique, PZT based screen printable paste are used to define thin film resonators on the surface of alumina substrates [45, 46]. Figure 1.14 [46] shows the typical configuration of such a mass sensor. These sensors are called Resonant Piezo

Layers (RPL) and offer an easy but effective way to realize mass sensors. Similar to a

QCM, RPLs also operate in thickness shear mode when an alternating field is applied on its electrodes. These sensors are strictly planar, require no clamping or shaping of the substrate, can be integrated with electronics on the same substrate allowing compactness and mechanical reliability and can be realized in an array format at a relatively low cost. However, the mass sensitivity obtained is a modest one ng/Hz and also the scaling of the mass sensors is limited by the resolution of the screen printing method used for depositing the PZT films. Also, due to poor control over the quality of the PZT films, the obtained Q-factor are relatively poor (~200-500).

1.3.7 Carbon nanotubes based mass sensors

From the discussion until now, it is clear that for enhanced sensor performance and for pushing the limits of mass detection, resonators should be made as small as possible. Traditional methods of miniaturizing resonators are reaching their scaling limits, and it is not possible to further scale down these resonators without introducing significant cost and reliability issues. However, carbon nanotubes are inherently nanoscale materials, with a typical diameter of 1-2 nm and lengths of 1-10

µm. Hence, carbon nanotubes onfigured as resonators are expected to display 37

excellent mass sensing properties. Single walled or double walled carbon nanotubes

configured as cantilevers (clamped) or bridge (clamped-clamped) resonators are

expected to exhibit flexural resonance frequencies in the range of 10 GHz-1.5 THz,

depending on the nanotube dimension and length [47-50]. This frequency is much

higher than the highest attainable frequencies for existing nanomechanical resonators.

It is expected that the combination of the small mass of carbon nanotube resonators

with high resonance frequencies, a mass sensitivity of 10-21 grams is expected, thus

(a)

(b)

allowing single molecule detection. For carbon nanotube based sensors, it has been

observed that for masses larger than 10-20 attograms, the relationship between

frequency and mass is logarithmically linear. Figure 1.15 [47] shows the schematic

diagram of a cantilevered and bridge resonator based mass sensor and the relationship

between attached mass and resonance frequency of the cantilevered carbon nanotube

oscillator.

1.3.8 Comb Drive Resonator

Comb drive resonator can be used for mass sensing [51, 52]. Figure 1.16 shows a

fabricated comb drive actuator. The shown comb drive actuator consists of a

polysilicon mass suspended with polysilicon springs that oscillate laterally (in-plane)

above the substrate surface. This device uses electrostatic forces between interleaved

Figure 1.16: The comb drive resonator uses electrostatic forces between interleaved combs to excite and detect a polysilicon mass suspended by polysilicon springs (from http://www.ee.ucla.edu/~wu/ee250b/Electrostatic%20Actuators-2.pdf). 39 combs to drive the suspended mass at its resonance frequency. A second set of combs is used to sense motion of the suspended mass based on changes in the capacitance.

The comb drive actuators operate at moderate frequencies (~ 5 kHz). They suffer from high losses due to air damping and exhibit low Q factors. Also, operation in liquid environments cannot be achieved due to high viscous losses, and the deposition of the mass onto the comb structure itself can cause false readings due to change in capacitance.

1.3.9 Comparison with QCM

The QCM sensor exhibits most of the desired characteristics that are required in a typical mass sensor. These include, frequency stability, insensitivity to temperature, specificity by functionalization, high reliability, ruggedness, integration with drive and sensing electronics, ability to work in highly viscous and corrosive environments,

Table 1.2: Comparison of various mass sensing techniques.

Typical Mass Q-value Temperature Ability to be Device Frequency Sensitivity IC compatibility Ruggedness Packaging in air Stability Functionalized (MHz) (cm2/g) 9 FBAR 1000 10 250 Medium Medium High High High

9 SAW 100 10 10000 Medium High High High High

FPW 2.6 109 1000 Poor Poor Medium High Medium (Piezo) FPW 0.5 109 1000 Poor Poor Medium High Medium (Magnetic) -18 Cantilever 300 10 g 25 High Medium Poor High Medium Beam (absolute) Comb 0.005 109 1 High Poor Poor High Poor Drive -21 Carbon 106 10 g NA Poor Medium Medium High Medium Nanotube (absolute) Thin Film 3 108 50 Poor Poor Medium Medium Medium Piezo 10 Thin Rod 5 10 NA Poor Poor Poor Poor Medium

9 QCM 5 10 100,000 Medium High High High High

40 and most importantly low cost. Table 1.2 gives a comparison of different sensing techniques compared in this section.

1.4 Applications of QCM

Commercial QCMs are used in such large number of applications that a comprehensive review is beyond the scope of this introduction. Hence, in this section, attempt has been made to cover some of the applications to give the reader an idea about the versatility of the sensor. The biggest problem with use of a QCM as a sensor is its non-specific nature. It can only measure mass changes, it cannot measure the nature (or rather source) of the mass change. For example, it will give a frequency signal for a specific change in mass on its surface, irrespective of whether the mass change is because of the analyte in question or some other molecule that is present but not intended to be sensed. Hence, the greatest challenge is to make sure that only the analyte being sensed expresses as a Figure 1.17: The quartz crystal microbalance is essentially a non-specific platform. By use of different sensing functionalization layers, the QCM can be used for a large number of applications, few of which are depicted schematically in this figure. 41 42 change in frequency, while other substance in the test sample are not able to cause a change in frequency. There have been numerous methods employed to achieve the same. Here is a discussion about some of the applications of QCM and the functionalization schemes used that enable use of QCM for that particular application, with an overview of the discussed techniques and applications depicted schematically in Figure 1.17.

1.4.1 QCM as a immunosensor

The use of antibodies to coat the surface of the QCM enables it to function as an immunosensor. The antibody coating renders the QCM surface bioselective. The first use of QCM as an immunosensor was given by Shons et al. [53], wherein he detected

BSA (Bovine Serum Albumin) antibodies by coating the resonator with nyebar C and

BSA. Adsorption of antibodies is a method widely used for detection of various analytes [54-57], including HIV antibodies [58, 59]. Protein A is one of the most widely used pre-coatings used to aid antibody immobilization and has been used in the detection of pesticides [60-62], bacteria [63-67], viruses [68, 69], and various other analytes [70-72]. Protein G is another protein that has been used for antibody immobilization [69]. Other methods to immobilize antibodies on the surface of the resonator include silanising the surface using γ-aminopropyltriethoxysilane activated with glutaraldehyde [73-76], polymers such as polyethyleneimine activated with glutaraldehyde [60, 64, 65, 77], copolymers of HEMA-MMA [78], electropolymerised films [79], Langmuir Blodgett films [80], self assembled monolayers of thiols and sulfides [81-86], etc,.

1.4.2 DNA Biosensors

Fawcett et al. [87] were the first to demonstrate QCM for studying DNA by detecting the mass changes in a DNA crystal after hybridization. Ito et al. [88] have used QCM to study specific solid phase DNA hybridization reactions. Aslanoglu et al.

[89]investigated the binding of metal complex onto DNA immobilized on the QCM surface. Caruso et al. [90, 91] have showed the suitability of QCM for in situ detection of hybridization of a complementary 30 unit DNA oligonucleotide. These studies have been further complemented by studies from Fawcett et al. [92] and Storri et al. [83, 84] showing further promise of QCM as a diagnostic tool for DNA studies.

1.4.3 Drug Analysis

QCM because of high sensitivity can detect drug components present in very small quantities of the sample. This is accomplished by coating the crystal with specific adsorbents. Nie et al. [93] determined quinine in some pharmaceutical preparations using a ring coated QCM. The sensor can also be used for detection of drugs of abuse.

For example, Attili and Suleiman [69] were able to detect cocaine using the benzoylcyanine antibody. The same authors were able to detect cortisol in another study [94]. Atropine was assayed by Wei et al. [95] in very small concentrations of

0.05-32 nM. Reviews on applications to other compounds (for example, vitamins, etc) were published by Walton et al. [96].

1.4.4 Vapor Phase Chemical Sensor

The QCM was first developed to create chemical sensors for detection of species in the vapor phase. Vapor phase sensors utilize polymers as an active binding phase for 44 vapor phase molecules. For example, in the case of humidity sensor, poly(D,L-

Lactide) and poly(lactide-co-glycolide) can be used [97]. For application of QCM as odor sensors, polypyrrole films on the QCM surface acts as the vapor species binding element [98].

1.4.5 Protein Adsorption

Understanding protein adsorption at the solid liquid interface is critical for investigation of crucial phenomena such as blood coagulation or solid phase immunoassays. This is because the adsorption of protein on the solid surfaces appears to be the initial step in both the events. The complex structure of protein molecules and the existence of the considerable structural variety among the protein population, together with the essentially irreversible nature certain adsorption processes, make the study of surface phenomena particularly complex. Often, in many cases, the frequency responses could not be correlated to the adsorption of protein as predicted by the Sauerbrey equation, i.e. the mass response concept cannot be applied to predict the amount of adsorbed protein. The change in frequency is governed not only by the mass loading but also by the boundary conditions at the sensor liquid interface, such as interfacial free energy, liquid structure and coating film properties. It has been proposed that the formation of a viscoelastic, highly hydrated protein layer at the interface produces changes in frequency response through viscous losses together with alteration of energy and dissipation processes. Let us discuss a few examples in which frequency changes not conforming to the Sauerbrey equation were observed.

For adsorption of albumin on polysulfone, the frequency responses had to be corrected by the introduction of a protein bulk concentration dependent term to obtain 45 linear relationship [99]. The increased frequency shift than that predicted by

Sauerbrey equation was attributed to the hydration of adsorbed protein molecules.

The importance of size, shape and hydrophobicity of adsorbed protein has been associated with the enhancement of frequency response (in solution compared to air) for the adsorption of ferritin on the gold electrodes of piezoelectric crystals [100]. On the basis of amount of protein, calculated from Sauerbrey’s equation for the frequency measurement in air, the authors concluded that the protein adsorbed on the surface was less than monolayer coverage. The information extracted through protein film characterization using X-ray photoelectron spectroscopy, atomic force microscopy (AFM) and surface plasmon resonance (SPR) confirmed this fact. The experimental result of another study indicated the adsorption of fibrinogen on the gold electrodes of the TSM devices modified with hydrophobic SAM (self assembled monolayer) resulted in an increased biosensor response compared with the case for a relatively hydrophilic gold surface. The same study presented evidence that the tertiary structure of avidin might have been compromised by adsorption on hydrophilic surfaces [101]. As can be seen, in many studies attempt has been made to associate experimental frequency responses with Sauerbrey’s equation. It appears that the prevailing explanation for the enhanced frequency response of QCM sensors in a liquid medium involves the role of loosely bound water molecules. It is likely that this type of association with protein might increase their motional freedom and, therefore, energy losses through conformational changes in the structure. However, all the efforts made to emphasize the contribution of water molecules to the effective 46 mass load appear to be completely inappropriate for a system where the protein film is surrounded by bulk water.

1.4.6 Cell Adhesion and Cell Function

The monitoring of cell adhesion, spreading and proliferation on solid surfaces is crucial for a better understanding and evaluation of the capability of biomaterials for assimilation within the natural tissue and activation of tissue repair mechanisms.

However, there have been only a few studies using a QCM for studying such phenomena. In this section, an overview of some of these studies and their conclusions will be provided, for example, for attachment of platelets [102], osteoblasts [103], and epithelial cells [104] to gold electrode of QCM. In each study, the amount of adhered cells derived from a mass based response could not be correlated with experimentally determined values. Several explanations were provided for the observed phenomena. First, it was proposed that QCM did not detect the total mass of the adherent cell body, rather only the weight of the contact region of the cell with the surface. However, data obtained from simultaneous measurement of resonance frequency and quality factor of the resonator enabled the authors to conclude that the combined QCM response provides a fingerprint of the cell adhesion process reflecting different cell adsorption kinetics for various cell types and various surfaces. Additionally, experimental results have suggested that protein adsorption is the initial event during blood interaction with surfaces goes back to studies on protein adsorption [105, 106]. Further, it has been shown that proteins such as fibrinogen strongly promote platelet adhesion and spreading, whereas the same process is inhibited by pre-adsorbed albumin [107]. Further studies involving monitoring of 47

interactions of blood clotting factors with cell membranes would be extremely helpful

for extending our knowledge of processes involved in the blood coagulation system,

and consequently, the short term blood compatibility of biomaterials.

1.5 Optical techniques and comparison with QCM

There are several optical detection methods that can be used for bioanalytic purposes.

There are several methods for detection, for example surface plasmon resonance

(SPR) [108-110], grating coupler, reflectance interference spectroscopy (RIfS) [111],

and ellipsometry [112]. These techniques involve measurement of change of

properties of light, such as frequency, amplitude, phase, or polarization due to

He-Ne PRISM

DETECTOR α

METAL

AQUEOUS COMPARTMENT (b) (a)

n4=1.45

n3=1.4

n2=1.52

n1=1 (c) (d)

Figure 1.18: Schematic representation of the device principles of different optical label free techniques. (a) Surface Plasmon Resonance Spectroscopy (SPR), (b) resonance mirror (RM), (c) Grating coupler, (d) reflectometric interferometric spectroscopy (RIFS). 48 interaction with the analyte being detected. The general principles of various optical techniques are depicted in Figure 1.18.

Surface plasmons are longitudinal electron density oscillations at the interface of a metal and a dielectric medium, for example. Surface plasmon resonance occurs by optical excitation only if the wave of the incoming light interacts with the free electrons of a metal and if the energy and momentum of the incident light beam correspond to those of the surface plasmon. In this technique of Surface Plasmon

Resonance (SPR), the compound under investigation is immobilized on a glass prism covered with a thin evaporated metal film. P-polarized light is incident on the sample as shown in Figure 1.18(a). Plasmons are excited by the evanescent electromagnetic field which induces oscillation of free electrons in the metal. These plasmons generate another electromagnetic field, which penetrates the dielectric medium

(compound under investigation) closely attached to the metal surface. Only at a certain angle of incidence do the wave numbers of radiation and surface plasmons match, which leads to a resonance phenomena in which the energy of photons is transferred to plasmons. Hence, plasmon resonance can be seen as a sharp peak in the reflectivity of the incident light beam.

The resonance mirror (RM) technique works on a similar principle as SPR. This technique is based on a prism coupler (as shown in Figure 1.18(b)); the coupling conditions for two orthogonal waves of linear polarized light are met at different angles of incidence. The polarized light experiences phase shift in the waveguide.

Depending on this phase shift, and interaction from adsorption layer on the interface, the refractive index of the surface bound analytes can be found. The grating coupler 49 works on the same principle as RM technique, except that the guided wave is accomplished by imprinting a grating on the surface.

The Reflection Interference Spectroscopy detects the effective thickness of the films on the surface, and hence provides quantitative data on the surface concentration of the analyte. When the film is illuminated with white light through a substrate (as shown in Figure 1.18(d)), it is reflected at both the interface of the film. For white light, there is destructive and constructive interference depending on the wavelength, and hence a periodic modulation of the reflecting light intensity results. The positions of the minima and maxima depend only on the film thickness at a particular refractive index and angle of incidence. This thickness allows measurement of thickness changes down to 1 pm resolution.

It is worth spending time to compare these optical techniques with QCM, particularly for (bio) chemical applications. Koblinger et al. [113] have done significant work in this field, wherein they compared SPR to QCM. According to their study, both techniques are equivalent in terms of sensitivity and cross reactivity. However, due to use of optical components for SPR, the cost is almost twice for SPR as compared to

QCM for same sensitivity. The great advantage of SPR is that it is smaller in area as compared to QCM. The QCM is however more versatile when it comes to determining the material properties such as viscoelasticity of polymer films.

1.6 Thesis Organization

In this chapter, we have looked at a large number of mass sensors. Also, the applications of QCM in a large number of areas were listed and the versatility of device for (bio) chemical sensing applications was emphasized. However, in order to 50 increase the versatility and applicability of the device and to compete with other mass sensing techniques, it is imperative that QCM be miniaturized to exploit the resulting mass sensitivity. Additionally, fabrication of QCM in an array format would result in unprecedented temporal and spatial sensing capabilities. Such resonators with improved mass sensitivity are expected to find applications in many more areas than present and are expected to reveal new phenomena which till today went undetected.

Hence, in this thesis an ultrasensitive micromachine QCM in an array format is presented. Detailed steps for fabrication of the proposed array using novel semiconductor batch fabrication techniques are presented (Chapter 2 and Chapter 3).

Data on preliminary device characteristics and preliminary mass calibration data for the device are also presented (Chapter 3). The operation of the device in highly viscous liquid ambient is demonstrated, rendering the device suitable for (bio) chemical applications which inherently involve aqueous ambient conditions (Chapter

3).

As already mentioned in the chapter, QCM is an inherently non-specific platform. For example, for a given mass change on its electrodes, its resonance frequency will change irrespective whether the mass change was due to analyte being detected.

Hence, there is a need for a functionalization scheme that imparts specificity to this highly versatile sensor platform. With recent research involving functionalization of carbon nanotubes and given their sensing capabilities, carbon nanotubes were thought to be as ideal materials for integration with QCM for imparting functionality to it.

The thought process behind this was rather simple. Sensing capabilities of CNTs depend on their interaction with analyte in question, whether the analyte is just 51 flowing by, is colliding with the carbon nanotube or is bound to the nanotube itself. In all the cases, the analyte will express itself as mass on the carbon nanotube, which can be very accurately sensed with ultrasensitive QCM. Additionally, carbon nanotubes can be easily deposited on individual pixels of a QCM array allowing for different functionalities on different pixels and thereby allowing realization of a truly integrated sensing platform. In this thesis, we also present results on our observations after deposition of carbon nanotubes on the surface of the resonator, which caused an increase in the Q-factor of the resonating crystal (Chapter 4). Additionally, we present results on gas sensing capabilities of QCM integrated with single walled carbon nanotubes (Chapter 5). The work in this thesis will open avenues for more advanced functionalization strategies for QCM integrated with carbon nanotubes. 52

Chapter 2

ETCHING FOR MINIATURIZATION

2.1 Introduction

In the previous chapter, it was indicated that the mass sensitivity of the quartz crystal microbalance can be increased by decreasing the thickness of the resonator and also by decreasing the area of the electrodes, provided a sufficiently high Q of the resonators is maintained. However, the thin resonators are extremely fragile and break easily upon handling. For example, the thickness of a 50 μm thick resonator will be 30 MHz, thereby making it impossible to work with the thinned crystal.

However, this problem can be alleviated if we define diaphragms in a thick quartz crystal disc. This approach has several benefits. First, it allows monolithic fabrication of an arrayed resonator, in which the individual pixels can be addressed independently. Second, because the adjacent pixels are separated by a thick quartz crystal whose resonance frequency is different from that of the quartz crystal in the diaphragm, the coupling between the adjacent pixels is minimized. Third, it allows mechanical handling of the high frequency thin resonator array, for example, for functionalization, testing, etc.

However, in order to fabricate diaphragms in the thick quartz crystal, a dielectric etch process is required such that

(a) Inverted mesa structures with almost vertical sidewalls can be defined.

(b) The rms surface roughness of the etched diaphragm is the minimum. 53

membrane is maintained.

(d) The etch process has to be fast enough to allow for reduced processing times

and hence reduced costs.

In this chapter, a generalized dielectric etch process, using an Inductively Coupled

Plasma Reactive Ion Etching system, is presented which is capable of etching a variety of substrates, at a high etch rate while maintaining anisotropy of the etched features. Design of Experiment (DOE) is used to find the value of the optimized processing parameters for highest etch rate and the minimum surface roughness. A combination of gases, including SF6, C4F8, O2, Ar, and CH4 were investigated to obtain the optimum etch parameters. Regression using least square fit was used to define an arbitrary etch rate number (Wetch) and an rms surface roughness number

(Wrms) as a function of ten correlated process parameters, namely ICP power (WICP), substrate power (Wsub), flow rate of gases (QSF6, QC4F8, QAr, QO2), operating pressure

(Pprocess), temperature of substrate (Tsub), and the distance of the substrate from the source (D). The developed process was used to etch PyrexTM 7740, AT-cut quartz crystals, bulk PZT, Y-cut quartz crystal, which makes the etching technique presented useful for applications, for example in navigational grade inertial microsensors, optical waveguides, high frequency crystal oscillators and filters, etc. Given the large surface to volume ratio of MEMS devices, the developed process is particularly useful since it yields minimum rms surface roughness at maximum etch rate. An etch rate of 0.536 µm/min at a rms surface roughness of 1.97 nm was obtained at SF6 flow rate of 5 sccm, Ar flow rate of 50 sccm, 2000 W of ICP power, 475 W of substrate 54 power, substrate holder temperature of 20°C, and distance of substrate holder from

ICP source to be 120 mm. A maximum etch rate of 0.75µm/min was obtained however at a high rms surface roughness of 102 nm by increasing flow rate of SF6 to

50 sccm. By addition of 5 sccm of C4F8 and 50 sccm of O2 to the mixture of etch gases, we were able to obtain an etch rate of 0.55 µm/min (at an rms surface roughness of ~25 nm). The etching process and its optimization and quantification techniques presented in this chapter present very useful tool for MEMS fabrication and packaging applications.

Etching processes are characterized by four important parameters of the etched features resulting from the process. These parameters are

(a) Etch Rate – which is usually defined as μm/min and is measured by

dividing the etch depth achieved by the used interval of process time.

(b) Anisotropy – This is defined in terms of the sidewall angle of the etched

feature. The closer the sidewall angle is to 90 degrees, the more

anisotropic the etch process is defined to be. Anisotropic etching is usually

defined as an etch process in which the etch rate downwards into the

substrate is greater than the lateral etch rate under the mask, often called as

the undercut rate.

profilometry, AFM, white light interferometry, etc. and is a measure of the

smoothness of the surface obtained after the etch process. 55

(d) Selectivity – In order to protect the features and area on the wafer that we

do not want to etch, a masking layer is usually employed. This masking

which protects the underlying areas of the wafer from the etching process

can be fabricated out of photoresists, metal, oxide, nitrides, etc. The

parameter “selectivity” is the ratio the etch rate of the exposed portions of

the wafer to the etch rate of the masking layer. This parameter is very

important for MEMS processes since typically deep etches are required

for fabricating MEMS devices. For example, if we want to etch 500 μm

deep trenches in the wafer and if the maximum thickness of the masking

layer that can be deposited is 20 μm, then the selectivity of the masking

layer should be at least 25 for a successful etch run in which the exposed

portions of the wafer are etched while the masked areas of the wafer are

not affected by the etch process.

2.2 Literature Review

Micromachining is an integral process for microsystem fabrication. Silicon dioxide in its crystalline form (quartz) as well as its amorphous form (glass) is finding increasing applications in microsystems, as active resonating structure as well as passive support and packaging components. Owing to the large surface area to volume ratio of MEMS devices, it is desirable that the properties of the etched surface be controlled for optimum device performance. For example, the rms surface roughness of micromachined resonators has an adverse effect on their performance wherein etch created asperities on the surface of the resonators result in increased energy loss mechanisms thereby lowering their quality (Q) factor [114]. In these 56 applications, it is also important to control the surface roughness of the sidewalls since they are part of the resonating structure. The rms surface roughness of the sidewall assumes special importance in cases where the etched structure is used as an optical or acoustic waveguide [115, 116]. Additional constraints on the etching process are in terms of the anisotropic nature of the etched feature and also the etch rate obtained. Ability to control the etch profile via variations in process parameters is very important. For example, while a typical backside through the substrate lead transfer typically requires a V-shaped feature [117]; a deep high aspect ratio feature requires maximum anisotropy so that the etch does not stop before reaching the desired depth [118, 119]. Finally, deep etches typically used in MEMS applications also require that the etch process is optimized for a high etch rate to achieve high throughput and reduced fabrication cost. History is rich with attempts to micromachine quartz, both in crystalline and amorphous forms. In this section, a brief overview of some of these attempts is presented.

2.2.1 Micromachining using wet etching techniques

There are several methods available for reducing the thickness of the crystal blank.

One such popular method is to mechanically lap the crystal blank. However, lapping causes defects on the surface of the crystal in terms of microroughness, microfractures, and a quartz layer on the surface consisting of defects in the crystalline lattice [120]. These defects can be detected by X-ray diffraction microscopy [121]. Additionally, lapping processes are difficult to control (i.e. it is difficult to achieve a required thickness accurately for accurate frequency determination). In order to remove these crystal imperfections introduced due to 57

lapping and to make the surface smooth, wet chemical micromachining techniques

are conventionally used. In order for the liquid phase chemical to etch the surface of

the quartz uniformly, it must go through the following five steps –

(a) Etchant should diffuse to the surface.

(b) It should be adsorbed on the surface.

(d) After the chemical reaction, the reaction products should desorb from the

surface.

(e) After desorption, the reaction products should diffuse away from the surface.

The etching of a crystal may be limited by any of the five steps shown above. When

the etching is reaction rate limited (i.e., when there is a plentiful supply of etchant

molecules at the surface), the morphology of the etched surface is determined

primarily by the properties of the material being etched. Reaction rate limited etching

(a) (b) Lapped Surface Chemically Polished Surface Figure 2.1: (a) High surface roughness that results when the surface of the quartz resonator is mechanically polished. (b) However, after subjecting the rough surface to chemical etching, due to diffusion limited etching, planar smooth surface results. 58 of an anisotropic material usually results in a rough, faceted surface However, when the etching is diffusion limited, i.e., the inherent rate at which a reaction can take place is higher than the rate of diffusion of etchant molecules to the surface, a depleted surface layer of etchant molecules exist, outside which the etchant concentration is uniform, and inside which the concentration decreases to near zero at the surface. When starting with a rough, e.g., a lapped, surface consisting of hills and valleys, as illustrated in Figure 2.1(a), the probability of an etchant molecule diffusing to the top of a hill will be greater than the probability of it diffusing to the bottom of a valley. The hills will, therefore, be etched faster than the valleys, and the surface will become smoother as the etching progresses, i.e., the surface will become “chemically polished”. Chemically polished surfaces are not perfectly flat. They are microscopically undulating, but atomically smooth, as illustrated in Figure 2.1(b). Vig et al. showed that etching in a saturated solution of buffered HF (NH4F:HF) is capable of producing chemically polished quartz [122]. This concept of achieving chemically polished quartz was considered counterintuitive and rather impossible by researchers then, when this report was first published. This is because it was widely known that the etch rates of quartz vary greatly with crystallographic directions [123].

The rate along the fastest etch direction, the z-direction was almost 100 times faster than the slowest X-direction. Hence, achieving chemically polished quartz surface was deemed impossible. However, Vig et al. using careful experimentation showed that this could indeed be achieved. They also observed that most of the crystal blanks were not suitable for chemical polishing. Only vacuum swept quartz [124, 125] was found to result in etch channel free surface after chemical polishing step. 59

Typically, for wet etching of quartz in ammonium bifluoride, it is required that the bath be maintained at a steady temperature. Hence, the etching is performed in a double walled Teflon beaker with water in the double wall used to control the temperature of the etching solution inside the beaker. Constant gentle stirring of the etching solution is also desired to prevent formation of air bubbles on the surface of the sample during etching.

Even with high control over the surface roughness of the micromachined crystals, average rms surface roughness of greater than 100 nm was obtained for the best crystals. Such high rms surface roughness is not acceptable for micromachined small sized resonators which are more sensitive to rms surface roughness than the large sized resonators owing to their increased surface area to volume. Additionally, chemical polishing using this method could be achieved only for singly rotated quartz crystals (such as AT, BT and ST cut plates) and not for doubly rotated quartz blanks

(such as 10°v, FC, IT and SC cut). However, for SC cut quartz blanks, it was found that diluting the ammonium bifluoride solution five times with water resulted in chemical polishing to the crystal blank [126]. Also it was found that chemically polished surface was obtained only for natural and vacuum swept crystal blanks which had no etch channels to begin with. For normal crystals, chemically polished surface could not be obtained. This is because normal crystals have edge dislocations, and preferred etching along these dislocations result in the formation of etch channel.

The dominant source of edge dislocations in the cultured quartz were determined to be latent seed dislocations and the seed crystal interface, using techniques such as X- ray diffraction, and optical and scanning electron microscopy [127]. Since the cost of 60 natural and vacuum swept quartz it at least 50% higher, an etching method capable of achieving an rms surface roughness of less than a few nm which is independent of the quality of the quartz blank is required.

2.2.2 Micromachining using controlled dissolution of quartz blanks

The process of thinning the quartz crystal using controlled dissolution is very different from that of etching using conventional fluorine based wet chemistries as outlined in the previous section. While etching is an irreversible process, controlled dissolution is a reversible process. Additionally, the process of chemical etching relies on fluorine radicals and ions; the process of dissolution is achieved in a NaOH or KOH bath. By varying the temperature and pressure of a NaOH or KOH bath

Figure 2.2: Dissolution rate at different temperature of AT-plates plotted against the removal depth in a NaOH.H2O solution [128]. 61 having dissolved quartz crystals, the process of dissolution or crystal growth can be achieved. While at room temperature and pressure dissolution of quartz takes place, use of higher temperature of 350ºC and a pressure of ~100 MPa result in growth of quartz crystals. Deleuze et al. [128] have shown a NaOH (sodium hydroxide) and

KOH (potassium hydroxide) based dissolution process for quartz blanks to reduce the thickness of the quartz blanks. The dissolution process was studied in a basic medium, which is also the growth medium for quartz crystals. It was found that for

AT cut quartz blanks, the best results in terms of rms surface roughness of the crystal blanks was observed for the most concentrated solvent of NaOH.H2O. An rms surface roughness, as small as 50 nm, was achieved by the controlled dissolution process using a NaOH.H2O bath at 166ºC. The dissolution rate was found to depend on the temperature of the concentrated NaOH solution. Figure 2.2 [128] shows the viewgraph depicting variation of dissolution rate with temperature and depth of dissolution. As can be seen from the Figure 2.2 the dissolution rate increases with temperature. Also, all the curves of the figure can be divided into two parts:

(a) The first part of rapidly decreasing etch rate is related to chemical lapping of

the surface layer disturbed by cutting and polishing.

(b) In the second part, the dissolution rate becomes constant and is characteristic

of the intrinsic dissolution rate for a given orientation of the material at a

given temperature.

However, the demonstrated process is inherently isotropic and is strongly dependent on the surface roughness prior to the dissolution process. Additionally, the demonstrated etch rates are moderate, even at very high temperature of 178°C. 62

2.2.3 Modeling of chemical wet etching processes

The applicability of the wet etching processes for reducing the defects on the crystal surface after mechanical lapping step and to achieve an atomically smooth macroscopically undulating surface with rms surface roughness around 100 nm is well established. But when such wet etching methods are used to define diaphragms in the quartz blank for realizing high frequency quartz resonators, the preferential etching along different crystal planes results in non-vertical sidewalls of the inverted mesa structure and also non-planar diaphragms whose frequency characteristics are difficult to predict. Hence, efforts have been made in recent past to develop accurate models to predict the etch rates of different planes as a function of etch process conditions [129], such as concentration of ammonium bifluoride solution, temperature, and initial rms surface of the surface to be etched (or “controllably dissolved”). In recent history, the prediction of etching shapes has often been based on the kinematic model of dissolution proposed by Frank et al. [130] which gives the necessary tools to construct geometrically limiting etching shapes. Additionally, tensorial representation of the anisotropic etching has been used to develop for deriving analytical expressions for dissolution surface. Since the trajectory of a moving surface element can be determined from the equation of the dissolution surface it becomes possible to numerically construct various etching shapes. 63

Polar plot of etch rates

Etching Mask

a1 a2

Etching Profile

Figure 2.3: 2D Wulff Jacodine plots.

For example, a simple scheme to construct these three dimensional etch diagrams was

also shown by Delapierre et al. in 1991 [131]. As shown in Figure 2.3, point’s a1 and

a2 are the limits of the etching mask. The origin of the etching diagram (i.e. the

variation of the etching rate with direction of the material) is placed at a1 and a2, the

left side of the diagram being taken for a1 and the right side of the diagram for a2. The

perpendiculars to the rate vectors are drawn in Figure 2.3. The etching curve is the

envelope profile of these perpendiculars: it is the set of points on these lines that can

be reached from a1 and a2 without crossing any other line. This method, as proposed

by Delapierre, can be extended to form three dimensional etching diagrams. 64

2.2.4 Dry Etching Techniques for micromachining

There are several ways to accomplish dry etching, which can be primarily divided into three categories –

(a) Glow Discharge Methods: The glow discharge method utilized plasma to

accomplish etching. When reactive gas plasma is used to produce low energy

ions, then the process is called as plasma etching. In case the ions are of high

energy when a reactive gas is used to generate plasma, then the process is

called as reactive ion etching. In case when an inert gas is used to generate

plasma of high energy ions, then the process is called as glow discharge

sputter etching. In this chapter, dry etching processes based on reactive ion

etching are developed and evaluated.

(b) Ion Beam Methods: In this method, a beam of ions is generated by applying

high bias to the substrate, which is located far away from the plasma. The ions

accelerate under the influence of the applied bias on the substrate and pass

through a screen thereby resulting in the formation of an ion beam. When an

inert gas with no reactive neutrals is used to generate the ion beam, then the

process is called as ion milling. In case when the ion beam is generated from

the inert gas with reactive neutrals added, then the process is called as

chemically assisted ion beam etching. In case wherein reactive gas is used to

produce the ions beam with the additional of certain neutrals, then the process

is called as reactive ion beam etching.

the sample causes the reaction products of the atoms on the surface chemically 65

bound to a reactive species to vaporize from the surface, and thereby resulting

in high resolution etching of substrate. However, the speed of etching is slow,

and it takes a long time (several hours) to etch a single wafer. Also, the cost of

etching is prohibitively high. Hence, this technique is used for applications

where very small features need to be defined in local areas on the substrate.

Makimura et al. [132] have recently demonstrated a precise method to etch

quartz. They used laser plasma soft X-rays together with UV laser to achieve

the same.

2.2.4.1 What is plasma?

Dry etching of features in quartz blanks is usually accomplished using plasma based systems. Plasma is a collection of electrically charged and neutral particles in which the density of negatively charged particles (electrons and negative ions) is equal to the density of positively charged particles (positive ions). It is formed when a gas is forced to conduct electric current. The neutral species (called as radicals), including reactive atoms such as F, Cl, Br, O, H, etc. are responsible for the unique chemical reactions that can be accomplished in the plasma environment. Negative ions are created very efficiently in plasmas involving electronegative gases such as the halogens, halocarbons, oxygen, etc. Negative ions are not found in rare gas plasmas or in the plasmas of electropositive gases such as nitrogen. Positive ions in the plasma are created due to collision processes between particles. Whenever plasma is in contact with a surface, a boundary layer known as a “sheath” is formed. In a sheath, there are more positive charges than electrons. Large electric fields exist in the sheath regions causing positive ions in the plasma to accelerate towards the surface while 66 electrons and negative ions are held away from the surface. The sheath is needed to ensure that the current of the positive charged species leaving the plasma equals the current of the negatively charged species leaving the plasma. Plasmas are described in terms of their charge particle density (cm-3) and the electron temperature (eV). The plasmas used for etching and other material processing typically have densities in the range between 109 and 1013 electrons/cm3 and electron temperatures between 1 and

10 eV.

2.2.4.2 Ions and Radicals in Plasma

As discussed previously, plasma consists of ions and radicals along with energetic electrons. In processing glow discharges (plasmas) used for etching, the ion to neutral fraction ranges from about 10-2 for high density plasma to as low as 10-6 for low density plasma. Hence, there are significantly more neutrals in high density plasma as compared to low density plasma. Positive ions are more important than negative ions for etching. This is because the sample surface is negative (normally the cathode) with respect to the plasma, which means that the negative ions cannot reach the surface of the sample to be etched. High density plasmas cause complete dissociation of gases and results in the production of a large number and variety of ions and radical, as compared to low density plasmas. For example, CF4 dissociates primarily

+ into CF3 in low density plasma, while for high density plasma CF4 dissociates into

+ + + + CF , CF2 , C , and F . As already mentioned, radicals are more abundant in plasma as compared to ions. This is because 67

(a) The electron energy required to break chemical bonds in the molecules used in

the plasma etching processes is usually less than the energy needed to ionize

these molecules.

(b) Often the ionization process is dissociative creating both an ion and a radical

at the same time.

Radicals have a longer lifetime in the plasma compared to ions largely because an ion is almost always neutralized during a collision with a surface whereas radicals often do not react with a surface and are reflected back into the plasma.

2.2.5 Evolution of Plasma Etching Equipment

Plasma etching systems were in the form of barrel shaped etchers in the 1960s. Then they evolved into the capacitively coupled planar geometry in which independent control of ion energy and ion flux was first introduced in the early 1980s. This led to the combination or integration of sources with highest density with capacitively coupled wafer bias. In this section, a short discussion of these different plasma etch chamber geometries follow –

(a) Barrel Systems: Figure 2.4(a) [133] shows the schematic illustration of a

barrel geometry based plasma etching system. These systems were available

in 1960s and their main application was to remove photoresist residue from

wafers using oxygen glow discharge. In these systems, plasma can be

generated with rf powered electrodes or with a coil wrapped around the tube.

Experiments were conducted to demonstrate CF4 based etching using this 68

(a)

(b)

Figure 2.4: Schematic illustration of (a) Barrel RIE system, (b) Downstream etching system [133]. system, but because of lack of directionality of the ion flux, the etching was

predominantly isotropic.

(b) Chemical Downstream Etching: Figure 2.4(b) [133] shows the schematic

illustration of a chemical downstream etching system. In these systems, the 69

wafer chamber is separated from the plasma source by a tube with no line-of-

sight connection to the plasma source. Few ions, electrons, etc. reach the

surface of the substrate and etching is carried out by thermally energetic

neutral radicals. Hence the process does not introduce damage onto the

surface but the etching process is isotropic and therefore these machines are

not used for high definition pattern transfer applications.

schematic illustration of a planar diode system. The planar diode geometry

shown in this figure was the work horse of the 1980s for reactive ion etching

applications. The wafer is placed on the powered electrode and the best results

are usually obtained at low pressures (<100 mTorr). This approach does not

allow independent control of the ion energy and the ion current at a fixed

pressure and rf frequency. Typically ion energies of hundreds of eV are

required to achieve the desired etch rate. A particularly effective

implementation of the diode approach was the “hexode” machine developed

by Applied Materials, which was a dominant batch processing machine in the

1980s.

(d) Capacitively coupled single frequency planar triode system: The triode

geometry shown in Figure 2.5(b), was well known in sputter deposition

technology and introduced in plasma etching technology to allow independent

control of ion energy and ion flux. This approach allowed the ion energy to be

reduced while keeping the etch rate constant by increasing the ion current

density. The wafer is placed on the lower electrode; the lower electrode power 70

(a) (b)

(bias power) is used to control the ion energy while the upper electrode power

(source power) is used to control the ion flux. Typically the source power is

much larger than the bias power and this result in high energy ion

bombardment of the upper electrode. This can cause serious difficulties in the

process, often simply from the inevitable sputtering of the electrode. This

problem is most serious at low pressures when the applied voltages are the

largest.

(e) Capacitively coupled dual frequency triode: The problems caused by high

energy ion bombardment of the source electrodes in the single frequency

triode system are alleviated by using a higher rf frequency to power the source

electrode. It is well known that the rf voltage needed to deliver a fixed power

to the plasma decreases strongly as the frequency is increased. Thus large

power can be delivered to the plasma through the high frequency (typically

tens of MHz) without high energy bombardment of the electrode. The ion

bombardment energy at the wafer surface (lower electrode) can be controlled 71

by a lower frequency rf power applied at the lower electrode. The frequency

ratio between the upper and lower electrode should be atleast 20 or so. The

term “triode” is used for this two electrode system to recognize the fact that

the grounded wall serves as a third (reference) electrode.

(f) Capacitively coupled dual frequency diode: Another implementation of the

dual frequency approach to RIE is the dual frequency diode in which both

high and low frequency rf power are applied to the same electrode. Special

filters are required to keep the two rf power supplied from interfering with

each other. Usually the high frequency power will be much larger than the low

frequency power so that the plasma density is determined primarily by the

high frequency power. In this diode two frequency diode approach, all the rf

current passes through the wafer whereas in the triode approach relatively

little rf current passes through the wafer.

(g) Inductively Coupled Plasma: In the preceding discussion, it has been

emphasized that achieving independent control of ion flux and ion density is

critical for achieving high speed etching without introducing ion induced

defects in the substrate. This involves separating the power supplies

responsible for generating the plasma and for providing the wafer bias. In a

planar diode reactor with only one power supply, the ion current density and

ion energy are coupled to each other. Capacitively coupled plasma with two

frequency sources were used initially. However, capacitively coupled bias

power often produces high plasma potentials. Ion bombardment induced

sputtering and heating of the capacitively powered electrode limit the plasma 72

density that can be obtained. Hence, the trend has been to use inductively

coupled bias supply where the high density plasma can be generated without

(a) (b)

Figure 2.6: Electrode geometries for ICP power supplies, (a) Pancake or stove top, (b) Planar, (c) Cylindrical, (d) Hemispherical and (e) Helical [133].

(e) 73 causing undue increase in plasma potential.

There are numerous electrode geometries by which the source power can be inductively coupled into the plasma. The planar inductively coupled plasma

(ICP), as shown in Figure 2.6(a) [133], is one the most popular reactor geometries. The “pancake or stove top” coil is very similar in shape to the coils used on electric stoves. The thick dielectric must be strong enough to withstand atmospheric pressure and the thickness serves to reduce capacitive coupling from the coil to the plasma. Inductive coupling allows the generation of high density plasma without high voltages in the system; thus eliminating the sputtering problem associated with capacitively coupled system. Another version of the planar ICP geometry involves the use of two concentric separately powered coils as shown in Figure 2.6(b) [133]. This approach introduces the ability to adjust the radial uniformity of the etch process.

Another version is to use the cylindrical ICP source. However, this source is commonly used in application other than RIE. As shown in Figure 2.6(c)

[133], the rf current in the external coil induces an rf axial magnetic field in the plasma volume. The rf axial magnetic field induces an rf azimuthal electric field which imparts energy to the plasma electrons. Instead of cylindrical coil, we can also use the hemispherical coil or the helical resonator as shown in Figure 2.6(d) [133]. The helical coil (Figure 2.6(e)) [133] is similar in configuration to the cylindrical coil, only that the coil in case of helical configuration is tuned to a resonance condition by means of a movable tap on the coil and a capacitance to a nearby ground shield. 74

Figure 2.7: Different geometries for the Electron Cyclotron Resonance based RIE system [133].

(h) Electron Cyclotron Resonance: This RIE equipment is based on the fact that

the power can be propagated into the plasma more efficiently in the presence

of a magnetic field wherein the electrons follow the magnetic field lines.

Hence a resonance condition can be established when the frequency at which 75

the electrons orbit around the magnetic field lines is equal to the frequency of

the applied electric field. In the ECR system, the pressure should be low

enough so that the electrons can undergo many obits without colliding with

gas molecules (usually less than 10 mTorr). Figure 2.7 [133] shows many

configurations in which ECR RIE system can be realized. One of the concerns

with use of ECR for RIE applications is the non vertical incidence of electrons

and ions on the sample which causes some isotropic behavior in the etch

profile.

(i) Microwave excitation: Microwaves can be used to establish glow discharges.

Figure 2.8: Etching equipment using microwave excited non-equilibrium atmospheric plasma [134]. 76

Recently, Yamakawa et al. [134] have demonstrated very high speed etching

of silica using microwave excited non-equilibrium atmospheric pressure

plasma. The set up used by these authors is shown in Figure 2.8 [134]. The

authors demonstrated an ultrahigh etch rate and ultrahigh selectivity with this

process. They used a fusion of liquid and gaseous phases to accomplish

etching. The etch rate of SiO2 14 microns/min using NF3 and He gas mixtures

along with addition of H2O. Selectivity of the etching process with respect to

Si was as unprecedented 200. It was proposed that the high performance of

- etching was likely due to the HF2 induced reaction with Si-OH bonds under

low energy ion bombardment.

2.3 ICP source used in the current experiments

In a typical inductively coupled plasma system the coil power (plasma density) and the substrate power can be controlled independently of each other [135, 136]. This enables excellent control over plasma density and kinetic energy of etchant ions. As discussed, traditional RIE processes are limited by the fact that the substrate power and RF plasma power are coupled to each other often resulting in etch non-uniformity across the wafer, low density of plasmas, and limited control over the processing conditions. ICP based RIE systems can sustain plasma even at relatively low pressures in the range of 10-3-10-4 Torr. The density of the plasma generated can be further increased by lining the etch chamber with high power magnets. The use of magnets thus helps to achieve higher ion current density, higher etch rate and better plasma uniformity across the wafer being processed [137]. At such low pressures, the plasma in traditional RIE systems is not stable. Low processing pressure and high 77 plasma density (which essentially results in high ionic current and greater radical flux density), improves the mass transfer rates of the reactant gases and the etch products in addition to being instrumental in the removal of stray particles. The presence of stray particles typically generated from the masking materials, the substrate holder, the reaction chamber walls, or as reaction by products, results in micro-masking causing high surface roughness (often referred to as grass), micro-trenching and formation of plateau-like structures. Additionally, the increased mean free path at low pressures improves the anisotropy of the etched features by minimizing the randomizing collisions between the radicals, ions and other plasma species.

ICP-RIE processes for silicon dioxide etching based on C4F8/Ar/CH4/O2 chemistry are well established [136, 138-140]. Recently, there has been effort towards developing etch processes based on SF6/Ar based chemistry [141, 142]. Also, a combination of C4F8 and SF6 gases are used in high aspect ratio deep reactive ion etching (DRIE) of silicon for fabrication of MEMS structures [143]. In this chapter we investigate dielectric etching processes based on combination of

SF6/C4F8/Ar/CH4/O2 gases. The role of additional gases, i.e. of oxygen, argon, and methane is multifold. They influence the properties of the etchant species, the electron temperature, the major radical or ion produced and its abundance with respect to other ions and radicals, the density of the plasma, the residence time of gases in the etching chamber, and also provide radicals and ions which suppresses or enhances the effect of radicals and ions produced as a result of dissociations of SF6 and C4F8. By varying the amount of these additional secondary gases, the properties of the etch process can be varied to suit the needs in terms of properties of the etched 78

RF Power Supply RF Matching Network Gas Inlet

ICP Source

Antenna

Magnetic Pieces Diffusion Chamber Circling the Chamber

Substrate Holder or the Wafer Substrate Holder in Two Different Positions

Helium Backside Cooling

Figure 2.9: Schematic illustrating the ICP RIE set up used in this work. The vertical position of the substrate holder which is backside cooled using He can be adjusted with respect to the ICP source. Also, the diffusion chamber is lined with magnets to increase the density of the plasma. feature. In this work a detailed study of the effect various process parameters (ICP power, substrate power, operating process pressure, gas flow rates

(SF6/C4F8/Ar/CH4/O2), ratio of gas flows, substrate temperature and distance from source) on the etch rate and rms surface roughness of features in PyrexTM 7740 glass substrates was performed. The PyrexTM 7740 glass is known to have a typical 79

composition of SiO2 (79.6%), B2O3 (12.5%), Na2O (3.72%), Al2O3 (2.4%) and K2O

(0.02%).

2.4 Experimental Procedure

Figure 2.9 shows a schematic drawing of the Alcatel AMS 100 ICP-RIE etcher used in this work. The diffusion chamber was lined with magnetic pieces enabling generation of denser plasma. The top coil was connected to RF generator operating at

13.56 MHz and capable of generating up to 2500 W of power. The substrate holder was similarly connected to another RF generator operating at 13.56 MHz capable of generating up to 500 W of power. A magnetically levitated turbomolecular pump with capacity of 1400 l/s for nitrogen was used to generate the high vacuum. High pumping capacity is essential to maintain low ambient pressures enabling fast refresh rate of gases and rapid removal of reaction products from the surface of the sample.

The substrate holder was designed for 4” wafers and a specially designed aluminum holder with screw on clamps was devised for etching smaller sized samples. The substrate holder was backside cooled using Helium gas and a dedicated chiller.

Additionally, the relative vertical position of the substrate holder with respect to the plasma could be set using the computer interface on the machine. The voltage generated at the substrate holder was read off from the computer interface.

Double sided polished 4” diameter, 500 μm thick PyrexTM 7740 wafers were cleaned thoroughly with Acetone/Isopropyl Alcohol (IPA) followed by piranha clean (1:1

H2SO4:H2O2) for one hour. A seed layer, consisting of 200 nm of gold with 20 nm of chromium as an adhesion layer, was subsequently e-beam evaporated on the cleaned glass (PyrexTM® 7740) surface. The etch patterns were then delineated on the seed layer 80 using standard lithography and wet etching steps [144]. The patterned 4” wafers were diced into individual 1” dies. A thick layer (5-10µm) of Nickel was then electroplated onto the seed layer on the 1” dies. The fabrication sequence is illustrated schematically in Figure 2.10. Control over the quality of the electroplated nickel was maintained using constant stirring of the electroplating solution and the use of a pulsed power supply. This was necessary to minimize the formation of stray particles from the nickel acting as micro-masks. The electroplated dies were then clamped into

ICP RIE (a) (d) Etching

(b) (e)

Chromium (~ 20 nm)

Gold (~ 200 nm)

Nickel (~ 5-10 µm)

Figure 2.10: Schematic illustration of sample preparation and etching. (a) E-beam evaporation deposition of Au/Cr on 4” Pyrex® wafer. (b) Delineation of the seed layer using lithography and wet etch steps followed by dicing into one inch dies. (c) Electroplating of a thick (5-10 µm) of Nickel on the seed layer. (d) Etching of glass using ICP-RIE process. (e) Stripping of nickel using Piranha clean. 81 the aluminum substrate holder and loaded into the ICP RIE system for etching. The temperature of the substrate holder was controlled using a chiller and back side cooling using helium gas as shown in Figure 2.9. A standard run time of one hour was used for all the samples. SF6/C4F8/CH4/Ar/O2 based chemistry was used for the etching of the samples. The etch rate was determined from the step height of the etched feature. The rms surface roughness along with step height was measured using a stylus profilometer. Additionally, atomic force microscope (AFM) and scanning electron microscope (SEM) was used to characterize the properties of the sidewalls and for accessing the quality of the etched features in terms of their rms surface roughness.

2.5 Results and Discussion

2.5.1 Design of Experiment (DOE)

A standard DOE methodology employing factorial design was used to study the variation of etch rate and rms surface roughness as a function of the process parameters [145]. Given the large number of process parameters, 10 in the current study (Table 2.1), the task of optimizing them to yield the desired etch characteristics in terms of etch rate and rms surface roughness will require a large number of experiments. Even using the statistical methods, such as 2 factorial DOE design would result in 210 etch experiments to be performed, which is not practical. A two factorial design normally involves running the experiments at two extremes of each process parameter in the design space with a center point for added accuracy. Hence we will have two factors for each of the ten process parameters, resulting in a minimum of 210 experiments to be performed. In order to further reduce the number 82

Table 2.1: Process design parameters for optimizing the etch parameters, namely rms Surface Roughness and Etch rate

Process Design Units of measurement Experimental Range Parameter

ICP Power Watts 500-2000

Substrate Power Watts 100-475

O 2 Flow Rate sccm 5-100

SF6 Flow Rate sccm 5-50

C 4F 8 Flow Rate sccm 5-50

CH4 Flow Rate sccm 5-50

Ar Flow Rate sccm 5-50

Operating Pressure mTorr 1-20

Temperature of °C 5-30 Substrate Holder

Distance of Substrate mm 120-200 Holder from ICP

of experiments for optimization, we split the process space into four subsets. Thereby,

we were able to reduce the number of runs from 1024 (210) to only 74; reducing cost and time for process optimization to obtain the desired etch characteristics. We were also able to run middle points for each process parameter for increased accuracy of our optimization process. 83

Traditionally, optimization of the etch process for silicon dioxide, has aimed at achieving high etch rates with minimum oxide damage and improved selectivity with respect to the masking material (typically Si) [143]. However, for MEMS applications, we need to optimize the process not only in terms of etch rate, but also surface roughness of the etched features, the sidewall angle, and dimension control.

In this work, we aimed at optimizing the etch process in terms of etch rate and rms surface roughness of the etched features. Since we used a “thick” (3-5 μm) nickel hard mask for etching, we did not investigate the selectivity as a function of process parameters. In order to reduce the number of runs, we split up the process space into four subsets for optimization. Also, to unambiguously validate the conclusions of the

DOE, the order of the runs was completely randomized. Since the etching is dependent on the conditions of the walls of the reaction chamber [146], the reaction chamber was thoroughly conditioned by dummy runs before etching of the actual samples to minimize the chamber memory effect. During the dummy run, the chamber was exposed to identical conditions of plasma and flow rate of gases without the introduction of the sample into the chamber. During all the DOE experiments, the operating pressure was kept at a minimum as determined by the dynamic equilibrium between the pumping speed of the vacuum system and the flow rate of the gases.

Also, the distance of the substrate holder from the source was kept at 120 mm while the temperature of the substrate holder was kept at 20°C.

For the first subset, a standard 24 factorial design was used with the four process parameters of importance, namely, ICP power (500 W - 2000 W), substrate power

(100 W – 475 W), SF6 flow rate (5 sccm – 50 sccm) and Ar flow rate (5 sccm – 50 84

(i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii) (ix)

(xii) (x) (xi)

Figure 2.11: Surface plots of (i-vi) rms Surface Roughness (nm) and (vii-xii) Etch Rate (µm/min) as a function of flow rates of SF6, Ar, and ICP and substrate power. sccm). Analysis of the results, as shown in Figure 2.11(i-xii), indicate that it was

possible to obtain an etch rate of 0.536 μm /minute and rms surface roughness of 1.97

nm at an ICP power of 2000 W, substrate power of 475 W, SF6 flow rate of 5 sccm,

and Ar flow rate of 50 sccm [147]. Note that the surface plots were generated by a

linear interpolation between the four data points at the corners of the rectangles, four 85

data points at the center of the side of the rectangles, and one data point at the center

of the rectangle. Looking at surface plot in Figure 2.11(xi), it is interesting to note

that while etch depth increases with increasing flow rate of SF6 at very high ICP

power (2000 W), it actually decreases with increasing SF6 flow rate at very low ICP

power (500 W). For generating Figure 2.11(i,xii), the unplotted variables were kept at

substrate power of 475 W, ICP power of 2000 W, Ar flow rate of 50 sccm, and SF6

flow rate of 5 sccm.

From the first subset of DOE, the best etching parameters are obtained at very high

ICP and substrate power, low operating pressures and optimum ratios of flow rates of

gases. Hence, in the second subset, ICP power, substrate power, and Ar flow rate

were fixed at 2000 W, 475 W, and 50 sccm respectively. A two factorial design was

used for O2, C4F8 and SF6. Additionally, middle levels for flow rates O2, SF6 and C4F8

(i) (ii) (iii)

(iv) (v) (vi)

Figure 2.12: Surface plots of (i-iii) rms Surface Roughness (nm) and (iv-vi) Etch Rate (µm/min) as a function of flow rates of O2, SF6 and C4F8. 86 were also tested for consistency of the results. Hence a total of 18 experiments were performed. Figure 2.12 presents results for this subset of design of experiments.

Several important and interesting conclusions can be drawn from the Figure 2.12(i- vi). We can conclude from Figure 2.12(iv-vi)) that the minimum rms surface roughness of ~ 50 nm is obtained at 50 sccm of O2, 5 sccm of SF6 and 5 sccm of

C4F8. For these conditions, we obtained an etch rate of 0.66 µm/min. The plots were generated by holding the value of the third variable at the above mentioned flow rate of gases. If the objective is not to minimize the surface roughness, then a much higher etch rate of 0.74 µm/min can be obtained at the expense of worsening rms surface roughness. In Figure 2.12(ii), the etch rate is observed to decrease unexpectedly with higher flow rates of SF6 and C4F8. At very high flow rate of both SF6 and C4F8, we believe that there is deposition of carbon polymers on the surface of the sample, causing a decrease in the etch rate. This was confirmed by inspection of the surface of the sample wherein a thin layer of carbon deposits was confirmed by wiping with a clean wipe.

For the third subset of DOE, the flow rates of CH4, SF6 and C4F8 were varied.

Oxygen could not be introduced into the system since it forms an explosive mixture with methane (CH4). Without the carbon scavenging as provided by oxygen flow, there is only limited removal of carbon deposits on the sample from the oxygen coming from dissociation of oxides in the sample. As in the second subset of DOE,

ICP power, substrate power, and Ar flow rate were fixed at 2000 W, 475 W, and 50 sccm respectively. As can be seen from Figure 2.13 (i-iii), the minimum surface roughness occurs for minimum flow rate of the gases. At such processing conditions, 87

(i) (ii) (iii)

(iv) (v) (vi)

Figure 2.13: Surface plots of (i-iii) rms Surface Roughness (nm) and (iv-vi) Etch Rate (µm/min) as a function of flow rates of SF6, C4F8, and CH4. the etch rate is significant at 0.7 µm/min. For generating surface plots of Figure 2.13,

the unplotted variables were kept at 5 sccm of flow rate of SF6, C4F8 and CH4

respectively. As compared to second subset of DOE, the etch rate is 33% higher but

at the same time results in a rms surface roughness of 288 nm, which is 10 times

higher than that of first subset [148]. Since surface roughness cannot be tolerated for

microsystem applications, we did not investigate the use of CH4 as an additive gas to

the mixture further in the current study. However, the given processing conditions can

be used for fast etching for definition of vias, removal of sacrificial layer, etc.

For the fourth subset of DOE, the power at the ICP and the substrate were varied. As

discussed in above paragraph, CH4 was no longer used for etching. In this case a

generalized 2 factorial design with middle point was used for accessing the impact of

variation of ICP and substrate power on rms surface roughness and etch depth after an

etch period of one hour. From the previous subsets of design of experiment, the flow 88

rate of gases was set to 50, 50, 5 and 5 sccm for Ar, O2, SF6 and C4F8 respectively.

Figure 2.14 (a, b) shows the surface plots of rms surface roughness and etch depth obtained for different combination of ICP and substrate power. As can be seen from the figure 2.14, best etch rates along with minimum surface roughness is obtained at maximum values of the ICP and the substrate power. Since in our experiments we observed that use of higher flow rates of O2 generally caused an improvement in the etch rate as well as rms surface roughness, we repeated the third subset of DOE for oxygen flow rate of 100 sccm. However under such excessive flow rates, very small etch rates of less than 20 µm/hour, at rms surface roughness of 50-200 nm were obtained. Hence, the idea of using higher oxygen flow rate for etch process optimization was not further investigated.

To summarize, using four subset DOE approach we were able to find optimum conditions for etching of PyrexTM® using just 74 runs rather than 210 as previously described. Hence factorial design is a powerful tool which indicates possible values of optimum process parameters with minimum number of runs, thereby enabling rapid determination of process parameters for optimum etching results. The optimum process parameters for etching for both the SF6/Ar chemistry as well as

SF6/C4F8/Ar/O2 based chemistry are summarized in Table 2.2 and Table 2.3 respectively. Figure 2.15 (a) shows the AFM image of the surface generated after the etch step. Also shown in Figure 2.15 (b) is the side view of the etch profile. Almost vertical side walls were obtained. The apparent non-vertical angle of the sidewall in the stylus profile is due to finite dimension of the tip of the 89

(a) (b)

Figure 2.14: Surface plots of (a) rms Surface Roughness and (b) Etch Rate (µm/min) as a function of ICP and substrate power. 90

Table 2.2: Optimum process variables for maximum etch rate of 0.536 µm/min, at an rms surface roughness of 1.97 nm.

Process Parameter Value Units

ICP Power 2000 Watts Substrate Power 475 Watts

Ar Flow Rate 50 sccm

SF6 Flow Rate 5 sccm

Operating Pressure < 2 mTorr

Distance From Source 120 mm

Substrate Holder Temperature 20 °C

(a) (b)

(c)

Table 2.3: Optimum process conditions for the etching process

Process Design Units of measurement Optimum Value Parameter

ICP Power Watts 2000

Substrate Power Watts 475

O2 Flow Rate sccm 50

SF6 Flow Rate sccm 5

C4F8 Flow Rate sccm 5

CH4 Flow Rate sccm Not used

Ar Flow Rate sccm 50

Operating Pressure mTorr Minimum possible

Temperature of °C 20 Substrate Holder Distance of Substrate mm 120 Holder from ICP 92 profilometer and hence is not a true measure of the sidewall angle. Inset to Figure

2.15 (b) shows the SEM image of the sidewall after the etch step.

2.5.2 Effect of Variation of Process Parameters

Once having found the optimized process conditions to obtain best etch parameters in terms of etch rate and rms surface roughness, the process parameters were varied one parameter at a time, keeping other parameters constant at values corresponding to the optimum process. As already discussed in the previous paragraphs, CH4 was no longer used for the etching processes because of high rms surface roughness obtained with a relatively small gain in the etch rate. In the following sections, we will present data on the variation of etch rate with the individual process parameters. The factors that influence the rms surface roughness and the etch rate in the current study can be summarized as follows

a. There is dissociation of SF6, C4F8 in the plasma resulting in the formation of

fluorine ions and radicals along with other species denoted as CFx, SFx, etc [149,

150]. There is more than 90% dissociation in ICP plasma, resulting in the

+ + formation of S and some SF5 ions in the plasma [151]. b. Dissociation of oxygen results in formation of oxygen ions and radicals which

not only help in sputtering but also remove carbon based polymers formed on the

surface of the wafer. In the case of SF6/C4F8/Ar/O2 based chemistry, the etching

is interplay between etching and deposition of fluorocarbon deposition. It has

been shown that for high operating pressure, low ICP and substrate bias, and high

flow rates of gases, there is increased deposition of fluorocarbon films on the

surface of the sample, not only resulting in lower etch rate but also increased rms 93

surface roughness [152]. But a high flow rate of oxygen essentially eliminates the

fluorocarbon deposition on the surface of the sample [153]. c. Dissociation of Ar results in formation of ions which help in efficient sputtering

of the surface of the sample resulting in:

(i) Deeper penetration of the reacting species and radicals inside the surface,

(ii) Efficient removal of non volatile reaction products from the surface of the

sample. Ichiki et al. [154] have shown, for SF6/Ar chemistry, using XPS

techniques that high rms surface roughness is primarily due to residues of

fluorine and metals and non-volatile fluoride on the surface of the sample.

The metal compounds are formed due to particular composition of PyrexTM®

glass samples used in the current study.

(iii) Dislodging of any stray particles which might act as micromasks resulting

in formation of plateau like features and degrading the surface roughness

[153, 155, 156].

In the subsequent text, we will present and explain results on variation of etch parameters based on above three simple assertions for both SF6/Ar chemistry as well as SF6/C4F8/Ar/O2 based chemistry.

2.5.2.1 Effect of operating pressure

For both the gas chemistries, we found that the etching parameters were critically dependent on the operating pressure inside the etching chamber. The minimum limit of operating pressure in the chamber during etching was determined by the pumping speed and the flow rate of gases. Naturally, operating pressure increases with increase 94

(a) 0.55 560 (b) 0.6 2500 Etch Rate Etch Rate fit - Etch Rate 0.55 2250 0.525 480 fit - Etch Rate rms Surface Roughness rms Surface Roughness fit - rms Surface Roughness 0.5 2000 fit - rms Surface Roughness 0.5 400 0.45 1750 ess (nm) ess (nm) 0.4 1500 m/min) m/min) 0.475 320 μ μ 0.35 1250 0.45 240 0.3 1000 Etch Rate ( Rate Etch Etch Rate ( Rate Etch 0.425 160 0.25 750 0.2 500 rms Surface Roughn Surface rms rms Surface Roughn Surface rms 0.4 80 0.15 250

0.375 0 0.1 0 0 2 4 6 8 10 12 14 16 18 20 22 2 4 6 8 10 12 14 16 18 20 22 Operating Pressure (mTorr) Operating Pressure (mTorr)

seen from Figure 2.16 (a, b), there is degradation in rms surface roughness and etch

rate as operating pressure increases. For the SF6/Ar based chemistry, process

pressures of more than 5 mTorr results in degradation in both etch rate and rms

surface roughness. At the high pressures we observed severe surface roughness (rms

surface roughness > 100 nm) in the etched areas. Goyette et al. [157] have shown that

with increasing pressure for SF6/Ar based chemistry, the total ion flux reduces. We

believe that this causes decrease in the sputtering rate and uniformity of the surface

resulting in an decrease in etch rate and increase in rms surface roughness

respectively. For the SF6/C4F8/Ar/O2 based chemistry, for a modest 16 mTorr

increase in operating pressure, there is 70% drop is etch rate and 100 times increase in

rms surface roughness. Hence it is critically important to maintain the operating

pressure inside the chamber at a minimum during processing of the sample. We

believe that lower the operating pressure, the lower are the energy loss collisions 95 experienced by high energy incident Ar and other ions on the sample surface and hence more efficient is the removal of reaction products and stray particles. The increase in plasma density due to magnetic confinement is more effective at the lower the pressure as shown by Li et al. [158]. Additionally, low operating pressure will reduce the residence time of gases in the reaction chamber thereby not allowing any significant deposition of carbon based polymers on the surface of the sample [159,

160].

2.5.2.2 Effect of ICP power and Substrate power

As ICP power is increased, there is increased dissociation of gases in the plasma resulting in an increase in the etch rate. Earlier researchers [157] have shown that with increasing ICP power, the total ionic flux density increases multifold. Also, because of the greater number of ions and radicals formed, the plasma density increases resulting in smooth surface of the etched features due to more uniform sputtering and chemical etching at the surface of the wafer. This was confirmed by

Goyette et al. [157] wherein ion flux densities of Si and its compounds formed after etching increased by a order of magnitude when the ICP power was increased three fold. Figure 2.17 (a, b) shows the variation in etch rate and rms surface roughness with variation in the ICP power for both the gas chemistries. Similar trends were observed for variation of etch parameters with substrate power (Figure 2.18 (a, b)).

With increase in substrate power, the rms surface roughness reduces and the etch rate increase. Due to increased bias on the substrate with increase in substrate power (bias increased from 15 V for substrate power of 100 W to 77 V for substrate bias of 475

W), the ions in the plasma are accelerated towards the substrate with progressively 96

higher energies. This results in ions striking the substrate surface with greater

momentum aiding in not only the etching process but also reducing the surface

roughness by effectively dislodging reactions products and stray particles from the

0.55 48 0.7 280 (a) (b) Etch Rate Etch Rate fit - Etch Rate 0.6fit - Etch Rate 240 0.5rms Surface Roughness 40 fit - rms Surface Roughness rms Surface Roughness fit - rms Surface Roughness 0.5 200 0.45 32 m/min) m/min) 0.4 160 μ μ 0.4 24 0.3 120 0.35 16 Etch Rate ( Rate Etch Etch Rate ( Rate Etch 0.2 80 rms SurfaceRoughness (nm) 0.3 8 rms SurfaceRoughness (nm) 0.1 40

0.25 0 00 400 600 800 1000 1200 1400 1600 1800 2000 2200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 ICP Power (W) ICP Power (W) Figure 2.17: Variation of rms surface roughness and etch rate as a function of variation in ICP power during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis.

0.6 200 0.6 450 (a) (b) Etch Rate 0.55Etch Rate 400 fit - Etch Rate fit - Etch Rate rms Surface Roughness rms Surface Roughness 0.48fit - rms Surface Roughness 160 0.5 350 fit - rms Surface Roughness 0.45 300 0.36 120 m/min) m/min) 0.4 250 μ μ

0.35 200 0.24 80 0.3 150 Etch Rate ( Rate Etch Etch Rate ( Rate Etch 0.25 100

0.12 40 (nm) Roughness Surface rms rms Surface Roughness (nm) Roughness Surface rms 0.2 50

000.15 0 60 120 180 240 300 360 420 480 80 120 160 200 240 280 320 360 400 440 480 Substrate Power (W) Substrate Power (W)

Figure 2.18: Variation of rms surface roughness and etch rate as a function of variation in substrate power during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis. 97 sample surface. The increased velocity of the incoming stream of ions affects the velocity of the steady stream of radicals coming in from the plasma. The energetic ions impart a fraction of their momentum to the stream of radicals and neutral species thereby speeding them up and further accelerating the etching process. The energetic

Ar ions bombardment additionally removes particles generated from the masking material and the walls of the chamber thereby preventing in effects such as micromasking causing improvement in the rms surface roughness. Additionally, increased physical bombardment is expected to cause an increase in the local temperature of the surface, causing the chemical reactions on the surface to speed up resulting an increase in the etch rate.

2.5.2.3 Effect of flow rate of gases

The flow rate of gases determines the relative composition of ions and radicals in the plasma. For the SF6/Ar based chemistry, the interplay between Ar and SFx ions and the fluorine radicals determine the variation in etch rate and rms surface roughness as the flow rate of the two gases is varied. While the charged ions are responsible for physically sputtering the surface of the sample causing removal of non-volatile reaction products and stray particles on the surface of the wafer, the radicals provide the chemistry by reacting with the broken dangling bonds at the surface of the sample.

If insufficient number of charged ions is present, then the non-volatile reactions products will not be efficiently removed from the surface thereby resulting in surface roughness. Goyette et al. [157] have shown that with increasing percentage of SF6 in the etching gas mixture, the total ion flux decreases. Additionally, for predominantly

Ar based plasma, the ion flux of Ar ions is dominant. As we increase the SF6 flow 98 rate, the ionic flux of Ar ions decreases by an order of magnitude. But at the same

+ + + time, the increase in ionic flux of SF5 , SF3 and S ions in not significant. Hence, the etch rate decreases and rms surface roughness increases. This fact was confirmed by earlier studies [157], where it has been shown that with increasing percentage of SF6 the ion mass flux of Si and its compounds formed after etching decreases confirming the observed decrease in etch rate and increase in rms surface roughness. Similar trends were observed by Ichiki et al. [154] where they observed using XPS that fluoride residue on the surface of the sample decreases with increasing Ar percentage in the mixture of the etching gases. Similar effect were observed for C4F8 based chemistry [150]. In the present case, the optimum ratio of the flow rate of the two gases was found to be 10:1 Ar:SF6. With our current tool, we could flow SF6 at a minimum flow rate of 5 sccm. Hence a flow rate of 50 sccm was chosen for Ar.

Decrease in Ar flow rate causes degradation in the etch rate and rms surface roughness (Figure 2.19(a)). Also, increase in SF6 flow rate resulted in increase in etch rate (Figure 2.19 (b)) due to increased chemical etching at the oxide surface.

However, due to insufficient sputtering by charged ions, the rms surface roughness also increased. According to this argument is should be theoretically possible to increase Ar flow rate accordingly in the ratio of 1:10 to obtain very high etch rates while maintaining a very low rms surface roughness. But since we were limited by the pumping capacity of the turbo-molecular pump, use of higher flow rates results in process pressures to be in excess of 5 mTorr. As can be seen from Figure 2.16 (a), process pressures of more than 5 mTorr results in degradation in both etch rate and rms surface roughness. 99

Similar trends were observed for the SF6/C4F8/Ar/O2 based chemistry. When the flow rates of C4F8 or SF6 were increased while keeping all other factors constant as in

Table 2.2 and Table 2.3, the etch rate increased along with deterioration in rms surface roughness of the etched features. Figure 2.20(a) shows the etch rate and rms surface roughness obtained with variation in C4F8 flow rate. The etch rate increases by 30% from 0.55 µm/min to 0.675 µm/min when the flow rate of C4F8 is increased

10 time from 5 sccm to 50 sccm. However, with such an increase there is a 20 times deterioration in the rms surface roughness from ~25 nm to ~450 nm. Similar trends are observed for increase in flow rate of SF6 wherein 30% improvement in etch rate and 40 times deterioration in rms surface roughness is obtained with 10 times increase in flow rate (Figure 2.20(b)). Hence increase in flow rate of these two gases does not help much in terms of increase in etch rate but causes undesirably large increase in the rms surface roughness. This is because the fluorine ions and radicals as provided by 5 sccm flow rate of the two gases are sufficient for providing the required chemistry.

Any flow rate higher than that causes formation of carbon polymer compounds on the surface and reduces the effectiveness of sputtering by charged ions thereby causing an increase in the rms surface roughness. When we increase the flow rate of Ar for

SF6/C4F8/Ar/O2 based chemistry, there is an increased and a more uniform stream of

Ar ions incident on the surface of the wafer. This causes not only increase in the etch rate but also an improvement in the rms surface roughness due to rapid and efficient removal of non-volatile reaction products and stray particles from the surface of the wafer (Figure 2.20 (c)). Li et al. [150] have shown that there is rapid decrease in the generation of depositing fluorocarbon species as the Ar flow rate is increased. 100

(a) 0.6 40 0.76 120 (b) Etch Rate Etch Rate 0.54 35 fit - Etch Rate fit - Etch Rate 0.72rms Surface Roughness 100 rms Surface Roughness fit - rms Surface Roughness 0.48fit - rms Surface Roughness 30 0.68 80 0.42 25 m/min) m/min) μ μ 0.36 20 0.64 60

0.3 15 0.6 40 Etch Rate ( Rate Etch ( Rate Etch 0.24 10

rms SurfaceRoughness (nm) 0.56 20 rms SurfaceRoughness (nm) 0.18 5

0.12 0 0.52 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Ar Flow Rate (sccm) SF6 Flow Rate (sccm) Figure 2.19: Variation of rms surface roughness and etch rate as a function of variation in flow rates of (a) Ar and (b) SF6 gases during etching for SF6/Ar based chemistry. All other parameters are kept at their optimum value as in Table 2.2. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis.

0.675 500 0.7 960 (a) Etch Rate (b) 0.69Etch Rate 900 0.66fit - Etch Rate 450 fit - Etch Rate 0.68 840 rms Surface Roughness rms Surface Roughness fit - rms Surface Roughness 0.645 400 0.67fit - rms Surface Roughness 780 0.66 720 0.63 350 0.65 660 ess (nm) ess (nm) 0.64 600 m/min)

m/min) 0.615 300 μ μ 0.63 540 oughn 0.6 250 oughn 0.62 480 0.61 420 0.585 200 0.6 360 0.59 300 Etch Rate ( Etch Rate ( 0.57 150 0.58 240 0.555 100 rms Surface R Surface rms rms Surface R Surface rms 0.57 180 0.56 120 0.54 50 0.55 60 0.525 0 0.54 0 0 5 10 15 20 25 30 35 40 45 50 55 0 5 10 15 20 25 30 35 40 45 50 55 C4F8 Flow Rate (sccm) SF6 flow rate (sccm) (c) 0.64 560 (d) 0.6 600 0.6Etch Rate 520 fit - Etch Rate 0.56Etch Rate 540 0.56rms Surface Roughness 480 fit - Etch Rate fit - rms Surface Roughness rms Surface Roughness 0.52 440 0.52fit - rms Surface Roughness 480 0.48 400 0.48 420

0.44 360 ess (nm) m/min) m/min) 0.44 360 0.4 320 μ μ

0.36 280 oughn 0.4 300 0.32 240 0.36 240 0.28 200

Etch Rate ( 0.24 160 Etch Rate ( 0.32 180 0.2 120 0.28 120 rms Surface R Surface rms rms Surface Roughness (nm) 0.16 80 0.24 60 0.12 40 0.08 0 0.2 0 0 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 70 80 90 100 110 Ar Flow Rate (sccm) O2 flow rate (sccm)

101

However, when the flow rate of Ar is increased to 70 sccm, the etch rate drops and the rms surface roughness increases. This effect was confirmed by Li et al. [150] showing that the fluorocarbon etch rate decreases once the % of Ar gas additive to the etching gas mixture become more than 70%. This effect can also be attributed to the increased operating pressure inside the etching chamber due to enhanced flow rates of Ar gas.

As already shown in Figure 2.16(b), there is significant reduction in the etch rate and increase in the rms surface roughness with increase in the operating pressure inside the etching chamber. Additionally, with an increase in operating pressure the randomizing collisions experienced by the Ar and other charged species increases causing them to loose energy thereby making the sputtering process at the surface of the sample less efficient. Similar trends are obtained when flow rate of oxygen is varied from 5 sccm to 100 sccm (Figure 2.20(d)). However, the etch rate does not increase when flow rate of oxygen in increased from 5 sccm to approximately 50 sccm. This is because oxygen does not participate in the actual etching process but provides oxygen ions and radicals to scavenge carbon polymers formed on the surface of the wafer. Li et al. [153] have shown that there is no significant increase in ion flux density with increase in oxygen percentage in the reacting gas mixture and also that the flux of oxygen ions is small as compared to Ar ion flux for similar flow rates. It also provides ions which assist Ar and other charged species in sputtering the sample surface. However, it does not play an active role in the etching process. Hence the etch rate does not increase for initial increase in the oxygen etching process.

However, the rms surface roughness reduces significantly from 480 nm to ~ 30 nm when the flow rate of oxygen is increased from 5 sccm to 30 sccm. From 30 sccm to 102

70 sccm the improvement in rms surface roughness is not significant and it is almost constant. This is because at very low oxygen flow rates, there is insufficient removal of polymers formed on the surface thereby resulting in formation of micro-asperities on the sample surface due to micromasking resulting in high rms surface roughness.

With increase in oxygen flow rate the removal becomes efficient thereby yielding smooth surface finish. With further increase in the flow rate of oxygen above 70 sccm, the effect of high operating pressure kicks in thereby causing reduction in the etch rate and also increase in the rms surface roughness.

2.5.2.4 Effect of substrate temperature

Etch parameters were found to be rather independent of the substrate temperature as shown in Table 2.4 for both the gas chemistries. A slight improvement in the etch rate was obtained when the temperature was increased which means that elevated temperatures accelerate the kinetics of reactions occurring at the oxide surface. But this effect is minimal and improvements in etch rate obtained is rather insignificant.

Similarly, the effect of substrate temperature on the rms surface roughness was minimal with its value remaining essentially constant. An increase in substrate temperature should have an exponential effect on the chemical reactions at the surface according to the Arrhenius equation and hence should have had a profound impact on

Table 2.4: Variation of etch rate and rms surface roughness of etched samples, as a function of temperature of substrate holder, for both the gas chemistries.

SF6/Ar chemistry SF6/C4F8/Ar/O2 chemistry Temperature Etch Rate rms Surface Roughness Etch Rate rms Surface Roughness (°C) (µm/min) (nm) (µm/min) (nm) 5 0.498 2.1 0.5275 80 10 0.5 2 0.53 50 20 0.536 1.97 0.55 24.6 30 0.554 1.95 0.566 19.7

103

the etch rate and rms surface roughness. The observed independence of etch

parameters of the substrate temperature can be attributed to a couple of factors. First

and the principal reason for this is the thermal contact between the PyrexTM wafer and

the aluminum substrate holder; which is not perfect resulting in unsatisfactory back

side cooling by Helium. Second, the local temperature at the surface of the wafer is

rather large due to physical bombardment and hence small changes in the temperature

set on the chiller has little effect on the etch rate, which is primarily determined by

the local temperature at the surface. We believe that use of a thermally conductive

grease between sample and aluminum holder would cause the effect of temperature to

be manifested on the etch rate.

2.5.2.5 Effect of distance of substrate holder from ICP source

Lastly, we also investigated the effect of distance of substrate holder from ICP source

and temperature of the substrate holder on the etch rate and rms surface roughness of

(a) 0.55 56 (b) 0.56 300 Etch Rate 0.54Etch Rate 270 fit - Etch Rate fit - Etch Rate 0.5rms Surface Roughness 48 fit - rms Surface Roughness 0.52rms Surface Roughness 240 fit - rms Surface Roughness 0.45 40 0.5 210

m/min) m/min) 0.48 180 0.4 32 μ μ 0.46 150 0.35 24 0.44 120

Etch Rate( 0.3 16 Etch Rate( 0.42 90 0.4 60 rms Surface Roughness (nm) Roughness Surface rms (nm) Roughness Surface rms 0.25 8 0.38 30

0.2 0 0.36 0 110 120 130 140 150 160 170 180 190 200 210 110 120 130 140 150 160 170 180 190 200 210 Distance From Source (mm) Distance from Source (mm) Figure 2.21: Variation of rms surface roughness and etch rate as a function of variation in distance of substrate holder from ICP source during etching for (a) SF6/Ar based chemistry, and (b) SF6/C4F8/Ar/O2 based chemistry. All other parameters are kept at their optimum value as in Table 2.2 and Table 2.3. The solid line is the estimate of etch rate and broken line is the estimate of rms surface roughness as obtained from quantification equations presented in later section in this chapter of the thesis. 104 the etched features. From figure 2.21(a, b), as the distance of the substrate holder is increased thereby moving it away from the ICP source, the etch rate reduces and the rms surface roughness increases. For the SF6/C4F8/Ar/O2 based chemistry, while the reduction in etch rate is only 30%, there is a 10 times increase in the rms surface roughness. This is because as we move the substrate holder away from the ICP source, the uniformity of the reactive species and the aerial density of the energetic particles bombarding the oxide surface decreases. Hence this causes a significant increase in rms surface roughness. The decrease in etch rate is not significant because even though the incoming stream of reactive radicals and ions in less uniform, the bias experienced by them increases. For example, increasing the distance from 120 mm to 200 mm increases the bias at the substrate holder from 77 V to 108 V. Hence increased energy of the incident ions partially compensates for the non-uniformity of the incident stream of reactive species and ions.

2.5.3 Quantification of the Etching Process

For the quantification of the etch process, it is useful to define a quantitative measure of the etch rate and rms surface roughness in terms of process parameters. Etch characteristics which vary monotonically with respect to the process parameters can be easily modeled using power law. Use of such power law metrics, for parameters which do not vary monotonically with process parameters, results in significant errors in the quantization process. However such errors can be significantly reduced by use of additional higher order terms in the quantization metric. For the quantization process, the data was arranged in a m by (n+1) matrix, where m are the total number of runs and n is the total number of process parameters used in the quantization 105 process. The last column in the matrix consists of value of the etch parameter, i.e. rms surface roughness or etch rate, that is being quantized. This is followed by using mathematical software such as Mathematica® to regressively fit a nonlinear power law equation to the data by minimizing the least square error. The fitting equation can be expressed as

n 3 n k ln(W ) = ln(a0 ) + ∑ ai ln(PPi ) + ∑ ∑ a j ln(PPj ) (2.1) i=1 k=2 j=1 where, W is the arbitrary number relating etch characteristics to the process parameters, ai and aj are the fitting parameters, PPj are the process parameters whose effect on the etch characteristics are being quantized. Rewriting the equation by taking exponentials on both sides

n 3 n ai k W = a0 (∏ PPi )exp[ ∑ ∑ a j ln(PPj )] (2.2) i=1 k=2 j=1 which is the form of equation that is being used in this chapter to express the etch parameters in terms of process parameters. The higher order terms, given by the third term in equation (1) are required only when the variation of etch characteristics with respect to process parameters are not monotonic. We can call these terms as

“correction factors” to the power law model used for the quantization process. The correction terms are a result of interaction between different components of the process space or where the change in etch parameters as a function of process parameters is not monotonic. Without the correction factors the spread of data is significant and hence the description in terms of the reduced etch parameters becomes less meaningful. 106

The definition of such etch numbers based entirely on the process parameters enables rapid quantification and characterization of the etch process to yield the desired etch parameters and is useful particularly in high volume production environments. Also, such empirical equations can be used as the basis of statistical process control wherein the coefficients are determined and adapted in real time based on the output of the machine in terms of etch rate, rms surface roughness or any other etch parameter. This results in a rapid determination of process parameters to yield desired etch characteristics and process drift specifications in terms of machine parameters or any other extraneous factors, such as depositions on the side walls, drift in matching capability of the rf generators, drift in electronics or gauges, etc.

(a) For SF6/Ar Etch Process: From the least square fit to the data, an etch rate number (Wetch) was defined, as

W 0.52W 1.36Q0.135Q0.48T 0.065P0.2 W = ICP sub SF6 Ar sub process exp(−0.094(ln P )2 ) (2.3) etch D1.67 process

where WICP is the ICP power in Watts, Wsub is the substrate power in Watts, QSF6 is the flow rate of SF6 in sccm, QAr is the flow rate of Ar in sccm, Tsub is the substrate temperature during the process in ºC, Pprocess is the ambient pressure during the process in mTorr, and D is the distance from the ICP source of the substrate holder in mm. The etch rate can now be defined as

Retch = aWetch or ln(Retch ) = ln(a) + ln(Wetch ) (2.4)

where Retch is the etch rate in µm/min and “a” is a proportionality constant that relates etch rate to the etch rate number. The parameter a and the powers of the process parameters in equation (2.3) were determined using least square fit to the data. The 107

value of ln(a) from the least square fit from the data was obtained to be -3.2.

Expression of the data in this form results in the plot of ln(Retch) with respect to

ln(Wetch) to be a straight line with a slope of unity as shown in Figure 2.22 (a). A

surface roughness number (Wrough) was defined in a similar way as

-0.2 6.4 y=-3.228+0.9711x y=14.95+1.02x -0.4 5.6

-0.6 4.8

-0.8 4 m/min)) μ -1 3.2

-1.2 2.4

ln (Etch Rate ( -1.4 1.6

ln (rms Surface Roughness (nm)) 0.8 -1.6 (a) (b) -1.8 0 1.5 1.65 1.8 1.95 2.1 2.25 2.4 2.55 2.7 2.85 3 -14.4 -13.8 -13.2 -12.6 -12 -11.4 -10.8 -10.2 -9.6 -9 -8.4 ln (Wetch) ln (Wrms)

Q1.58 P 2.18 D5.726T 0.197 SF6 process sub Wrough = 3.173 2.8 1.172 (2.5) WICP Wsub QAr

where the parameters are defined as in equation (2.3). The rms surface roughness can

now be defined as

Rrough = bWrough or ln(Rrough ) = ln(b) + ln(Wrough ) (2.6)

The parameter “b” and the powers of the process parameters in equation (2.5) were

determined using least square fit to the data. The value of ln(b) from the least square

fit from the current data was obtained to be 14.95. The plot of ln(Rrough) to ln(Wrough)

lie along a straight line with a slope of unity as shown in Figure 22. Once etch rate 108 and rms surface roughness numbers are defined for a given etch tool and a given material, it can be used to predict the expected etch rate for any given set of process parameters.

(b) For SF6/C4F8/Ar/O2 Etch Process: Similar process of quantization was repeated for SF6/C4F8/Ar/O2 based chemistry. In this case the Wetch can be defined as

W 1.38W 0.68Q 2.78Q1.32Q 0.19 Q 0.23T 0.000424 W = icp sub Ar O2 C4F8 SF6 sub exp{}corr (2.7) etch D 0.465 P 0.47 1 where the correction terms can be defined as

corr = −0.42(lnQ )2 − 0.18(lnQ )2 (2.8) 1 Ar O2

where QC4F8, and QO2 are the flow rates of C4F8 and O2 in sccm, and the rest of the terms are as defined for equation (2.3). We need the correction factor in this case because the variation in etch parameters (etch rate and rms surface roughness) with respect to process parameters is not a monotonic function and also the coupling between different factors is significant. The etch rate can now be defined as

Retch = cWetch or ln(Retch ) = ln(c) + ln(Wetch ) (2.9)

where Retch is the etch rate in µm/min and “c” is a proportionality constant that relates etch rate to the etch rate number. As before, the parameter ln(c) was obtained to be -

19.95. Expression of the data in this form results in the plot of ln(Retch) to ln(Wetch) to be a straight line as shown in Figure 2.23(a). A surface roughness number (Wrough) was defined in a similar way as

W 66.39Q 30.13Q 0.78 Q 0.83 W = icp Ar C4F8 SF6 exp{}corr (2.10) rough W 1.79Q 50.5 D130.4 P 2.23T 0.67 2 sub O2 sub 109

0 8.8 y=117.8+1.009x y=-19.95+1x 8 -0.4 7.2

6.4 m/min)] -0.8 μ 5.6

-1.2 4.8

ln [Etch Rate ( 4 -1.6

ln (rms Surface Roughness (nm)) Roughness Surface (rms ln 3.2 (a) (b) -2 2.4 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 -114 -112.8 -111.6 -110.4 -109.2 ln (Wetch) ln (Wrms)

corr = −11()lnQ 2 +1.2(lnQ )3 +13.4(ln D)2 + 27.6(lnQ )2 2 Ar Ar O2 (2.11) − 6.8()lnQ 3 + 0.6 ()lnQ 4 + 0.2()ln P 2 − 0.04 ()lnT 2 − 4.8()lnW 2 O2 O2 icp

where the parameters are defined as in equation (2.7). The rms surface roughness

number can then be defined as

Rrough = dWrough or ln(Rrough ) = ln(d) + ln(Wrough ) (2.12)

where Rrough is the rms surface roughness nm and “d” is a proportionality constant

that relates rms surface roughness to the roughness number. The parameter d and the

powers of the process parameters in equation (2.11) were determined using least

square fit to the data. The value of ln(d) from the least square fit from the data was

obtained to be 117.8. Expression of the data in this form results in the plot of ln(Rrms)

to ln(Wrms) to be a straight line with a slope of unity as shown in Figure 2.23(b).

110

2.6 Conclusions

We have demonstrated a high speed dielectric etch process while maintaining control over the rms surface roughness of the etched features which is important for MEMS applications. We used an ICP-RIE system lined with magnets for generating high density plasma at minimum operating pressures. By use of 2000 W of ICP power, 475

W of substrate power, SF6 flow rate of 5 sccm, Ar flow rate of 50 sccm, substrate holder temperature of 20°C, and distance of substrate holder from ICP source to be

120 mm, we were able to obtain an etch rate of 0.536 µm/min and a rms surface roughness of ~1.97 nm was obtained. A maximum etch rate of 0.75µm/min was obtained however at a high rms surface roughness of 102 nm by increasing flow rate of SF6 to 50 sccm. By addition of 5 sccm of C4F8 and 50 sccm of O2 to the mixture of reacting gases, we were able to obtain an etch rate of 0.55 µm/min and an rms surface roughness of ~25 nm. Also, we demonstrated an etch rate of 0.7 µm/min at an rms surface roughness of ~800 nm by increasing the SF6 flow rate to 50 sccm while keeping all other process parameters the same. An etch rate of 0.67 µm/min at an rms surface roughness of ~450 nm was obtained by increasing the C4F8 flow rate to 50 sccm while keeping all other process parameters the same. Addition of CH4 did not contribute significantly to the etch rate while causing significant increase in the rms surface roughness. Using a standard factorial Design of Experiment (DOE) methodology, we were able to ascertain effect of various parameters on etch rate and rms surface roughness with only 74 samples. Additionally quantitative metrics called etch rate number and rms surface roughness number were defined by least square fitting the etch data to a function dependent entirely on the process parameters. The 111 demonstrated process can be used for rapid and controlled anisotropic etching of dielectrics for MEMS fabrication and packaging applications.

112

Chapter 3

DESIGN, FABRICATION AND CHARACTERIZATION OF QCM

3.1 Introduction

In this chapter, general concepts for designing, fabricating and testing quartz crystal microbalances (QCM) are presented. Section 3.2 deals with concepts on choice of electrode dimension in terms of its thickness and lateral extent (diameter) to achieve maximum Q-factor while at the same time minimizing the presence of spurious modes in the resonance spectrum of the resonator. Discussion is also included on the design of QCMs in inverted mesa configuration and the materials of choice for the

electrode of QCM crystal. Section 3.3 deals with issues relating to fabrication of

QCM arrays. Section 3.4 is devoted to measurement of resonance parameters of the

QCM and section 3.5 deals with preliminary device characteristics of the QCM, and

also the mass calibration measurements performed.

3.2 Design of Quartz Microbalance Array

To achieve mass sensing using an array of QCMs fabricated monolithically, it is critical that the interference between pixels be minimized. This is particularly important for high frequency QCM, because we are trying to measure fractional changes in the resonance frequency and any sort of cross coupling would result in a frequency signal due to an “event” on the nearby electrodes. In order to understand the concept of frequency coupling between adjacent principles, we first need to understand the principle of energy trapping in quartz resonators, which is the topic of the next section. 113

3.2.1 Energy Trapping and Spurious Modes

Pioneering work in the field of energy trapping in quartz resonators was done by

Curran & Koneval [161-164] and Mindlin et al. [165-167] in the 1960s. The following discussion is a summary of their work and lists important conclusions from their theoretical and experimental analysis of quartz crystals. We know from our

previous discussion that the application of an AC field on the electrodes of a quartz

crystal results in thickness shear distortions. The quartz crystal and the reference

scheme are illustrated in Figure 3.1 [164]. Using Mindlin’s notation and sinusoidal

excitation, the resulting waves propagating in the X direction are called as Thickness

Shear (TS1) and in the Z` direction Thickness Twist (TT3). The presence of flexural

waves, face shear waves, and extensional waves that normally coexist with TS wave

Figure 3.1: Schematic illustration of partially electroded AT-quartz wafer of infinite extent [164]. 114

has been neglected, but will be included in the discussion in the next chapter. Further,

the plane wave thickness shear resonance in the thickness or Y` direction is a cut off

frequency for waves propagating in the plane of the wafer. The thickness shear and

thickness twist waves with frequencies below cut off cannot propagate in any direction in the plane of the wafer. Let us consider the present situation in which the electrodes are defined in a limited portion of the AT cut wafer. Then we will have different cut off frequencies for the electroded (denoted by subscript “e”) and surrounding (denoted by subscript “s”) region of the electroded quartz crystal. These cut off frequencies, denoted by ωe and ωs respectively, divide the spectrum of interest

in three frequency ranges. Below ωe, TT3 and TS1 waves cannot propagate in either of

the regions and standing wave resonance cannot occur. Between ωe and ωs, waves

can propagate in the “e” region but not in the “s” region, and total internal reflection

occurs at the boundary between the regions. This is illustrated in Figure 3.2(a) [164].

Above ωs, waves can propagate in both regions (Figure 3.2(b)), so that vibratory energy generated in region “e” will propagate away and therefore cannot contribute to a localized standing wave response.

Excitation at frequencies between ωe and ωs will produce in the “e’ region trapped

waves that cannot escape into the “s” region. Because of boundary conditions, a

portion of this vibration energy fringes out into the cutoff region, but tails off

exponentially with distance away from the electrode (Figure 3.2(c)). Thus, trapped energy mode responses are usually acoustically isolated from other portions of the

wafer. At specific excitation frequencies, standing waves will occur in the “e” region,

resulting in trapped energy mode response. Its resonance or eigenfrequency is 115

dependent on the relative values of ωs and ωe and on the lateral dimensions of the “e” region with respect to the thickness of the

Figure 3.2: Schematic illustration of the principle of energy trapping [164].

b/2 Ps Ps Pe

b/2 x3

a a

Figure 3.3: Schematic illustration of plate with energy trapped structure. 116

plate “b”. It is obvious that a whole series of such responses could occur. These are

called the inharmonic overtone series; and the lowest of these is considered to be the

fundamental thickness shear response of the resonator. It should be noted that the

series ends at ωs, because at this frequency standing wave amplitudes approach zero

as the wave escape into the “s” region.

Using an idealized two dimensional model, which among other things, neglects the effects of coupling to flexural or face shear modes, depending on direction, an expression is derived for these eigenfrequencies as a function of ωe, ωs, electrode

diameter “2a” and wafer thickness “b” for both fundamental and overtone modes. An

expression for inharmonic overtone series can be obtained as follows. Let us consider

an idealized two-dimensional wafer of the form shown in Figure 3.3. The thickness of

the wafer is in x2 (Y`) direction and is of infinite extent in the x3 (Z`) direction.

Solutions of the wave equation for particle displacement u (in the x1 direction) for

thickness/twist modes propagating in the x3 direction are of the form

u = U sin(ηx2 )exp[ j(ξx3 −ωt)] . (3.1)

To satisfy the zero stress boundary condition at the major faces (∂u/∂x2 = 0 at x2 = ±

b/2), displacement u can have non-vanishing solutions only for

η = pπ /b , (3.2)

where p = 1, 3, 5, …, is the order of the harmonic overtone. Substitution of equation

3.1 into the wave equation

1 ⎛ ∂2u ∂2u ⎞ ∂2u ⎜c' + c' ⎟ = (3.3) ⎜ 55 2 66 2 ⎟ 2 ρ ⎝ ∂x3 ∂x2 ⎠ ∂t 117 gives the expression relating the propagating constants

1 ω 2 = (c' ξ 2 + c' η 2 ) (3.4) ρ 55 66

' ⎡ 2 2 ⎤ c66 ⎛ ω ⎞ ⎛ pπ ⎞ ξ = ' ⎢⎜ ⎟ − ⎜ ⎟ ⎥ , (3.5) c55 ⎣⎢⎝ v ⎠ ⎝ b ⎠ ⎦⎥

` 1/2 ` ` where v = ( c66 /ρ) is the velocity for propagation of shear waves and c66 and c55

` are elastic constants for the AT cut quartz. The elastic cross coupling constant c56 is very small for the AT cut and has been taken to be zero in this treatment.

Stress waves can propagate freely for all real values of ξ, but reduce to non- propagating vibrations that decay exponentially with distance for imaginary values of

ξ. The angular frequency ω = πpv/b, below which wave propagation cannot occur, is called the cut off frequency, and is the thickness shear resonant frequency in the x2 direction. Referring back to Figure 3.3, the electroded “e” and the surrounding “s” regions of the wafer will have cutoff frequencies that differ slightly because of the mass loading and electrode elastic effects of the electrodes. The cut off frequencies for the fundamental-mode propagation in the “e” and “s” regions, respectively, are

th given by ωe = πve/b and ωs = πvs/b. Cutoff frequencies for the p harmonic mode are in turn given by pωe and pωs. For each mode, resonant responses associated with limited electrode areas can occur only at frequencies between the mode’s respective

“e” and “s” cut off frequencies. These mode resonant frequencies, or eigenfrequencies, can be determined by application of boundary conditions at the edges of the electroded region x3 = ± a. 118

Solutions of the wave equation for the electroded and the un-electroded regions are of the form of equation 3.1. Continuity of particle displacement and shear stress across the interfaces at x3 = ± a, impose four boundary conditions on these expressions. As a result, non-vanishing resonant solutions that satisfy the following equation for symmetric TT3 modes can occur only at specific frequencies between ωe and ωs.

These frequencies satisfy the condition

γ s tan(ξea) = (3.6) ξe where,

2 ⎛ π ⎞ c' ⎡⎛ ω ⎞ ⎤ ξ = ⎜ ⎟ 66 ⎢⎜ ⎟ − p2 ⎥ (3.7) e b c' ⎜ ω ⎟ ⎝ ⎠ 55 ⎣⎢⎝ e ⎠ ⎦⎥ and

2 ⎛ π ⎞ c' ⎡ ⎛ ω ⎞ ⎤ γ = − jξ = ⎜ ⎟ 66 ⎢ p2 − ⎜ ⎟ ⎥ (3.8) s s b c' ⎜ ω ⎟ ⎝ ⎠ 55 ⎣⎢ ⎝ s ⎠ ⎦⎥ are obtained from equation (3.5). Substitution of equations 3.7 and 3.8 in equation 3.6 yields

2 ⎛ πa ⎞ c' ⎡⎛ ω ⎞ ⎤ ω p2ω 2 −ω 2 tan⎜ ⎟ 66 ⎢⎜ ⎟ − p2 ⎥ = e s (3.9) b c' ⎜ ω ⎟ ω ω 2 − p2ω 2 ⎝ ⎠ 55 ⎣⎢⎝ e ⎠ ⎦⎥ s e

The solution to this equation ω = ωte, which are the eigenfrequencies of all non- vanishing mode resonances, can be expressed more conveniently as a fraction of the frequency lowering 119

ω − pω ψ = te e , (3.10) pωs − pωe giving

⎧ ⎡ ⎤⎫ ⎪ 2 ⎛ ωe ⎞ ωe ⎪ 2 ⎨p − ⎢ pψ ⎜1− ⎟ + p ⎥⎬ ' ⎡ ⎤ ⎜ ω ⎟ ω ⎛ pπa ⎞ ⎛ c ⎞ ⎛ ⎛ ω ⎞ ⎞ ⎩⎪ ⎣ ⎝ s ⎠ s ⎦⎭⎪ tan⎜ ⎟ ⎜ 66 ⎟⎢⎜ψ ⎜ e −1⎟ +1⎟ −1⎥ = , (3.11) ⎜ ' ⎟ ⎜ ⎜ ⎟ ⎟ 2 ⎝ b ⎠ ⎝ c55 ⎠⎢⎝ ⎝ ωs ⎠ ⎠ ⎥ ⎧ ⎫ ⎣ ⎦ ⎪⎡ ⎛ ω ⎞ ⎤ 2 ⎪ ⎨⎢ pψ ⎜1− e ⎟ + p⎥ − p ⎬ ⎜ ω ⎟ ⎩⎪⎣ ⎝ s ⎠ ⎦ ⎭⎪ where it can be noted that the order of the harmonic p will cancel out of right hand side of this expression. Noting that this expression is of the form tan(α) = β, and can have only one solution or many, depending on the magnitude of α, where α = nπ+tan-1 β, equation 3.11 can manipulated to obtain a useful expression relating mode frequencies with resonator parameters.

We define Ω0 = ωe/ ωs. And p = 1, 3, 5, etc. is the order of the harmonic mode and n

= 0, 1, 2, 3, etc. give the symmetric inharmonic mode series for each value of p. It should be noted that fundamental and basic harmonic mode series are given by n = 0 and p = 1, 3, 5, etc.

Having found the formula for the inharmonic overtone modes, let us focus our discussion to the origin and quantitative description of trapped energy modes in AT- cut quartz crystals. In any piezoelectric element, a strong resonant response can be observed electrically only for those modes of vibrations that have a high mode Q- factor and/or large electromechanical coupling. In quartz with moderate to weak coupling, strong resonances are dependent on high mode Q-factor. For example using a half lattice bridge, the response of a mode with Q-factor of 1000 would be 40 dB 120 below that for a comparable mode with Q-factor of 100,000. However, even the weaker of these responses (which in many cases would be considered to be negligible as compared to the stronger) at any given time must contain approximately 99.9% of its incident energy as coherent vibrations.

An electroded area of limited extent on an infinite quartz wafer, or even on a finite wafer that in turn is mounted on low Q supports, can have a high Q-factor only if a very large fraction of its vibration energy is restricted to its electrodes and surrounding regions. The applications of energy trapping in case of such limited electroded resonators can be easily explained in terms of total internal reflection of vibrations at the edge of the electrodes. However, in case the extent of electrodes is very small as compared to the thickness of the wafer, then the effect of these total reflections at the edges of the electrode is limited. This is because there is a large leakage of vibrations through the volume of the wafer, wherein the influence of the edges of the electrode is minimal. In such cases where the extent of the electrodes is rather limited as compared to the thickness of the wafer, poor Q-factors are observed because of “inefficient” total internal reflection from the edges of the electrodes.

The total internal reflection can occur not only for the fundamental mode but also for the spurious inharmonic modes. If the reflected wave is equal in amplitude to the incident wave then we can say that “total” internal reflection has occurred, and there is no loss of energy in the form of refracted wave. On the other hand, if the normalized reflected wave amplitude is less than unity, then the response of the resultant mode must be relatively weak and will have a low quality factor. The 121 amplitudes of the reflected wave as a fraction of the amplitude of the incident wave can be obtained using wave-functions in the convenient exponential form as

⎡ ⎤ ue = ⎢Ae exp( jξe x3 ) + Be exp(− jξe x3 )⎥ ×sin(ηx2 )exp(− jωt) (3.12) ⎢1424 434 1424 434 ⎥ ⎣ INCIDENT REFLECTED ⎦ and,

us = As sin(ηx2 )exp(− jωt + jξs x3 ) (3.13) where again “e” and “s” refer to electroded and surrounding regions of the wafer. The usual boundary conditions of continuity of stress and displacement at the electrode edge x3 = a gives

Ae exp( jξea) + Be exp(− jξea) = As exp( jξsa) (3.14) and

ξe []Ae exp( jξea) − Be exp(− jξea) = ξs As exp( jξsa) (3.15)

Values of the ratio Be/Ae can be calculated as a function of frequency, if values of ξe and ξs are substituted in equations 3.14 and 3.15. However, conclusions can also be drawn from the form of the resulting Be/Ae equation, the knowledge of the frequency regions in which ξe and ξs are real and imaginary, and the relative magnitudes of these propagation constants.

For ωe<ωs<ω, both ξe and ξs are real and ξe > ξs. This gives

Be ξe −ξs = exp(2 jξea) (3.16) Ae ξe +ξs and, 122

B e < 1. (3.17) Ae

For ωe<ω<ωs, ξe is real and ξs = jγ is imaginary. Then

Be = exp2 j(ξea −θ ), (3.18) Ae

-1 where θ = tan (γs/ξe), and

B e = 1. (3.19) Ae

For ω<ωe<ωs, both ξe and ξs are imaginary and ξe < ξs. This gives

Be γ e −γ s = exp(−2γ ea) , (3.20) Ae γ e + γ s and

B e < 1. (3.21) Ae

From equations 3.17, 3.19, and 3.21, it can be concluded that modes of vibration associated principally with the electroded region can have strong responses and high

Q-factor only when their mode resonance (fte) falls between the resonance frequency of electroded (fe) and the surrounding region (fs). In addition to the fundamental or harmonic trapped energy modes, which obviously satisfy this condition, one or more inharmonic overtone modes could also have their mode resonance fall in this favorable region for high Q-factor. These inharmonics, if unwanted, would usually be called as spurious responses. A much more simplified empirical design criteria for 123 quartz resonators was suggested by Bechmann [168, 169], which has since become popular as the Bechmann’s criteria as is given by the following formula

2a M Ω ≤ n 0 (3.22) b p 1− Ω0

where Mn, is an empirically determined constant and is given as

n = 1...... M n = 2.17;

n = 2...... M n = 4.35; . (3.23)

n = 3...... M n = 6.53;etc.

From the detailed mathematical calculations given above, the following qualitative conclusions can be drawn –

(a) An elastic plate having a set of dimensions, bounded by reflecting edges, has

an overtone spectrum of discrete, inharmonically related frequencies.

(b) The boundary between the plated and the un-plated regions of an AT-cut plate

acts as a reflecting edge for all acoustic waves having frequencies less than

that of the resonant frequency of the un-plated area.

lowest frequency, then the plated area can be excited into resonance only at its

own harmonic frequency, i.e. only fundamental mode of resonance is

observed in the spectrum and spurious modes associated with inharmonic

overtone modes are avoided in the spectrum.

(d) According to equation 3.22, the spurious modes can be avoided by making the

electrodes of the resonator sufficiently small in diameter or by making the 124

electrodes of the resonator extremely thin. At the beginning of the discussion,

it was emphasized that a very small electrode diameter (2a) with respect to the

thickness of the resonator (b) results in leakage of energy into the region

outside of the electrodes due to “inefficient” reflection at the edges of the

electrodes. Use of very thin electrodes can cause large resistance associated

with the electrodes themselves which can cause lowering of the resonator

performance due to insufficient oscillation of the actuating AC field at its

electrodes. Hence, a balance between suppression of spurious modes and

achieving high Q-factor needs to be achieved.

Going back to equation 3.22, it indicates that the extent of the electrodes with respect to the thickness of the resonator should be less than a certain value to suppress the presence of spurious modes. This value is determined by the thickness of the electrodes. Since we are mostly working with the fundamental mode, hence p = 1 for our calculations. For example, for a 50 MHz and 34 μm thick crystal with electrode thickness of 200 nm of gold, in order to suppress the spurious modes and to achieve a high Q-factor a minimum electrode diameter to thickness ratio of 10 is required. We designed the resonator to have a diameter to thickness ratio of 30, and hence obtained unprecedented Q factor of 7500 in air and 2000 in water. At the same time, the spurious modes were observed for the particular resonator as shown in Figure 3.4.

However, for a different resonator which was ~90 microns thick and had a resonance frequency of 19 MHz, a maximum ratio of 17 could be tolerated for suppression of spurious modes. We designed the resonator to be of electrode diameter of 500 microns, thereby giving a ratio of 5.55 and no surprise, the spurious modes were 125

5E+2

0E+0

-5E+2

-1E+3

-1.5E+3 Rs (arbitraryunits) -2E+3

-2.5E+3

-3E+3 4.8E+7 4.88E+7 4.96E+7 5.04E+7 5.12E+7 5.2E+7 Resonance Frequency (Hz)

Figure 3.4: Presence of spurious modes in the resonance spectrum of the resonator with 2a/b of 15. A maximum ratio of 10 could be used according to the design criteria. 6.4E+3

5.6E+3

4.8E+3

4E+3

3.2E+3

2.4E+3

1.6E+3 Rs (arbitraryunits) 8E+2

0E+0

-8E+2

-1.6E+3 1.9E+7 1.92E+7 1.94E+7 1.96E+7 1.98E+7 2E+7 Resonance Frequency (Hz)

Figure 3.5: Absence of spurious modes in the spectrum of a resonator with 2a/b of 5.5. 126 suppressed as shown in Figure 3.5. However, due to “non optimal” reflections at the edges of the electrodes, the energy leaking into the surrounding regions of the QCM was not insignificant, thereby giving a low Q-factor of only ~2500 as compared to the previous resonator. Hence, when designing the resonator the diameter to thickness of the wafer as well as the thickness of the electrode should be chosen carefully so that optimum performance in terms of suppression of spurious modes along with maximum mode Q-factor is obtained. For the current work, the resonators were defined in an inverted mesa configuration, which is the topic of the next section.

In the present work, the value of ωe was obtained from measurement of the resonance

1.6E+2

1.4E+2

1.2E+2 )] 0 Ω 1E+2 /(1- 0 Ω [ √ 8E+1 2.27* 6E+1

4E+1

2E+1 0E+0 5E-9 1E-8 1.5E-8 2E-8 2.5E-8 3E-8 3.5E-8 4E-8 4.5E-8 thickness of electrode (nm)

frequency of the resonator. The value of ωs was obtained by adding the mass loading due to thickness of gold electrode according to the Sauerbrey equation to the value of

ωe. Figure 3.6 plots the value of right hand side of Bechmann’s criteria (equation

3.22) as a function of electrode thickness for gold electrode and for a crystal having thickness of 34 microns and diameter of the electrode to be 1 mm. The shaded portion of figure represents the region for the allowed thickness of electrode which will prevent formation of spurious modes and conserve the high Q-factor of the resonator.

3.2.2 Inverted mesa and energy trapping

It is desired that high frequency resonators operate in their fundamental mode to obtained maximum amplitude of oscillation. However, high frequency resonators operating in their fundamental mode are extremely thin. For example, a 50 MHz resonator operating in its fundamental mode will have a thickness of only ~35 μm.

Such thin resonators are extremely fragile and very difficult to handle. However, the use inverted mesa configuration enables fabrication of high frequency resonators.

Since the rims of the resonators are the thickness of the wafer typically 100 μm thick, they provide mechanical robustness to the resonator during handling and transportation. All the general energy trapping principles as described in the previous section are also applicable for the resonators fabricated in an inverted mesa configuration. Resonators in an inverted mesa configuration offer excellent acoustical isolation between adjacent pixels of the array since there is additional reflection at the boundary of the inverted mesa structure. However, this reflection can sometimes cause additional spurious modes to appear in the spectrum of the crystal as well. As shown in Figure 3.2(c), because of boundary conditions, a portion of this vibration 128 energy fringes out into the cutoff region, but tails off exponentially with distance away from the electrode. Hence, it is necessary to make sure that the electrodes are located sufficiently far from the walls of the inverted mesa structure so that this untrapped vibration energy dies down before it reaches the wall of the structure. In case of reflections, spurious vibrations might be sustained in the resonator due to reflection of evanescent energy from the walls of the inverted mesa structure. With this in mind, in the current study the electrodes were fabricated far away from the walls of the resonator. For example, the ratio of the diameter of the electrode to the diameter of the inverted mesa structure was kept at 0.5 in order to ensure that there are no reflections from the walls, as the leaked vibrational energy dies down before reaching the wall.

3.2.3 Choice of Materials for QCM Electrodes

There are several materials that can be used for fabricating the electrodes of the

QCM. But first we have discuss the important issue of aging of quartz crystals [170,

171], which is affected by material of choice for the electrode of the resonator. Aging is defined as the systematic change in frequency with time due to internal changes in the oscillator. Aging can be positive or negative. Occasionally, a reversal in aging direction is observed. At a constant temperature, aging usually has an approximately logarithmic dependence on time. Typical (computer-simulated) aging behaviors are illustrated in Figure 3.7, where A(t) is a logarithmic function and B(t) is the same function but with different coefficients. The curve showing the reversal is the sum of the other two curves. A reversal indicates the presence of at least two aging mechanisms. The aging rate of an oscillator is highest when it is first turned on. When 129

Figure 3.7: Computer-simulated typical aging behaviors; where A(t) and B(t) are logarithmic functions with different coefficients (from http://www.ieee-uffc.org/freqcontrol/quartz/vig/vigaging.htm). the temperature of a crystal unit is changed a new aging cycle starts. The primary causes of crystal oscillator aging are stress relief in the mounting structure of the crystal unit, mass transfer to or from the resonator's surfaces due to adsorption or desorption of contamination, changes in the oscillator circuitry, and, possibly, changes in the quartz electrode material.

The most commonly used materials for fabricating the electrodes of QCM are silver, gold and aluminum. Silver used to be one of the most widely used materials for electrode fabrication. Silver iodide or silver oxide layer were used historically to passivate the silver electrodes to make sure that the silver in the electrodes did undergo any chemical reactions with time, which could cause aging. However, silver is not compatible with modern functionalization requirements of QCM because of its high reactivity and hence was not used in the present QCM electrode design.

Aluminum is another commonly used material for high frequency resonators.

Aluminum adheres well to quartz because of the nature of the silicon to oxygen to 130 aluminum bonding. The acoustic impedance of aluminum closely matches that of quartz, thereby minimizing the effects of acoustic reflections at the quartz-aluminum interface. However, aluminum reacts slowly with oxygen to from Al2O3 or sapphire.

The result is that aluminum plated units usually exhibit rather poor aging characteristics with the frequency decreasing roughly logarithmically with time for periods up to a year or more. It is possible however, to minimize and to virtually eliminate aging due to oxidation of the aluminum electrodes by the use of anodic oxidation. However, with problems associated with aluminum aging and reactivity of aluminum with chemicals agents, the use of aluminum as electrode material was not pursued in this study. Also, the resonance frequency of the crystals was less than 100

MHz in the current study. However, with the use of higher frequency crystals achieved by aggressive micromachining techniques, it is expected that aluminum electrodes have to be used in the future because of its excellent acoustic impedance matching with respect to the quartz crystal.

Gold is also extensively used as an electrode material, especially in low frequency resonators and in those demanding excellent aging characteristics. Gold has the advantage of being chemically inert and also being easy to deposit. However, it does not adhere well to quartz and hence thin layer chromium has to be used as the adhesion layer. Also, its high density and low electric conductivity make it less compatible with high frequency resonators in which mass loading of the resonators seriously degrades the performance of the device. However, in the current study since we are using low fundamental frequency resonators of less than 100 MHz, and the potential use of the device as a mass sensor in which the surface of the resonator 131 needs to be functionalized with numerous chemical agents, it was decided to use the gold as the electrode material of choice.

3.3 Fabrication of Quartz Microbalance Array

Having developed the dielectric etch techniques for realizing inverted mesa configuration, as described in chapter 2 of this thesis, three by three arrays of resonators on 8 mm by 8 mm dies of AT-cut quartz were fabricated. The choice of 3 by 3 resonators was arbitrary, and yields 9 resonators per chip. The QCM design procedure as described in the previous section was followed wherein –

(a) The electrode edges were fabricated away from the edges of the inverted mesa

structure.

(b) The thickness of the diaphragm formed as a result of etching and the lateral

dimension of the electrode were chosen so that the spurious modes are

suppresses and at the same time, the highest possible quality factor is

achieved.

A generalized process flow for fabricating quartz resonators arrays is shown in Figure

3.8. Figure 3.9 (a), (b), and (c) show the three masks that were designed to define etch patterns and the top and bottom electrodes of the QCM array. The various steps in the fabrication of the QCM array are as depicted below –

(1) Defining Etching Mask: One inch double sided polished AT-cut quartz crystal

dies were obtained from Boston Piezooptics Ltd. The crystals were then

cleaned in Piranha solution (1:1 H2SO4:H2O2) for a period of one hour. The

crystals obtained were typically 100 μm thick. In order to reduce the defects 132 introduced into the crystal during handling and processing, the crystals were mounted onto 500 μm thick Pyrex wafer of similar lateral dimensions, using

Shipley® photoresist as the adhesion agent. After mounting, the whole assembly was baked at 125°C for 10 minutes to ensure removal of solvents from the photoresist. But such hard baking causes hardening of the photoresist which would ultimately cause removal of processed quartz discs from the

Pyrex mount wafer almost impossible. Hence, four holes were drilled into the

Pyrex mounting wafer to ensure that de-mounting solvent (any popular solvent, for example, acetone, or photoresist remover) can penetrate and dissolve the photoresist between the PyrexTM and quartz wafer in a timely fashion. For example, for one of assembly in which there were no holes in the

Pyrex wafers, the mounted assembly had to be left in the solvent for more than one week before all the photoresist was dissolved.

Subsequently, the mounted crystals were loaded in an evaporator and a thin layer of gold with chrome as an adhesion layer was e-beam evaporated onto one of the surface of the wafer. This was followed by lithographically patterning the gold/chrome layer using standard lithographic steps of photoresist spinning, exposure through a mask in EV601 aligner, developing for 60 seconds in 1:5 diluted MF 351 developer, followed by etching the exposed gold using Transene® TFA type etchant, and etching of chrome using a 1:5:25 mixture of ammonium cerium nitrate, concentrated HNO3 and de- ionized water in that order. The gold chrome pattern on top of the quartz wafer is shown schematically in Figure 3.10(a). It must be emphasized that 133

Clean and mount Quartz on Handle Wafer

Evaporate and lithographically pattern Au/Cr to define etch areas

Etch in ICP-RIE to define inverted mesa structures

Dicing of the etched wafer followed by stripping of Nickel in piranha clean

Definition of top and bottom electrodes

Figure 3.8: Generalized process flow for fabrication of quartz resonators. 134

Figure 3.9: Mask designs for (a) Etching inverted mesa structure, (b) Top electrode for the un- etched side, (c) mask for bottom electrode on the etched side. The process is a three mask process. Each mask results in four chips, each having three by three arrays of resonators on it. Out of these four chips, two chips have electrode diameter of 100 μm, one chip has electrode diameter of 250 μm, and the remaining chip has electrode diameter of 500 μm. 135

this the etching mask and not the electrodes of the QCM which are defined

first. This is because it was observed that the subsequent ICP RIE etching step

caused deterioration of the defined electrodes. Hence it was decided to define

the electrodes on both sides of the crystal after the ICP RIE etching step is

completed.

(2) Electroplating and dicing: A thick layer of nickel (8-10 μm) was subsequently

electroplated on the patterned seed layer of gold and chrome. Before

electroplating, it was ensured that the photoresist on the gold layer was

completed removed. Even a thin layer on photoresist on the gold surface

would prevent electroplating from proceeding. A pulsed electroplating power

supply was used to prevent the formation of uneven excessive deposits of

nickel on the edges of the defined patterns. Also, the electroplating solution

(obtained from Alfa Aesar™ Ltd.) was constantly stirred and replaced

frequently. This was done to make sure that the nickel deposited was of the

finest quality. Loosely bound poor quality of nickel can cause generation of

Figure 3.10(a): Schematic illustration of the patterned gold and chrome as seed layer for deposition of Nickel. 136 particles which would cause roughness on the surface of the etched diaphragms. After the electroplating step, the one inch mounted quartz disc was diced into four 8 mm by 8 mm chips. As indicated in step (1), each of these chips has 9 pixels, in an 3 by 3 array geometry. Three different electrode dimensions were chosen for fabrication. Two of these four chips had electrode dimension equal to 100 μm, one had electrode diameters equal to 250 microns and the fourth one had electrode dimension of 500 microns. Correspondingly, the dimension of the inverted mesa structure defined was 200, 500 and 1000

μm respectively. During dicing, the mounted quartz wafer is subjected to large mechanical forces. These forces are due to (a) high velocity water flow on top of the wafer that is used to cool the dicing blades, (b) shearing action of blade cutting the mounted crystal, and (c) general mechanical vibrations of the machines. Additionally, a lot of particles are generated by the cutting process which are spread everywhere on the wafer, even on the areas that need to be etched. Hence, before dicing, a thin layer of Shipley® 1827 photoresist was spun on top of the mounted crystal. Particles generated during the dicing process typically collected on this photoresist layer, which was subsequently washed away with acetone after the dicing process. Additionally, to protect the thinned resonator regions from vibration and forces created during dicing, the mounted crystal is placed face down on the blue tape. This ensured that the thin resonator area was not exposed to high pressure flow of air and water.

Additionally this also minimized the problem of particles sticking on top of the crystal. After dicing, the four chips with different electrode sizes are 137

collected and immersed in acetone bath. This accomplishes two things: one it

delaminates the resonator arrays away from the PyrexTM handle by dissolving

the interfacial binding photoresist, and second it removes photoresist from top

of electroplated nickel. Figure 3.10(b) shows the schematic of the 8 mm by 8

mm wafer with electroplated Nickel on top of it.

(3) Etching: After the cleaning step, the 8 mm by 8 mm chip is mounted on top of

a aluminum plate (4” in diameter) using Fomblin™ Oil. It is important that

the surface of the aluminum plate on which the crystal is mounted be

extremely smooth. It was observed that if the surface of the aluminum was

rough or had a step, cracks developed in the quartz wafer during the etching

process. Also, the thickness of the Fomblin™ Oil needs to be optimized. For

too thick a film of Fomblin™ Oil, the crystal “floats” on the oil and this result

in breakage of the crystal during the etching process. Also, if film of the

Fomblin™ Oil is too thin, then it does not support the crystal uniformly at all

the points during the etching process, again causing the crystal to break during

Figure 3.10(b): Schematic illustration of electroplated nickel on the patterned seed layer of chrome and gold. 138

the etching process. A slight variation of the optimized recipe from chapter 2

was used to etch the quartz wafer which is given below: ICP power 2000W,

Substrate Power 400W, Ar flow rate of 50 sccm, SF6 flow rate of 5 sccm,

temperature of substrate holder to be 10°C, distance of substrate holder from

the source to be 120 mm, and the pressure to be between 1 and 2 mTorr. As

given above, there are a few changes that were incorporated from the

optimized recipe of Chapter 2. One, the value of substrate power used is not

475W but is 400W. This is because the previous etching recipe was optimized

using PyrexTM wafers. PyrexTM has numerous metallic inclusions and

additives which form involatile products during etching. Hence, a higher

substrate bias power is required to sputter away these involatile products from

the surface of the wafer to achieve high etch rate at minimum rms surface

roughness. However, quartz is devoid of such metallic additives and is purely

SiO2. Hence a lower value of substrate bias achieves similar results. During

the etch process, high temperatures are generated. Quartz is known to undergo

phase transitions at a temperature of 573°C. To better assist heat dissipation

from the heated crystal during the etching process, the backside cooling

temperature was reduced from 20°C to 10°C. As we know from Chapter 2,

temperature does not play a critical role in etching. Figure 3.10(c) shows the

schematic of the quartz wafer after the etching step.

(4) Delineation of electrodes: After the etching process, the remaining nickel on

top of the chip is stripped in piranha solution (1:1 H2SO4:H2O2). This also

accomplishes removal of FomblinTM Oil and any other impurities and loose 139 particles from the surface of the wafer. After this cleaning step, the crystals are again mounted on one inch square Pyrex carrier pieces. Gold with chrome as an adhesion layer is evaporated on both of the sides of the crystal and patterned using double sided EV601 aligner and standard lithographic and wet metal etching processes as described in detail in Step 1. Figure 3.10(d) shows the schematic

Figure 3.10(c): Schematic illustration of inverted mesa structures formed in the quartz wafer after the etching step.

Figure 3.10(d): Schematic illustration of the three by three resonator array formed after the etching step. 140

1 mm 500 µm

8 mm

illustration of the fabricated array of resonators. Figure 3.11 shows the picture

of the fabricated device array and zoom in of the individual pixel of the array.

(5) Packaging the device: The resonator array needs to be packaged to make sure

that the fabricated device is in a mechanically robust encasing for protection,

for example during functionalization, during measurement and also during

storage and transportation. A novel custom scheme was devised to package

the quartz chips. A bunch of 24 pin DIP ceramic packages were procured from

Spectrum Semiconductors Ltd. A 5 mm by 5mm square hole was drilled into

the center of the package using a water jet cutting machine at Sky Top

machining, located near State College. This was followed by delineating a

ring of GE silicone adhesive on the flat un-etched face of the chip. Micro- 141

spatulas procured from VWR Scientific Inc. were used for this purpose. The

ring of silicone grease was used to glue the chip to the 24 pin package.

Silicone adhesive also served the purpose of creating a water tight seal

between the package and the quartz chip. The adhesive was allowed to cure

for 24 hours. This was followed by wire bonding the electrode pads on the

etched top side, followed by use of silver paste to connect the common

electrode on the bottom planar face to one of the pins of the package. After all

the electrical connections had been made, the package was flipped over. The

hole that was drilled into the package now serves as the reaction chamber with

the silicone grease acting as the water tight seal. Figure 3.12 shows the picture

of the packaged device.

3.4 Measurement of Resonance Parameters of QCM

An HP4294A impedance analyzer was used to measure the resonance parameters of the QCM. A program was written in Labview to automate the data logging.

Impedance and phase of the resonating crystal were recorded as a function of time.

The front panel of the Labview data acquisition program is shown in Figure 3.12. The impedance analyzer was compensated using open, source and load by creating custom packages which were similar to the packages used for packaging the quartz chip.

Using the command “EQUCPARS04” in the Labview program, the equivalent circuit parameters were also recorded on the personal computer. A program was written in

Mathematica, to extract the center resonance frequency and the Q-factor of the resonator from the data recorded on the personal computer. The values of resonance frequency and Q-factor extracted from the data using the Mathematica program were 142

Figure 3.12: Optical picture of a packages resonator array. We can see in (b) that the un-etched side is on the top. Also visible is the GE silicone used to create a water tight reaction chamber using the walls of the hole drilled using water jet cutting through the package. 143

in excellent agreement with the parameters obtained directly from the HP4294A analyzer.

The Mathematica program used in the current study is detailed in Appendix A.

A sample resonance curve and the fit are shown below in Figure 3.13. A standard

Lorentzian line shape function was used to fit the curves, as given below

⎛ f cos(φ) ⎛ f 2 ⎞ ⎞ A⎜ + ⎜1− ⎟Qsin(φ)⎟ ⎜ f ⎜ f 2 ⎟ ⎟ 2 3 ⎝ 0 ⎝ 0 ⎠ ⎠ fitfn = a0 + a1* f + a2* f + . (3.24) 0 0 f 2 ⎛ f 2 ⎞ + ⎜ − ⎟Q2 2 ⎜1 2 ⎟ f0 ⎝ f0 ⎠

The first three terms in the equation for the fitting function take care of the non-linearity

and asymmetry in the resonance curve. The last term in equation 3.24

a1 -78

-84 Phase (degrees)

-90

28280000 28580000 28880000 Frequency (Hz) Figure 3.13: Output of the Mathematica based curve fitting program showing the resonance curve in black and the fitted curve in red. Excellent fits can be achieved by use of this program. 144 represents the equation for a Lorentzian line shape, which is fitted against the resonance data from the quartz chip.

3.5 Operation of the device in liquid ambient

One of the biggest problems with use of miniaturized resonators for mass sensing applications is that it has been long believed that such small resonators would not have sufficient oscillation amplitude to sustain the vibrations in liquid ambient. But by strict control over the rms surface roughness of the etched membranes, the operation of the resonator in liquid ambient was demonstrated. Figure 3.14 shows that

7E+3 in water 6.5E+3 after 30 minutes after 34 minutes 6E+3 in vacuum

5.5E+3 3E+2 5E+3 1.5E+2 0E+0 4.5E+3 -1.5E+2

4E+3 -3E+2 3.5E+3 -4.5E+2

Rs (arbitraryunits) -6E+2

3E+3 -7.5E+2

2.5E+3 -9E+2

-1.05E+3 1.954E+7 1.956E+7 1.958E+7 1.96E+7 1.962E+7 1.964E+7 2E+3 Resonance Frequency (Hz) 1.5E+3

Rs (arbitrary units) 1E+3 5E+2 0E+0 -5E+2 -1E+3 -1.5E+3 -2E+3 1.956E+7 1.9572E+7 1.9584E+7 1.9596E+7 1.9608E+7 Resonance Frequency (Hz)

Also, the figure shows the subsequent increase in resonance frequency and Q-factor of the resonator with time as the water on the surface of the resonator evaporates.

3.6 Mass calibration experiments of the QCM

The miniaturized resonators were calibrated for mass sensitivity. To accomplish this, a simple experiment was devised. The pixels were loaded with a 0.1 mM solution of glucose solution. 0.5 µliter drops of solution were dispensed onto the electrode using a syringe pump. The dispensed volume was allowed to evaporate, leaving behind glucose. Frequency shift was then recorded after all the water had evaporated. Mass

1.25E+4

y=99.78x

1E+4

7.5E+3

5E+3 Frequency Shift (kHz) Shift Frequency

2.5E+3

0E+0 0 20 40 60 80 100 120 Mass Deposited (ng)

Figure 3.15: Frequency shift obtained upon mass loading as compared to the theoretical value. 146 sensitivity of 99.78 Hz/ng (theoretical value = 101 Hz/ng) was obtained as shown in

Figure 3.15.

3.7 Conclusion

To conclude, design, fabrication and testing of miniaturized ultrasensitive quartz crystal microbalance has been demonstrated. However, the QCM is still a non- specific platform and the following chapters will concentrate on attempts to impart specificity to the device by functionalization using single walled carbon nanotubes.

We will also report the unique behavior of carbon nanotubes to increase the Q-factor of the resonating crystal. In chapter 5, QCM is used to study gas adsorption behavior of isolated Single Walled Carbon Nanotubes.

147

Chapter 4

USE OF CARBON NANOTUBES TO INCREASE THE QUALITY

FACTOR OF THE RESONATORS

4.1 Introduction

In this chapter, the use of carbon nanotubes to increase the quality factor of the resonators is demonstrated. Fundamental concepts about carbon nanotubes, their physical, chemical, and electrical properties and their applications in various fields are summarized in Section 4.2. Section 4.3 deals with equivalent circuit parameters of a quartz crystal microbalance and their relation with the Q-factor. In section 4.4, the importance of Q-factor is emphasized along with techniques to measure the same.

Section 4.5 describes the experimental methodology to show that carbon nanotubes can increase the quality factor of the resonating crystal. The results of these experiments and a discussion are described in section 4.6. The theoretical basis and experimental evidence for the existence of out of plane flexural vibrations of quartz resonators and their suppression due to carbon nanotubes resulting in improvement in

Q-factor are presented in section 4.7 and Section 4.8 respectively. Section 4.8 also includes a discussion on Laser Doppler Vibrometry and its application to measure these out of plane vibrations of QCM.

4.2 Carbon Nanotubes for Functionalization of QCM

4.2.1 Introduction

Since their discovery by Iijima in 1991 [172], research in the area of carbon nanotubes has exploded. Their properties make them useful materials for diverse 148 applications. For example, the phenomena of electron confinement along the tube circumference makes the nanotube metallic or semiconducting, with quantized conductance wherein pentagon and hexagonal rings of carbon atoms constituting the nanotube structure generates localized states. They are direct band gap materials and their one dimensional band structure make them ideal for optical applications with a large bandwidth of 300 to 3000 nm. Carbon nanotubes also exhibit remarkable mechanical properties. They have one of the highest Young’s modulus of 1 TPa and a tensile strength of 100 GPa. These superior mechanical properties of carbon nanotubes can be attributed to σ-π hybridization. Additionally, the electron orbits circulating around carbon nanotubes impart the nanotubes their interesting magnetic and electromagnetic properties such as quantum oscillations and metal-insulator transition. The large surface area of nanotubes facilitates molecular adsorption, doping, and charge transfer, which is turn modulates their electronic properties. This allows the possibility of their use as sensitive chemical and gas sensors. Apart from these unique properties, the carbon nanotubes exhibit very high thermal conductivity, and exhibit quantum effects at low temperature.

Given the exceptional physical and chemical properties of carbon nanotubes, it is no wonder that they are currently being explored for their potential use in areas such as chemical and biological separation, purification and catalysis, energy storage, and as composites for coating, filling and structural materials. The electronic properties of carbon nanotubes make them ideal candidates for use as devices, for example, as probes, sensors and actuators, transistors, memories, logic devices, and other nano- 149

(a)

sp2

Deformed sp2

(b)

4.2.2 Structure of Carbon Nanotubes

A carbon nanotube (CNT) is essentially a hollow cylinder formed by rolling graphene sheets. Bonding in nanotubes is essentially sp2, with their circular curvature causing 150 quantum confinement and σ-π re-hybridization [173] in which three σ bonds are slightly out of plane and for compensation, the π orbital is more delocalized outside the tube, as shown in Figure 4.1 (a). This makes nanotubes mechanically stronger, electrically and thermally more conductive, and chemically and biologically more active than graphite. In addition, they allow topological defects such as pentagons and heptagons to be incorporated into the hexagonal network, to form bent and capped nanotubes. A single walled carbon nanotube (SWNT) is made of single sheet of rolled up graphene, whereas a multiple walled nanotubes (MWNT) are made of several coaxial nanotubes as shown in Figure 1(b). Nanotubes can be imaged and characterized using a variety of techniques including transmission electron microscopy (TEM), scanning electron microscopy (SEM), atomic force microscopy

(AFM), scanning tunneling microscopy (STM), electron diffraction (EDR), x-ray diffraction (XRD), Raman Spectroscopy, and several other techniques.

As already discussed, carbon nanotubes are a network of carbon atoms, arranged in

The honeycomb structure of carbon nanotube was experimentally verified using a

STM [176], with the image shown in Figure 4.2 (b). A carbon nanotube can be characterized by a vector C in terms of a set of two integers (n,m) corresponding to graphite vectors a1 and a2 (Figure 4.3) [177], such that

C = na1 + ma2 (4.1)

Thus, the SWNT is constructed such that the two end points of the vector C are superimposed, i.e. points A and O are superimposed. The nanotube can be semiconducting or metallic depending on the choice of n and m. It has been shown that metallic conduction in nanotubes occurs when

n − m = 3q (4.2) where q is a positive integer. This suggests that one third of the tubes are metallic and

Figure 4.3: A 2-D graphene sheet showing the indexing used for carbon nanotubes. The large dots denote metallic tubes while smaller dots denote semiconducting tubes [175]. 152 two thirds are semiconducting.

4.2.3 Growth of Carbon Nanotubes

Several excellent references are available on the growth and characterization of carbon nanotubes. Here a very brief summary of the growth methods is presented with emphasis on the nanotubes used in this work. Carbon nanotubes can be produced by two techniques, arc discharge [178, 179] (or laser ablation [180, 181]) or Plasma

Enhanced Chemical Vapor Deposition (PECVD) [182, 183]. SWNTs produced from arc discharge of graphite generally have fewer defects than those produced by any other technique, particularly for multi walled carbon nanotubes. This is because of higher temperatures associated with the arc discharge technique, allowing annealing of defects in the carbon nanotubes. In the case of SWNTs, the quality of nanotubes produced from arc discharge and PECVD methods is essentially equivalent.

Alternative growth methods, such as PECVD are popular because they allow for high volume production of nanotubes. Comparing the arc discharge and laser ablation methods, the former remains the easiest and cheapest method to obtain significant quantities of SWNTs, but the as produced SWNTs are less pure than those produced from the latter technique.

4.2.4 Modulus of Carbon Nanotubes

TB molecular dynamic methods and ab-initio methods [184] have predicted the

Young’s modulus of carbon nanotubes to be 1 TPa and 5-10% elastic limit of the tensile strain before failure. These desirable elastic and mechanical characteristics of carbon nanotubes come from in-plane covalent C-C bonds. Using the Tersoff [184] and T-B potentials [185], Robertson et al. [186] showed that the elastic energy of a 153 single walled CNT scales as R-2, where R is the radius of the tube. For axial strains, the Young’s modulus (Y) of a SWNT can be defined as

1 ∂ 2 E Y = (4.3) V ∂ε 2 where E is the strain energy and V is the volume of the nanotube, and ε is the strain in the material. Using theoretical calculations, Lu [187] has found that the Young’s modulus of a SWNT is around 970 GPa. Portal et al. found the Young’s modulus to be around 1.2 TPa. The Young’s modulus of a variety of carbon and also non-carbon nanotubes as a function of tube diameter was experimentally determined in a study by

Hernandez et al. [188]. Initial calculations of the value of Young’s modulus of carbon nanotubes by Hernandez et al. had yielded values close to 5.5 TPa. This was because a very small value of CNT wall thickness (~0.06 nm) was used in these calculations.

Taking a value of ~0.34 nm, a more realistic value of around 1 TPa is obtained. Since then, there have been several experimental studies confirming the Young’s modulus of carbon nanotubes to be around 1 TPa [189-193].

4.3 Equivalent Circuit Parameters of Quartz Crystal Microbalance

The resonating QCM can be modeled as an equivalent electrical circuit, consisting of a capacitor C0 in parallel with the series circuit comprising of Lm, Cm, and Rm, as shown in Figure 4.4. These equivalent circuit parameters for a resonating quartz crystal can be derived under some simplifying assumptions –

1. The quartz crystal is an infinitely large, thin plate. This reduces the problem to

one dimension. 154

Figure 4.4: The electrical equivalent circuit of a resonating QCM. This circuit is called Butterworth Van Dyke equivalent circuit, and represents the resonating crystal in terms of discrete impedance elements. The capacitance Cq represents the mechanical elasticity of quartz, the inductance Lq the initial mass, the resistance Rq the energy loss arising from viscous effects, internal friction, and damping induced by the crystal holder. The static capacitance C0 determines the admittance away from resonance, while the motional components dominate near resonance. 2. The displacement is considered to be a wave traveling in the thickness direction

and polarized in the plane of the thin plate.

3. Anisotropy effects are neglected.

4. The electrodes are assumed to be deposited directly on the plates with negligible

mass, and perfect electrical conductance.

5. A single mode of vibration with no coupling to other modes is assumed.

6. The thickness of the plate is taken to be in the y-direction, with the origin of

coordinates at the center of the plate. The thickness of the plate is h and the

surfaces are therefore at y = ± h/2 (Figure 4.9).

7. The strain is considered to be constant in a plane parallel to the plane y = 0.

The equation of motion of each point in the plate, including the effect of damping, is

∂ 2ψ ∂ψ ∂ 2ψ ρ + r = c (4.4) ∂t 2 ∂t ∂y 2 where, ψ is the mechanical displacement, ρ is the density of quartz, c is the appropriate elastic constant (generalized stiffness constant for the QCM), and r is the 155 damping coefficient. The solution to the above equation can be found using separation of variables, i.e. by assuming that the displacement ψ is the product of a function A(y) and an exponential function exp(jωt)

ψ = A(y) exp( jωt) (4.5)

Substituting this in equation 4.4, we get

ψ = [C1 sin(γy) + C2 cos(γy)]exp( jωt) (4.6) where γ is the complex quantity

1/ 2 ⎡ω 2 jωr ⎤ γ = ⎢ 2 − 2 ⎥ (4.7) ⎣ v ρv ⎦ and the wave velocity v = (c/ρ)1/2.

From the boundary condition that ψ = 0 at the center of the plate where y = 0, it follows that C2 = 0, leaving

ψ = C1 sin(γy)exp( jωt) . (4.8)

To evaluate the constant C1, we need to make use of the fact that the stress at the surface is due to the electric field alone; the mechanical stress due to internal forces is zero. This is not the case in the interior of the plate, where stress (and strain) results from the combined mechanical and piezoelectric stresses. At the surface where y =

0.5*h, the strain

∂ψ V = d E = d m exp( jωt) (4.9) ∂y ij ij h 156

where Vmexp(jωt) is the applied voltage, assumed to be sinusoidal. Differentiating equation 4.8 and evaluating it at y = 0.5*h, we get

∂ψ ⎛ γh ⎞ = C1γ sin⎜ ⎟exp( jωt) . (4.10) ∂y ⎝ 2 ⎠

Equating the last two expressions for ∂ψ/∂y and solving for C1, we get

d V C = ij m . (4.11) 1 γh cos(0.5γh)

Hence the solution to the equation 4.8 is,

d V ψ = ij m sin(γy) exp( jωt) . (4.12) γhcos(0.5γh)

Next we would like to derive a relationship between the applied electric voltage and the current across the quartz resonator. We can define polarization P as P = εij∂ψ/∂y, where εij is the piezoelectric stress constant. Then the charge density qv is given by

∂P ∂ 2ψ q = − = −ε . (4.13) v ∂y ij ∂y 2

Differentiating equation 4.9 twice with respect to y gives

2 ∂ ψ γd ijVm = − sin(γy)exp( jωt) . (4.14) ∂y 2 h cos(0.5γh)

Using Poisson’s equation

2 2 ∂ V qv ε ij ∂ ψ 2 = − = 2 , (4.15) ∂y kε 0 kε 0 ∂y 157

where k is the dielectric constant of quartz and ε0 is the permittivity of free space; we can rewrite eq. (4.14) as

2 ∂ V ε ijγd ijVm 2 = − sin(γy)exp( jωt) . (4.16) ∂y kε 0 h cos(0.5γh)

Integrating twice with respect to y, we get

ε ijγd ijVm V = sin(γy)exp( jωt) + C3 y + C4 . (4.17) γkε 0 hcos(0.5γh)

From boundary conditions that V = 0 when y = 0, we get C4 = 0.and using the second

1 boundary condition V = V exp( jωt) at y = 0.5*h, we get 2 m

⎡1 2ε ij d ij ⎤ C3 = ⎢ − 2 tan(0.5γh)⎥Vm exp( jωt) . (4.18) ⎣h γkε 0 h ⎦

Substituting in equation 4.17, gives the equation for the potential V(y) within the quartz plate

⎡ ε ij d ij sin(γy) y 2ε ij dij ⎤ V = ⎢ + − 2 tan(0.5γh)y⎥Vm exp( jωt) . (4.19) ⎣γkε 0 h cos(0.5γh) h γkε 0 h ⎦

The electric field

∂V E(y) = − (4.20) ∂y and thus

⎡ ε ij dij cos(γy) 1 2ε ij d ij ⎤ E = ⎢ + + 2 tan(0.5γh)y⎥Vm exp( jωt) . (4.21) ⎣kε 0 hcos(0.5γh) h γkε 0 h ⎦ 158

At the surface y = 0.5*h, and hence

⎡1 ε ij d ij 2ε ij d ij ⎤ E 1 = ⎢ + + tan(0.5γh)⎥Vm exp( jωt) . (4.22) y= h 2 2 ⎣h kε 0 h γkε 0 h ⎦

The current density at the surface of the resonator is

∂D i = . (4.23) s ∂t

But D = kε0E, and hence

∂E i = kε , (4.24) s 0 ∂t and hence the current density on the surface of the resonator is

⎡kε 0 ε ij d ij 2ε ij d ij ⎤ is = jω⎢ + + 2 tan(0.5γh)⎥Vm exp( jωt) . (4.25) ⎣ h h γh ⎦

The total current into the resonator, assuming the current density (current per unit area) to be constant over the surface A, is

⎡ ⎛ kε ε d ⎞ 2ε d ⎤ i = jωA⎜ 0 + ij ij ⎟ + jωA ij ij tan(0.5γh) V exp( jωt) . (4.26) ⎢ ⎜ ⎟ 2 ⎥ m ⎣⎢ ⎝ h h ⎠ γh ⎦⎥

The two terms inside the bracket of the above equation have the dimensions of admittance, since each is a current divided by a voltage. The first term

⎛ kε 0 ε ij d ij ⎞ jωA⎜ + ⎟ (4.27) ⎝ h h ⎠ is the admittance of a capacitor having a capacitance 159

⎛ kε ε d ⎞ ⎜ 0 ij ij ⎟ C0 = A⎜ + ⎟ . (4.28) ⎝ h h ⎠

If the piezoelectric constants were zero or the plate was completely clamped so that all mechanical strains were zero then,

kε C = A 0 . (4.29) 0 h

This is the capacitance of an ordinary parallel plate capacitor. The term ε ij dij is about

1% of ε0k, so that the capacitance of a parallel plate capacitor having a mechanically free quartz dielectric would be reduced by about 1% by clamping the plate to suppress the strain.

The second term in equation 4.26 represents admittance in parallel with C0. This admittance is obviously complex, since the quantity γ is complex. Therefore, the quartz plate with its electrodes is electrically equivalent to a capacitor in parallel with a complex admittance whose value depends upon the frequency. In the subsequent discussion, the nature of this admittance is investigated.

Equation 4.7 can be rewritten as

1/ 2 1/ 2 ⎡ω 2 jωr ⎤ ω ⎡ jr ⎤ γ = ⎢ 2 − 2 ⎥ ≅ ⎢1− ⎥ (4.30) ⎣ v ρv ⎦ v ⎣ ρω ⎦

Under the approximation that |jr/ρω|<<1, the above expression can be approximated as

ω jr ω γ ≅ − = − jβ . (4.31) v 2ρv v 160

sin(2x) − j sinh(2y) where β = r/2ρv. Further, from the identity tan(x − jy) = we can cos(2x) + cosh(2y) expand

⎛ ωh βh ⎞ sin(ωh v) − j sinh(βh) tan(0.5γh) = tan⎜ − j ⎟ = . (4.32) ⎝ 2v 2 ⎠ cos(ωh v) + cosh(βh)

The angular frequency ω may be written as ω0 – Δω, where Δω is always very small

(almost always less than 0.1%) compared with ω0 or ω. This is because appreciable mechanical response occurs only when the applied frequency ω is very nearly equal to the resonant frequency ω0. The quantity ωh/v can be written as

ωh ⎛ ω h Δωh ⎞ ⎛ 2πf h Δωh ⎞ ⎛ Δωh ⎞ = ⎜ 0 − ⎟ = ⎜ 0 − ⎟ = ⎜π − ⎟ . (4.33) v ⎝ v v ⎠ ⎝ v v ⎠ ⎝ v ⎠

Where the identity f0=v/2h has been used in the above expression. With this substitution, the equation 4.33 can be written as

sin(π − Δωh v) − j sinh(βh) sin(Δωh / v) − j sinh(βh) tan(0.5γh) = = (4.34) cos(π − Δωh v) + cosh(βh) − cos(Δωh / v) + cosh(βh)

Since (Δωh/v) is a very small angle, we can make the following substitutions:

2 ⎛ Δωh ⎞ Δωh ⎛ Δωh ⎞ 1 ⎛ Δωh ⎞ 1 sin⎜ ⎟ ≈ ; cos⎜ ⎟ ≈ 1− ⎜ ⎟ ; sinh(βh) ≈ βh; and cosh(βh) ≈ 1+ (βh) 2 ⎝ v ⎠ v ⎝ v ⎠ 2 ⎝ v ⎠ 2 (4.35)

With these approximations and algebraic simplification, equation 4.34 can be written as

2v Δω − jα r tan(0.5γh) = , where α = . (4.36) h Δω 2 +α 2 2ρ 161

The second term in bracket of equation 4.26 may now be written as

4 jvωAε ij d ij Δω − jα Y = . (4.37) m γh3 Δω 2 + α 2

Using the approximation γ ≈ ω0 / v = π / h and ω ≈ ω0 we get

2 4 jω0 Aε ij d ij Δω − jα Y = . (4.38) m π 2 h Δω 2 + α 2

The reciprocal to the admittance Ym is the impedance Zm, which is

π 2 h Z m = 2 (Δω + jα) . (4.39) 4 jω0 Aε ij d ij

The resistance part of Zm is

π 2 hr Rm = 2 . (4.40) 8ω0 Aε ij dij ρ

-1 -1 Expressing dij=(cki) ekj,, in a simple one dimensional case, c is simply equal to 1/c, so that d=ε/c. Substituting for d and recalling that the resonance frequency is given by

1 c f = , (4.41) 0 2h ρ

Eq. 4.40 can be rewritten as

π 2hrc h3r Rm = 2 2 or Rm = 2 . (4.42) 8ω0 Aε ρ 8Aε

The expression above for Rm shows that the motional resistance in the equivalent network is directly proportional to the damping constant r, and to the cube of the thickness of the plate. At the same time, Rm is inversely proportional to the area of the 162 plate and to the square of the piezoelectric stress constant ε. It is not possible to compute the numerical value of R, since no direct measurement of the value of r is possible. It must be recalled that r is assumed to include all dissipative forces, and that they are proportional to the particle velocity in quartz. Other sources of damping, in addition to internal damping, are air damping, surface friction, and mounting losses. In most cases, these are greater than the internal losses and it is unlikely that each is exactly equal to the particle velocity.

The reactive part of Zm is given by

Δωπ 2 h X m = − 2 . (4.43) 4ω0 Aε ij d ij

Eliminating d as was done in the derivation of Rm gives

Δωρh3 X = − . (4.44) m 4Aε 2

Thus Xm varies directly with –Δω, the difference between the frequency of resonance and the operating frequency. This is precisely the behavior of a circuit consisting of an inductance and a capacitance in series. Therefore the reactance Xm behaves as if it were an inductance Lm and capacitance Cm having the value

ρh3 8Aε 2 L = and C = . (4.45) m 8Aε 2 m π 2hc

The equivalent circuit parameters calculated in this way agree closely with experimentally measured values. In order to determine the theoretical expressions with the experimental results, the applicable values of piezoelectric coefficient for

AT-cut quartz are 163

' −2 2 ' 9 2 ε 26 = 9.65×10 C / m and c66 = 29.3×10 N / m . (4.46)

An AT cut quartz resonator vibrating in thickness shear mode can be characterized by

recording the spectrum of the magnitude and phase of the complex impedance of the

Figure 4.5: Simulated impedance spectrum from the BVD-equivalent circuit with marked resonance frequencies fZmin, fs, fp, and fZmax for the case of Rq > 0 [194].

crystal as a function of frequency. A typical spectrum of such a crystal is as shown in

Figure 4.5 [194]. Four discernable frequencies are observed, if there is damping in the

crystal which is true for most of the cases. The first characteristic frequency is fZmin,

which is defined as the frequency at which the magnitude of the amplitude is the

minimum, and is given by 164

1 1 ⎛ C R2 ⎞ ⎜ 0 m ⎟ fZ min = ⎜1− ⎟ . (4.47) 2π LmCm ⎝ 2Lm ⎠

The second characteristic frequency is the fs, which is defined as the frequency at zero phase at the low frequency branch and is given by

1 1 ⎛ C R2 ⎞ ⎜ 0 m ⎟ fs = ⎜1+ ⎟ . (4.48) 2π LmCm ⎝ 2Lm ⎠

The third characteristic resonance frequency in Figure 4.5 is fp which is defined as the frequency at the zero phase at the high frequency branch, and is given by

1 1 ⎛ C C R2 ⎞ ⎜ m 0 m ⎟ f p = ⎜1+ − ⎟ . (4.49) 2π LmCm ⎝ 2C0 2Lm ⎠

Finally, the fourth characteristics resonance frequency is given by fZmax which is defined as the frequency at maximum impedance and is given by

1 1 ⎛ C C R2 ⎞ ⎜ m 0 m ⎟ fZ max = ⎜1+ + ⎟ . (4.50) 2π LmCm ⎝ 2C0 2Lm ⎠

Apart from these characteristic resonances, the central resonance which is defined as the average of fs and fp is usually monitored for determining the change in resonance frequency of the resonator.

4.4 Importance of quality factor

The equivalent circuit parameters of the resonator are directly related to the quality factor of the oscillating crystal. This relationship is given by the following equation

2πf L 1 Q = s m = . (4.51) Rm 2πfsCm Rm 165

This equation indicates that the quality factor of the resonator is directly proportional to the motional inductance of the resonator, and inversely proportional to the motional capacitance and motional resistance of the resonating crystal. Hence, to improve the quality factor, we can either increase the motional inductance or reduce the motional capacitance or resistance. In this chapter, we provide a mechanism to increase the Q-factor of the oscillating crystal by decreasing its motional resistance

(Rm) of the resonator by incorporating single walled carbon nanotubes (SWNTs) on its electrodes.

As mentioned in the first chapter, the quality factor of the resonating crystal is very important since it determines the instantaneous frequency stability of the resonator.

From equation 1.27, the oscillator detection limit, i.e. the smallest frequency deviation that can be detected in the presence of noise is equal to

Δf (τ ) = σ y (τ ) f 0 . (4.52)

But the smallest level of noise generated (σy(τ)) by an oscillator and the quality factor of the resonator, Q, are related according to equation 1.29 as

1×10−7 σ (τ ) = . (4.53). y min Q

Also, the maximum product of resonance frequency and quality factor of the resonating crystal is given by equation 1.30 as

13 Qmax f 0 = 1.6×10 Hz (4.54)

Combining equation 4.52, 4.53, and 4.54, we get

1.6×106 Δf (τ ) = 2 (4.55) Qmax 166 which means that to achieve low frequency noise in the resonator, we should achieve as high a Q as possible. For example, for a crystal with a Q of 1000, the minimum noise in the resonator that can be achieved is 1.6 Hz. To represent the minimum mass resolution obtainable due to the frequency noise due to finite Q-factor, we can write the Sauerbrey equation using eq. 4.52 and eq. 4.53 as

⎛ ρ μ ⎞⎛ 9.6 ×10−8 f (0) ⎞ Δm = −⎜ q q ⎟⎜ 0 ⎟ (4.56). A ⎜ 2 f 2 (0)⎟⎜ ⎟ ⎝ 0 ⎠⎝ Q ⎠

Hence, it is imperative that the value of the quality factor is as high as possible.

Research efforts have been typically directed towards maximization of the Q-factor of quartz resonators via reduction of surface roughness, reduction of support losses

[195], making resonator surface convex to increase energy trapping [142], and reduction of resonator thickness to increase the drive efficiency, etc. In this work we present a new method for the improvement of the Q-factor of quartz crystal resonators based on the use of an over layer of single-wall carbon nanotubes

(SWNTs) to increase the quality factor of the resonator.

4.5 Experimental Methodology

4.5.1 Preparation of Carbon Nanotubes

The preparation of carbon nanotubes has been described recently [196]. Here, a short description of the preparation route along with general characteristics of the carbon nanotubes is presented. Soot derived from arc discharge method was procured from

Carbolux Inc. The as delivered material typically consists of bundles of hundreds of

SWNTs, 1-5 μm long, and with a mean tube diameter of 1.4 nm. Also, present in the 167 soot were ~20-30 wt% amorphous carbon and ~30 wt% of ~20 nm diameter carbon coated Ni-Y particles, which was used as a catalyst during the growth process. The procured soot was first subjected to dry oxidation in air to selectively remove the amorphous carbon, by subjecting the soot to 365°C for 90 minutes in a flow of dry air

(100 sccm). Next, the metal catalyst was removed using a reflux in acid solution, using a weakly oxidizing 6 N HCl solution for 24 hours. The solid residues, including the SWNT bundles, were then trapped by vacuum filtration on a 5 μm pore size polycarbonate membrane filter. With the filter still in place, the filtrate was washed with about 2 L of hot deionzied water. The solution in the bottom container of the vacuum filtration apparatus was observed to be light in color. Next, ~3 mL of pH 10

NaOH solution was poured over the filtrate to reduce the acidity, till the pH was 7.

Ultrasound was then used to disperse and debundled the purified SWNT bundles in amide solvents, called as N-methyl-2-pyrrolidone (NMP). Typically, a mass of 0.02 mg of SWNT was added per milliliter of solvent, and ultrasonic agitation was carried out for a period of 4 hours in a low power bath. The solution was then immediately centrifuged at 14000 rpm for 90 minutes, and the supernatant liquid containing debundled SWNTs was withdrawn for spraying onto the quartz resonator. The nanotubes were ~1/3rd metallic and 2/3rd semiconducting. They had a mean diameter of 1.4 nm and were typically 800 nm long. The density of the nanotubes in the solution with NMP as the solvent was ~10 μg/ml.

4.5.2 Coating the quartz resonator with carbon nanotubes

As already explained in the previous chapters, using an inductively coupled plasma etcher and SF6/Ar gas chemistry, we were able to etch AT-cut quartz at an etch rate of 168

~0.2μm/min using a 10μm thick, patterned, nickel over-layer as the mask. The rms roughness of the etched surface was found to be ~1 nm (peak to valley roughness of

2.5 nm) after an etch depth of ~70 μm. In an 110 μm thick AT cut quartz substrate, we etched quartz resonators of three different thicknesses 90 μm, 56 μm, and 33 μm with two electrode diameters of 1 mm and 500 μm. We were able to fabricate resonators with Q-factors ranging from ~500 to ~7500. A solution of debundled

SWNTs was then sprayed in controlled bursts over the QCM surface using an air brush. The NMP solvent was allowed to evaporate, leaving behind a randomly oriented, uniform deposit of SWNTs on the gold electrode and the surrounding quartz surface of each resonator. The resonator was connected to an Agilent 4294A impedance analyzer and the in-phase and quadrature impedance of the resonator around the resonance frequency was acquired in real-time using a computer and

Labview® based program. At resonance, the phase of the resonator was numerically fitted with a Lorentzian lineshape thus yielding the center frequency and the Q-factor.

The measurements were taken before and after coating the surface with the nanotubes, in laboratory atmosphere and in vacuum (~6.5x10-4 mbar). The results and their analysis presented in this chapter are for a representative sample having electrode diameter of 500 μm and thickness of ~56 μm.

4.6 Results and Discussion

As expected, upon sequential loading of the crystal with SWNTs, the resonance frequency of the crystal decreased according to the Sauerbrey equation (Fig 4.6) with an average of 3.27 ng of SWNTs deposited on the resonator surface for each loading step. Since SWNTs are known to be store house of gases [177], we suspected that 169 these gases could cause viscoelastic dissipation in the resonating crystal. The typical desorption time constants of gases from SWNTs has been reported to be several days

[197]. Hence the coated resonators were subjected to vacuum (~6.5e-4 mbar) over a period of 24 hours and 48 hours. It was observed that desorption over such time periods shows a characteristic power law rise with respect to time, as shown in Figure

4.7. This indicates that the desorption process is probabilistic with desorption rate decreasing as the number of gas molecules physisorbed, chemisorbed and trapped on

SWNTs decrease with time in vacuum. Also, it was observed that the Q-factor of the resonator increased by as much as 15% when kept in vacuum over a period of 24 hours. As shown in Figure 4.6, this trend of an increase in the Q-factor was consistent for all cases of SWNT loading. Similar results were obtained for all the studied resonators. Table 4.1 summarizes the results for three representative samples. It is important to note that a significant increase in the Q-factor was observed for all the measured resonators indicating that the carbon nanotube coating is effective in reducing the losses in all cases. While the reported resonators in this work are definitely not the highest Q-factor devices, since micromachined resonators with Q- factors as high as 50,000 have been earlier reported [142], however it should be noted that the current phenomena is specific for carbon nanotubes and seems to be applicable to resonators with wide range of Q-factors as depicted in Table 4.1. 170

29.428 1200 Resonance Frequency in Air Resonance Frequency in Vacuum 29.424Quality Factor in Air 1120 Quality Factor in Vacuum 29.42 1040

29.416 960

29.412 880

29.408 800

29.404 720 Factor Quality

29.4 640 Resonance Frequency (MHz) Resonance 29.396 560

29.392 480 0 1 2 3 4 5 6 7 8 910 Mass of Carbon Nanotubes (ng)

1200 Rise in the Quality Factor in Vacuum Power Law Fit: y=1258x0-184.2x-0.2581 1160 Decay in the Quality Factor upon exposure to Air Exponential Decay 1120

1080

1040

1000 Quality Factor Quality 960

920 ΔQ = 944 - 914 = 30

880 0 6 12 18 24 30 36 42 48 54 60 Time (Hours)

Q-Factor of Q-Factor of the Resonator Q-Factor of as Resonator Coated Coated with SWNT in Fabricated Resonator with SWNT in Air Vacuum

580 989 1136.6 949 1588 1924 6986.3 8188.6 15141.8

The change in the Q-factor can be related to the throughput of degassing from the

SWNTs which is given by [198]

a1 A QPV, degas = , (4.57) tα

where QPV,degas is the rate of desorption from the SWNTs, a1 is the degassing rate per unit area, A is the area of the surface over which SWNTs have been deposited, t is the time, and α is determined by the desorption throughput decay. From the experimental curve shown in Fig. 4.7, the value of α was obtained as 0.26, which as compared to 1 for mild steel, is small. This implies that desorption process from SWNTs decays slowly as compared to steel surfaces. This is to be expected since the available surface area for adsorption of gases in SWNTs is much more than in case of steel or other metals.

As shown in Fig. 4.7, the above process is observed to be reversible, wherein upon the release of vacuum and operation of the resonator in air, the gas molecules are readsorbed causing the resonator to revert back to near its original Q-factor before the application of vacuum. However, the recovery of the resonator Q-factor is not 100%.

For the resonator shown here, the Q-factor of the crystal loaded with SWNTs increased from 914 in air to 1170 in vacuum after ~30 hrs. However, even a prolonged re-exposure to air ambient decreased the Q-factor to only 944. This is consistent with published reports that uptake of gas molecules for SWNTs is much slower than desorption in a vacuum ambient [197]. Additionally, contribution is also expected from the irreversible volatilization of NMP molecules from the surface of the resonator after vacuum desorption from SWNTs. 173

The resonance curves were fitted with the Butterworth Van Dyke (BVD) circuit model [199] and values of static capacitance (C0), motional capacitance (Cm), motional resistance (Rm) and motional inductance (Lm) were extracted. The carbon nanotube coating is expected to act as a rigidly attached layer as observed by the frequency decrease of the resonator with the number of coatings of carbon nanotubes.

Analysis of the motional impedance parameters shows a small but clear increase in the motional inductance and a much smaller increase in the motional capacitance of the resonator. This is in accordance to the expectation that the added mass of the carbon nanotubes primarily affects the motional inductance. However, as shown in

Figure 4.8, a significant decrease in the motional resistance Rm with sequential

1200 Experimental Data in Air Power Law Fit: y=1.308e+007x-1.066 1100 Experimental Data in Vacuum Power Law Fit: y=1.041e+007x-1.039

1000

900

800 Quality Factor Quality 700

600

500 6400 8000 9600 11200 12800 Motional Resistance (Ω) Figure 4.8: Q-factor of the resonator as a function of the motional resistance of the resonator shows the expected 1/x dependence for both air and vacuum ambients as seen by the curve fits. 174 loading of SWNTs and upon subjecting the nanotube coated resonator to vacuum is observed. As shown in Fig. 4.8, the experimentally measured Q-factor showed a 1/Rm

dependence and is consistent with the expression Q = ωLm Rm [199], when as in this case the product of ω the parallel resonance frequency of the resonator and Lm shows little dependence upon the nanotube deposition.

4.7 Existence and Suppression of Flexural Vibrations in quartz resonators

In chapter 1, the concept of energy trapping was proved mathematically, using the simple assertion that the presence of electrode at the center of the quartz disc causes a difference in the mode frequencies of the electroded and the unelectroded regions. In deriving the energy trapping considerations for the resonating quartz plate, the energy dissipation in flexural modes of vibration was ignored by dropping the flexural rigidity term from the full dispersion relations for elastic waves in quartz plates. In this section, a mathematical description of the existence of flexural modes of vibration in quartz plate which is resonating in the fundamental thickness shear mode is provided. The coupling between the thickness shear mode and the flexural mode is an energy loss channel whereby energy is lost from the thickness shear mode into the flexural mode of vibration. The magnitude of this energy dissipation depends upon the ratio of the thickness of the quartz disc to the diameter of the electrode on it.

Hence, the quality factor of the resonator is also a function of this ratio. The mathematical relationship between the Q-factor and the ratio of the quartz thickness to electrode diameter is explored in this section.

In the case of energy trapping, a propagating thickness shear wave is excited in the part of the plate under the electrodes; but the corresponding wave of the same 175 frequency decays exponentially in the remainder of the plate; resulting in total internal reflection phenomena where the thickness shear vibrational energy is trapped in the region under the electrodes. Such is not the case for the flexural and extensional waves, which can propagate at any frequency. These waves are excited at the boundary between the electroded and the unelectroded portions of the plate, and propagate into both the regions; so that even at frequencies between the mode frequencies of electroded and surrounding regions (ωe and ωs as defined in chapter 1), some of the energy escapes from the electroded regions – mostly in the outgoing flexural wave. In the subsequent discussion, it is shown that the coupling between thickness and shear mode is minimum when the diameter of the electrode is approximately an integral multiple of the wavelength of the flexural wave in the electroded regions of the plate.

It was shown by Mindlin et al. [200-209]and also by Curran et al. [164] that for an

AT-cut resonator, three coupled equations are sufficient for describing the propagation of thickness shear, face shear and flexural vibrations propagating in the plane of the crystal blank. If the coupling with face shear component is neglected, the remaining equations of coupled thickness shear and flexural have the same form as

Timoshenko’s equations [210] of flexural vibrations of beams in which transverse shear deformations and rotatory inertia are taken into account. These equations are given by

⎛ ∂2v ∂ψ ⎞ ∂2v k 2c ⎜ + x ⎟ = ρ (4.58a) 1 66 ⎜ 2 ⎟ 2 ⎝ ∂x ∂x ⎠ ∂t 176

2 2 2 2 γ11h ∂ ψ x 2 ⎛ ∂v ⎞ ρh ∂ ψ x − k1 c66 ⎜ +ψ x ⎟ = (4.58b) 3 ∂x2 ⎝ ∂x ⎠ 3 ∂t 2

where x is the diagonal axis in the plane of the plate, v is the deflection of the plate, ψx is the rotation of a line element initially normal to the middle plane of the plate, ρ is the density, 2h is the thickness of the plate (Figure 4.9), k1 is the shear correction

2h′ h

h x

a a

Figure 4.9: Schematic representation of the frame of reference, dimensions of the crystal and the electrode.

factor, c66 is the shear modulus of elasticity in the plane normal to the plate through the x-axis and γ11 is the Voigt’s stretch modulus of the plate in the x-direction. For the

9 2 AT-cut quartz plate, c66 = 29.01 and γ11 = 85.93 in units of 10 N/m , as calculated from Bachmann’s values of the principal constants [168, 169]. The transverse shear force, Vx, and the bending moment, Mx, both per unit width of the plate, are given by

3 2 ⎛ ∂v ⎞ 2h γ11 ∂ψ x Vx = 2hk1 c66 ⎜ +ψ x ⎟ and M x = (4.59) ⎝ ∂x ⎠ 3 ∂x

Considering the same plate with electrode plating, on each face, of like thicknesses

2h′ and density ρ′ . An alternating voltage, impressed across the electrodes, is mechanically equivalent to a couple, C per unit area, distributed uniformly over the 177 plate. If the remaining coupling with the electric field is neglected and if the stiffness of the electrodes are neglected, the equations analogous to equation 4.58 are

2 2 2 ⎛ ∂ v ∂ψ x ⎞ ∂ v k1 c ⎜ + ⎟ = ρ(1+ R) (4.60a) 66 ⎜ 2 ⎟ 2 ⎝ ∂x ∂x ⎠ ∂t

2 2 2 2 2 γ11h ∂ ψ x ⎛ ∂v ⎞ C ρh (1+ 3R) ∂ ψ x − k1 c ⎜ +ψ ⎟ + = (4.60b) 2 66 ⎜ x ⎟ 2 3 ∂x ⎝ ∂x ⎠ 2h 3 ∂t where the bar-symbols pertain to the electroded regions and

2ρ′h′ R = (4.61) ρh i.e. R is the ratio of the mass per unit area of both electrodes to the mass per unit area of the plate. The transverse shear force and bending moment, per unit width of plated plates are

3 2 ⎛ ∂v ⎞ 2h γ ∂ψ ⎜ ⎟ 11 x V x = 2hk1 c66 ⎜ +ψ x ⎟ and M x = . (4.62) ⎝ ∂x ⎠ 3 ∂x

Mindlin et al. solved the above equations using numerical methods; to express the

shear correction factor k1 in terms of R by equating the thickness shear cut off frequency, obtained from equation 4.60, with that obtained from the solution of the three dimensional equation of elasticity. They obtained

C = v = 0 and ψ x = Aexp(iω1t) (4.63) where A is a constant. Then

2 2 3k1 c66 ω1 = (4.64) ρh2 (1+ 3R) 178

For simple thickness shear motion, the three dimensional equations reduce to

∂2u ∂2u c = ρ (4.65a) 66 ∂y2 ∂t 2

∂u T = c (4.65b) xy 66 ∂y where y is the coordinate normal to the middle plane of the plate, u is the displacement in the direction of x and Txy is the shear stress on planes normal to x or y. For

u = Asin(ηy)exp(iωt) (4.66) then equation 4.65(a) yields,

η 2c ω 2 = 66 . (4.67) ρ

As boundary conditions, Mindlin et al. took

∂2u T = 2ρ′h′ on y = ±h, (4.68) xy m ∂t 2 i.e. the inertia of the electrode plating is balanced by the shear traction on the surface of the plate. Substituting equation 4.68 and 4.65(b) in equation 4.66, we get

2 c66η cos(ηh) = 2h′ρ′ω sin(ηh) (4.69)

And with equation 4.61 and 4.67, we can get

Rηh tan(ηh) = 1 (4.70)

For R << 1, the smallest root of the above equation is given as 179

π (ηh) = . (4.71) 1 2(1+ R)

Upon substituting the above equation into equation 4.67, and the resulting expression for ω2 into equation 4.64, we get

2 2 2 2 π (1+ 3R) π c66 k1 = , and ω1 = (4.72) 12(1+ R)2 4ρh2 (1+ R)2

The corresponding shear correction factor and cut off frequency for the unelectroded plate (R = 0) are

π 2 π 2c k 2 = , and ω 2 = 66 (4.73) 1 12 1 4ρh2

From equation 4.72 and 4.73, we get

ω 1 =1+ R (4.74) ω1

For an applied voltage mechanically equivalent to C0cos(ωt), with C0 being a constant, a particular solution to equation 4.60 a and b, is

v = 0 (4.75) and

C0 ψ x =ψ 0 cos(ωt) with ψ 0 = . (4.76) 2 2 2 2hk1 c66 (1−ω ω1 )

Also equations 4.58 and 4.60 admit free wave solutions, given by

ψ x = Aexp[i(ξx −ωt)] and v = iαAhexp[i(ξx −ωt )] . (4.77) 180

ψ x = Aexp[i(ξx −ωt)] and v = iα Ahexp[i(ξx −ωt)]. (4.78) if the amplitude ratios, α and α , satisfy the equations

ξh 1+ γˆ ξ 2h2 − Ω2 α = = 11 (4.79) ξ 2h2 − 3Ω2 ξh

~ 2 2 2 ξh 1+ γ11ξ h − Ω α = 2 2 = (4.80) ξ h2 − 3rΩ ξh where

ω γ ˆ 11 Ω = and γ11 = 2 (4.81) ω1 3k1 c66

ω ~ γ11 Ω = and γ11 = 2 (4.82) ω1 3k1 c66

1+ R r = (4.83) 1+ 3R

The resonance of the plate is primarily thickness shear when the value of α and α are less than one. This does not mean that the flexural vibrations are not present. When the value of α and α are greater than one, then the vibrations in the quartz disc are

primarily flexural. As already discussed in chapter 1, in the frequency range ω1 < ω <

ω1, the thickness shear waves are propagating waves in the electrode region but are non-propagating waves in the unelectroded regions. However, from the preceding discussion we can conclude that such is not the case for flexural waves. Flexural waves generated at the interface of the electroded and the unelectroded regions, are propagating in both the electroded and the unelectroded regions at all frequencies. 181

These flexural waves are a source of energy dissipation in the crystal lowering its quality factor.

Mindlin et al. also solved the energy dispersion equations to calculate the quality factor of the crystal. According to the authors, the Q-factor of the crystal can be defined as 2π times the ratio of the energy per cycle in the electroded portion of the disc to the energy per cycle in the escaping flexural waves at resonance. Resonance can be identified as the frequency with maximum current through the crystal. This current is proportional to the integral of the surface charge over the electrodes; and

∂v the surface charge, in turn, is a linear function of the thickness shear strain +ψ . ∂x x

a ⎛ ∂v ⎞ Hence the criterion for resonance is the maximum of amplitude of ⎜ +ψ x ⎟dx . ∫−a ⎜ ⎟ ⎝ ∂x ⎠

The kinetic and potential energies, per cycle, in the electroded portion of the crystal are given by

2 2 1 Ta⎡ ⎛ ∂v ⎞ 1 ⎛ ∂ψ ⎞ ⎤ K = ⎢ρh(1+ R)⎜ ⎟ + ρh3 (1+ 3R)⎜ x ⎟ ⎥dxdt , (4.84) T ∫∫0 −a ⎜ ∂t ⎟ 3 ⎜ ∂t ⎟ ⎣⎢ ⎝ ⎠ ⎝ ⎠ ⎦⎥

2 2 Ta⎡ 2 ⎤ 1 ⎛ ∂v ⎞ 1 3⎛ ∂ψ x ⎞ U = ⎢k1 c66h⎜ +ψ x ⎟ + γ11h ⎜ ⎟ ⎥dxdt , (4.85) T ∫∫0 −a ⎜ ∂x ⎟ 3 ⎜ ∂x ⎟ ⎣⎢ ⎝ ⎠ ⎝ ⎠ ⎦⎥ where T = 2π/ω, is the time period. The energy per cycle that escapes in the form of flexural waves into the unelectroded portions of the disc is equal to work done per cycle by the transverse shear force and bending moment on sections of the unelectroded disc perpendicular to the x-axis: 182

T ⎛ ∂v ∂ψ x ⎞ U = −2 ⎜Vx + M x ⎟dt (4.86) ∫0 ⎝ ∂t ∂t ⎠

Mindlin et al. solved the above integrals to calculate the Q-factor as

2π (K +U ) Q = . (4.87) El

For example, for a partially plated electroded disc with ω1 ω1 = 1.0354, the value of the Q-factor was published by the authors as a function of a/h. As seen in Figure 4.10

[209], the quality factor is almost periodic function of a/h with nearly five orders of magnitude difference between the minima and the maxima. Hence, presence of flexural modes of vibration coexisting with thickness shear modes in a quartz crystal can result in large changes in the Q-factor of the resonating crystal. Or conversely, by suppressing these other modes of vibrations, we should be able to engineer large improvements in the Q-factor of the resonating crystal.

In real crystals, there are additional losses which adversely affect the Q-factor. Losses through internal friction and the losses through the crystal support would result in great reduction in the maxima of the Q-factor and a lesser reduction in the minima of

Q. Also, the coupling of the thickness shear mode with other modes, apart from flexural mode, such as face shear, extensional, etc. would cause an additional reduction in the Q-factor by offering additional channels of energy loss. The periodicity of the waves generated in the face shear mode might be completely different to that of the periodicity of the waves generated in the flexure mode, thereby considerably distorting the periodicity as observed in Figure 4.10. However, one thing is certain from the above discussion, and that the presence of “untrapped” flexural, face shear, extensional, etc. modes of vibrations coexisting along with thickness shear vibrations in a quartz plate serve as energy loss mechanisms thereby lowering the Q factor of the resulting resonator.

184

4.8 Experimental proof of Suppression of Flexural Vibrations in QCM

Thus far we have experimentally observed that the addition of carbon nanotubes on the surface of the quartz crystal unambiguously improves its Q-factor. Further, in the previous section we were able to show that in a real resonator, driving at the resonance frequency of thickness shear mode can induce flexural vibrations on the surface of the quartz crystal. Based on these two facts, we hypothesize that the presence of carbon nanotubes with their high elastic modulus stiffens the surface of the quartz resonator, thereby suppressing the out-of-plane flexural motion thereby improving the Q-factor of the resonator. SWNTs deposited on the surface of the resonator have very high modulus in the tensile directions (elastic modulus ~ 1 TPa

[211]). The out of plane vibrations of the QCM can be thought of as being equivalent to the up and down motion of a trampoline. However, due to the presence of the stiff carbon nanotube layer on the surface of the QCM, the flexure mode is suppressed thereby eliminating the energy loss channel through flexural vibrations. In this section, a direct proof of the hypothesis is will be described where a Laser Doppler

Vibrometer with displacement resolution in the picometer range is used to measure the suppression of these out of plane flexural vibrations of QCM in the presence of

SWNTs.

4.8.1 Principle of Laser Doppler Vibrometry

In this technique, a coherent laser light incident on a small area of the test object gets scattered and the Doppler shift of the scattered light is measured. The object under examination scatters or reflects the light from the laser beam and the Doppler 185 frequency shift is used to measure the component of velocity which lies along the axis of the laser beam.

As the laser light has a very high frequency Ω (approx. 4.74 x1014 Hz), a direct demodulation of the light is not possible. An optical interferometer is therefore used to mix the scattered light coherently with a reference beam. The photo detector measures the intensity of the mixed light whose frequency is equal to the difference frequency between the reference and the measurement beam. Such an arrangement can be a Michelson interferometer as shown in Figure 4.11.

A laser beam is divided at a beam splitter into a measurement beam and a reference beam which propagates in the arms of the interferometer. The distances the light travels between the beam splitter and each reflector are xR and xM for the reference mirror M and object O respectively. The corresponding optical phase of the beams in the interferometer is:

Reference ΦR = 2kxR

Measurement ΦM = 2kxM

with k = 2π/λ. One usually defines Φ(t) = ΦR – ΦM

The photo detector measures the time dependant intensity I(t) at the point where the measurement and reference beams interfere.

I(t) = I R I M R + 2K I R I M R cos(2πfDt + Φ) (4.88)

Where IR and IM are the intensities of the reference and measurement beams, K is a mixing efficiency coefficient and R is the effective reflectivity of the surface. The 186 phase Φ = 2πΔL/λ where ΔL is the vibrational displacement of the object and λ the wavelength of the laser light.

If ΔL changes continuously the light intensity I(t) varies in a periodic manner. A

(a) MIRROR

LASER OBJECT

PHOTO DETECTOR

(b)

Figure 4.11: (a) Simple schematic illustration of basic set up for Laser Doppler Vibrometry.(b) Detailed set up of laser Vibrometry. 187 phase change Φ of 2π corresponds to a displacement ΔL of λ /2. The rate of change of phase Φ is proportional to the rate of change of position which is the vibrational velocity v of the surface. This leads to the well known formula for the Doppler frequency fD-

fD = 2v / λ (4.89)

Due to the sinusoidal nature of the detector signal, the direction of the vibration is ambiguous. The directional sensitivity can be introduced by using an acousto-optic modulator (Bragg cell) into one arm of the interferometer. The Bragg cell is driven at frequencies of 40 MHz or higher and generates a carrier signal at the RF drive frequency. The movement of the object frequency modulates the carrier signal. The signed object velocity determines sign and amount of frequency deviation with respect to the center frequency fB. This type of interferometer is called heterodyne interferometer. With the introduction of a shift frequency fB the intensity at the detector changes to

I(t) = I R I M R + 2K I R I M R cos[2π ( fD − fB )t + Φ] (4.90)

The heterodyne solution has significant advantages. As only high frequency AC signals are transmitted there is no disturbance from hum and noise, introduced from all types of power supplies. Non-linear effects of the photo detector as well as all the signal pre-processing stages do not affect the integrity of the Doppler modulation content. The high efficiency of the Bragg cells (>98%) enables minimizing losses in it.

188

4.8.2 Results and Discussion

The set up for measuring out of plane vibrations in QCM using Laser Doppler

Vibrometry is shown in Figure 4.12. The use of the instrument was facilitated by the courtesy of Polytec® Inc. To ensure maximum amplitude of vibrations, the peak to peak amplitude of the sine wave used to cause vibrations in the quartz resonator was set at 10V. Also, in order to increase the reliability of measurements, the value of the amplitude of out of plane vibrations was calculated to be the average of more than

100 distinctly located points on the electrode of the QCM. The quartz resonator was driven at 29.5 MHz using a sinusoidal signal from signal generator. The out-of-plane motion of the quartz resonator was first measured with the surface covered with arbon nanotubes. The output of the vibrometer in the presence of carbon nanotubes is

CONTROL OUTPUT LASER FOR OPTICS VIBROMETER

LASER BEAM CONTROL and PROCESING UNIT DUT

SINUSOIDAL GROUND SIGNAL SIGNAL MEAUREMENT FUNCTION OUTPUT GENERATOR

Figure 4.12: Schematic illustration of the set up used for measuring out of plane flexural vibrations of QCM using Laser Doppler Vibrometry. 189 as shown in Figure 4.13(a). Since we were measuring displacements in the picometer range, it was necessary to reduce the noise of the machine and the electronics to be less than a few picometers. As can be seen from the figure, the average amplitude of out-of-plane vibrations is only 13 pm. We then removed some of the nanotubes from the surface of the resonator using an IPA solution and subjecting the vibrating crystal to vacuum of 1 Torr while the IPA solution was allowed to evaporate. Measurement of the out-of-plane vibrations of the QCM was again repeated and an average out-of- plane vibration amplitude of 16 pm was obtained as shown in Figure 4.13(b). This process was repeated two more times and each time due to removal of additional nanotubes from the surface of the QCM, a higher value of amplitude out of plane vibration (19 and 26 pm respectively) was obtained as shown in Figure 4.13 (c and d).

This experiment presents a direct proof of the hypothesis that the presence of carbon nanotubes on the surface of the quartz resonators acts to suppress the out-of-plane motion and thus increase in its Q factor of the resonator by reducing the available channels of energy dissipation in the resonators.

4.9 Conclusion

To conclude, the quartz crystal resonator was modeled as an equivalent circuit, wherein the elements of the equivalent circuit were derived as a function of physical and material properties of the quartz crystal. The equivalent circuit parameters were related to the quality factor of the resonating crystal, a large value of which is highly desirable. Subsequently, the use of carbon nanotubes to increase the quality factor of the resonators was demonstrated. Finally, the Q-factor of the resonator was found to have a strong dependence on the existence of the out-of-plane flexural modes in the 190 (a)

(b)

(c)

(d)

Figure 4.13: Graphs showing the output of the vibrometer depicting the amplitude of the out of plane vibration of the QCM. The amplitude of vibration is (a) 13 pm for the case when the surface is covered with nanotubes, and (b) 16 pm when some of the nanotubes are removed from the surface of the QCM. When more nanotubes are removed from the surface of the resonator, the amplitude of out of plane vibration of the QCM increases to (c) 19 pm and then to (d) 26 pm, respectively. 191 resonator, wherein these modes serve as energy loss channels. It was proposed that the use of carbon nanotubes prevents leakage of energy from the fundamental thickness shear mode into flexural modes, by suppressing their generation. This is because of the unique material properties of carbon nanotubes (specifically the very high modulus of ~1 TPa), which causes an increase in the quality factor of the resonating crystal. This was proved by directly measuring the amplitude of out-of- plane vibrations of QCM as a function of varying amounts of SWNTs on the surface.

It was found that the amplitude of the out-of-plane vibrations increased as the number of SWNTs on the surface was reduced by washing the resonator in IPA. In the next chapter, the use of QCM to investigate gas adsorption behavior of isolated single walled carbon nanotubes will be presented.

192

Chapter 5

WEIGHING MOLECULES WITH QCM INTEGRATED WITH

CARBON NANOTUBES

In this chapter, results on gas adsorption and desorption properties of the QCM

functionalized with carbon nanotubes are presented. Section 5.1 introduces the concept of gas interaction with carbon nanotubes and discusses the gas sensing

properties of carbon nanotubes and encompasses a detailed literature review of the scarce work done in this field. Section 5.2 deals with experimental set up and the methodology used for measurements. Results of the measurements are discussed in

Section 5.3 with details of the underlying phenomena used to explain the observed results. Finally, the chapter ends with Section 5.4 wherein future work is suggested to shed more light on the observed phenomena.

5.1 Interactions of gases with carbon nanotube

5.1.1 Gas Uptake by Carbon Nanotubes

Carbon nanotubes have nanometer sized pores that they enclose. In case the single walled carbon nanotubes (SWNTs) occur in bundles, the adsorption of gases can occur in the nanotube pores as well as in the interstitial spaces between individual SWNTs.

There are two kinds of interstitials that are formed; one formed at the junctions of walls of three tubes, and the second formed at the outside surface of the bundle, at the junction of two adjacent SWNTs. Pederson et al. [212] had suggested that carbon nanotubes act as nano-straws, wherein the induction of fluids inside the pore enclosed by them would be due to interactions similar to those that exist for wetting and 193 capillarity. Dillon et al. [213] have suggested that for open ended carbon nanotubes, large amounts of gases can be adsorbed in them owing to the “attractive potential of the pore walls”. They also demonstrated in their publication in the journal Nature that the carbon nanotubes can take up as much as 5-10% of hydrogen by weight at 133 K

[213]. This study sparked considerable interest in gas uptake and storage properties of carbon nanotubes and numerous theoretical and experimental studies have since been published on this idea. Most of these studies were for adsorption and uptake of hydrogen at the surface and interstitial sites of bundled carbon nanotubes. Darkrim and

Levesque [214] calculated hydrogen adsorption in a square array of SWNTs. They reported a very high density of hydrogen in carbon nanotubes at room temperature.

Mays et al. [215] on other hand have concentrated on hydrogen uptake at 77 K and have found 6 time higher density of stored hydrogen as compared to Darkrim et al.

Bundles of carbon nanotube bundles were envisioned to find applications as molecular sieves, nano test-tubes and hydraulic actuators etc. [216-218]. Since then the studies of gas adsorption and uptake in carbon nanotubes has been extended to other gases, such as noble gases [219], and other gases [220, 221]. The storage and uptake of gases in carbon nanotubes has important consequences. The ability of carbon nanotubes to store a large amount of hydrogen within their pores assumes significant importance in the current “oil deficient” economy, wherein the hydrogen powered cars and fuel cells based on hydrogen are being touted as the solution for the current and impending energy crisis. Gadd et al. [222] have suggested that the trapping of 133Xe within carbon nanotubes can be used to enhance its use in medical imaging (for example, imaging 194

the lymphatic system), where it would be extremely useful to confine the gas in some

way before injection in patient’s body.

5.1.2 Interaction processes of carbon nanotubes with gas molecules

Interaction of gas molecules with carbon nanotubes causes modulation in the electronic properties of carbon nanotubes, indicated by changed in their local density of electronic states [223, 224], electric resistance [225] and thermoelectric power

[226]. These properties are also strongly dependent on the specific gas molecule in

question, with distinct effect observed for different gases such as noble gases [227],

ammonia (NH3) [228], Nitrous Oxide (NO2) and cyclic compounds such as C6H2n

(where n is an integer from 3 to 6) [227]. Recently, changes in electronic properties of carbon nanotubes have been studied by monitoring thermo electric power (TEP) and electrical resistance of thin films of bundled nanotubes. The observed changes in TEP and electrical resistance have in turn been attributed to the carrier scattering associated with perturbation of tube wall potential caused by collision with gas molecules [197].

Such changes are possible since the carbon nanotubes are flexible in the radial direction, even though they are stiff in the tensile direction [229]. The collision of gas molecules with carbon nanotubes are expected to manifest themselves as mass which can be measured very accurately on a micromachined, ultra-sensitive QCM. The collision processes are also a source of viscous dissipation on the surface of the resonating crystal, which can be measured by the quality (Q-) factor of the QCM.

Additionally, owing to the attractive potential experienced by gas molecules both inside and outside of the carbon nanotubes, a small amount of gas molecules get physisorbed on the inner and outer surfaces of open ended carbon nanotubes. It is 195

considered that these physisorbed molecules manifest themselves as tightly bound mass on the QCM and hence do not cause viscous dissipation in QCM and

subsequently should not cause a significant change in the Q-factor of the QCM. In this

chapter, results are presented on change in resonance frequency and Q-factor of an

ultrasensitive QCM (sensitivity of 1 pg/Hz) due to collisional interactions as well as

due to physisorption of gas molecules near the walls of the SWNTs. To date, research

on gas uptake by carbon nanotubes and their interaction with gas molecules (or atoms)

has been limited to the case of bundled tubes wherein the contribution from groove

and interstitial sites play an important role in the adsorption and interaction processes.

Due to the advent of ultrasensitive QCM, we were able to deposit isolated SWNTs on

the surface and study gas uptake by isolated SWNTs, along with basic processes of

interaction of gas molecules (or atoms) with isolated SWNTs.

5.2 Experimental Details

Anisotropic wet etching techniques and the recently developed fluorine based etch

chemistries in high density plasma systems (presented in Chapter 2) can be used to

realize quartz crystal shear-mode resonators with thicknesses less than 30 µm,

diameters down to 100 µm and nanometer level surface smoothness [230, 231]. These

resonators can be easily configured as high sensitivity mass sensors and are known as

a quartz crystal microbalance (QCM) [232] (presented in Chapter 3). Until now, the

large size of the QCMs has limited their widespread use for bio (chemical) sensing.

Planar arrays of these mass sensors can now be realized, and without the drawbacks

associated with flexural components [233]. These micromachined QCM arrays

promise to be a robust platform for future (bio) chemical sensors. 196

As discussed in Chapter 1, the concept of mass measurement quartz resonators was

first presented by Sauerbrey who found that the frequency change Δf is related to the

mass loading Δm by[6]

⎛ 2 f 2 (0) ⎞ Δf = −⎜ 0 ⎟Δm (5.1) ⎜ A ρ μ ⎟ ⎝ q q ⎠

where f0(0) is the unloaded resonant frequency, μq and ρq are the shear modulus and

density of quartz respectively, and A is the area of the electrode on the quartz crystal

[234]. The minus sign indicates the resonance frequency decreases upon mass loading.

A micromachined 55 µm thick and 500 μm diameter resonator is expected to have a

sensitivity of ~1 pg/Hz, a factor of ~20,000 improvement in absolute mass sensitivity

in comparison to a commercially available 5 MHz device having an electrode diameter

of 1 cm [232].

The results presented in this chapter are for a resonator ~56 µm thick, and having an

500 µm (b) 1 mm

(a) (d) SWNT 8 mm

electrode diameter of 500 µm defined on a diaphragm diameter of 1 mm as shown in

Figure 5.1(a) and (b). A solution of debundled SWNTs (a mixture of ~1/3 metallic and

~2/3 semiconducting nanotubes procured from Carbolux Inc.) in NMP (N-methyl-2-

pyrrolidinone) was prepared along the route described in detail recently [235]. The

density of the solution was 10 mg/ml (mass of SWNT/volume of NMP). AFM

measurements were made to determine the fraction (~80-90%) of tubes appearing as

single isolated mostly open ended tubes on the substrate. No characterization

technique was used to check if the tubes used in this step were indeed open-ended. The

SWNTs were typically ~1.4 nm in diameter and ~800 nm in length as shown in Figure

5.1(c and d). The same solution was then deposited on top of the electrode of the QCM using a syringe. The NMP solvent was allowed to evaporate, leaving behind a randomly oriented, uniform deposit of SWNTs on and around the gold electrode pattern of the QCM. Approximately 40 ng of nanotubes were deposited on the surface of the resonator.

The resonator was connected to a HP4294A impedance analyzer and the in-phase and quadrature impedance of the resonator were monitored as the frequency was scanned and the resonance spectrum recorded into a computer using data acquisition software.

At resonance, the phase of the resonator was numerically fitted with a Lorentzian line

shape. A program in Mathematica® (See Appendix A) was written to fit the acquired

data to a Lorentzian function. From the best fit to the data, the center resonance

frequency and the Q-factor were extracted numerically. The resonance frequency and

Q-factor were measured after coating the surface with the nanotubes in the laboratory

atmosphere and in vacuum (~1x10-6 Torr). 198

In order to study the adsorption and desorption of gases from carbon nanotubes, the

coated resonator was subjected to vacuum for a period of 48 hours or more to get rid

of moisture and gases from the surface of the resonator as well as to remove any

remaining solvent residue from the carbon nanotubes. This was followed by

introduction of the gas at an overpressure of 5 psi into the chamber until the resonance

frequency was observed to have a reached an equilibrium value. The gases used in this

current study were that of He, N2, Ar, and SF6. These gases provide a reasonable range of molecular weights of gases, starting with 4 amu for He to 146 amu for SF6. The set

up used to introduce gas in the chamber is shown schematically in Figure 5.2. As can

be seen from the figure, the pressure and flow of gases at the gas cylinder were

controlled using a two stage high pressure regulator. Near the chamber (in which the

QCM was enclosed), the flow of gases was regulated using an on/off valve and a

needle valve. The protocol used for introducing the gases in the chamber is as follows:

To turbomolecular pump

Chamber enclosing QCM To gas cylinder

To roughing pump

Needle valve Manual Butterfly Valve Turn off valve High vacuum turn off valve Two stage pressure regulator

Figure 5.2: Schematic illustration of the valves and the chamber for the processes of “fill in” and “evacuation” as described in the text. 199

first the two stage pressure regulator was used to set the pressure at 5 psi with the

needle and on/off valve closed and the chamber being still in high-vacuum. Then the

chamber was isolated from the vacuum pump followed by opening of the on/off valve

and then the needle valve. Due to flow of gases into the chamber, the pressure on the

two stage high pressure regulator decreases from the set-value of 5 psi. At this stage

the two stage regulator was readjusted to ensure that the pressure is 5 psi. These steps to evacuate the chamber using the desired gas at the desired over pressure of 5 psi could not be repeated exactly for the all the experiments, and hence the transient behavior of change in resonance frequency and Q-factor were not analyzed in this

work.

Once the resonance frequency was observed to have reached an equilibrium value

after introduction of the gas, the chamber was evacuated. The experimental procedure

for evacuation of the chamber involved shutting off the two stage regulator, the pin

valve and the on/off valve. This was followed by using a manual butterfly valve to

evacuate the chamber using a roughing pump. After the pressure in the chamber has

reached less than 200 mTorr, the butterfly valve was closed and a turbomolecular

pump was used to evacuate the chamber to high-vacuum in the range of 10-6 Torr. In

earlier experiments, it was observed that opening the manual butterfly valve fully

caused unexpected frequency fluctuation in the QCM. Hence, in the current

experiments, the manual butterfly valve was opened only partially in order to make

sure that no sudden stresses were generated in the QCM due to sudden reduction in the

ambient pressure. Since the butterfly valve was manual, control over the percent

opening of the butterfly valve could not be controlled accurately from one run to 200

another. Therefore, the transient responses of the change in resonance frequency and

Q-factor with evacuation of the chamber were not analyzed as well. After using the

turbomolecular pump to evacuate the chamber, typical pressures of 1e-6 Torr or lower

were achieved in the chamber. The QCM loaded with SWNTs was subjected to

vacuum till the resonance frequency was observed to have reached an equilibrium

value.

Since the basic processes of desorption and adsorption were thought to be different for

open ended isolated SWNTs and closed ended bundled SWNTs, the open ended

isolated SWNTs deposited on the surface of the resonator in the previous step were removed by subjecting the resonator to an oxygen plasma (O2 flow rate – 150 sccm,

substrate bias – 100 W, time - 30 minutes, ambient pressure – 100 mTorr), wherein the

carbon nanotubes were removed as a result of reaction of carbon atoms comprising the

nanotube with oxygen radicals and ions forming carbon oxide based volatile products

which were pumped-out through the vacuum system. After the removal of the

“nominally” open ended isolated SWNTs from the surface of the resonator,

“nominally” close ended bundled SWNTs (dispersed in Isopropyl Alcohol commonly

called as IPA), were dispensed on top of the resonator. Approximately 90 ng of

bundled close ended SWNTs were deposited on the surface. The established procedure

of introducing the gases and then evacuating the chamber was then repeated.

Finally, the “nominally” close ended bundled SWNTs were removed from the surface

of the QCM using oxygen plasma and experiments were repeated for unloaded bare

gold coated surface of the QCM.

201

5.3 Results and Discussion

5.3.1 Bare Gold Coated Quartz Surface

For the bare surface of quartz subjected to an overpressure of gases (5psi) followed by

the evacuation of the chamber in which the QCM to ~1e-6 Torr (referred to as “fill in”

and “evacuation” from this point in the text), the change in resonance frequency and

quality factor was monitored in real-time during the two events and is as shown in

Figure 5.3. As can be seen from figure 5.3, when the QCM (without carbon nanotubes

present on the electrode) is subjected to an overpressure of 5 psi of He, N2, Ar, and

SF6, the resonance frequency decreases along with decrease in quality factor of the

resonator. In the case

when the chamber in which the QCM is kept is subjected to vacuum, the resonance

frequency and the quality factor increase. One of the interesting observations as a

result of this experiment was that the change in resonance frequency and quality factor

during the process of fill in and evacuation varied as square root of the molecular (or

atomic in case of He) mass of the gas species in question. The relationship is shown

graphically in Figure 5.4. The change in the resonance frequency and the Q-factor in this case can be primarily attributed to viscous loading by the ambient gas. Let us first derive the change in frequency and Q-factor of the QCM due to viscous loading by gas.

The concept of viscous loading of the QCM due to ambient fluid can be understood simply in terms of the classical kinetic theory of gases. The gas molecules around the

QCM are in constant motion. During the collision of these gas molecules with the electrode of the QCM, energy is transferred from the QCM to the gas molecule by 202

"fill in" bare quartz resonance frequency 50 He y=-30+30e-29.39x Nitrogen y=-72+72e-28.53x Argon y=-88+88e-15.69x -6.036x SF6 y=-148+148e 0

-50

-100

-150 Change in Resonance Frequency (Hz) Frequency Resonance in Change

(a)

-200 0 0.5 1 1.5 2 2.5 33.5 Time (hrs) "evacuation" bare quartz resonance frequency 200 He y=27-27e-26.61x Nitrogen y=70-70e-20.32x Argon y=85-85e-14.91x -11.87x SF6 y=165-165e

150

100

50 Change in Resonance Frequency (Hz) Frequency Resonance in Change

(b) 0 0 0.5 1 1.5 2 2.5 33.5 Time (hrs) 203 "fill in" bare quartz quality factor 2 He y=-1.6+1.6e -29.39x Nitrogen y=-3.85+3.85e-28.53x 0 Argon y=-5.11+5.11e-11.61x -7.52x SF6 y=-10.9+10.9e

-2

-4

-6

Change in quality factor quality in Change -8

-10 (c) -12 0 0.5 1 1.5 2 2.5 33.5 Time (hrs) "evacuation" bare quartz quality factor 12 He y=1.6-1.6e-26.61x Nitrogen y=4-4e -15.86x Argon y=5.11-5.11e-11.63x -9.262x 10 SF6 y=10-10e

4 Change in quality factor quality in Change

(d) 0 0 0.5 1 1.5 2 2.5 33.5 Time (hrs) Figure 5.3: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for bare quartz surface without any nanotubes. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question. 204 imparting the gas molecule a non-equilibrium component of translational velocity. For such a molecule to come back to the equilibrium state there has to be a collision with another molecule. Such transfer of velocity components, from the quartz surface to the gas molecules and from one gas molecule to other, results in exponentially decaying transverse (shear) waves to be generated in the gas layer in the vicinity of the QCM.

Typically, the decay length (δ) of the shear wave in the gas is given by the following expression [236]

η δ = g (5.2) πfρg

Where ηg is the viscosity of the gas, and ρg is the density of the gas in question. Values of δ for the four gases studied in this work are given in Table 5.1 at room temperature and

Table 5.1 Table depicting the value of δ for the four gases being investigated in the current experiments.

-6 ρ (kg/m3) η x 10 -2 δ (m) (at an overpressure of 5 psi) (N-s m )

Helium 0.219 18.6 9.57E-07

Nitrogen 1.533 16.7 3.43E-07

Argon 2.19 22.17 3.30E-07

SF6 7.9935 16.1 1.47E-07 205

Bare Quartz Mass Relationship 300 30 "fill in" resonance frequency 200 "evacuation" resonance frequency 20 "fill in" quality factor "evacuation" quality factor log (y)=1.213+0.4464log (x) 100 10 10 10 log10 (y)=1.125+0.5026log10 (x) 70 log10 (y)=-0.1372+0.5303log10 (x) 7 log10 (y)=-0.04875+0.4731log10 (x) 50 5

30 3 20 2

10 1 7 0.7

5 0.5 Factor Quality in change

3 0.3 change in Resonance Frequency (Hz) Frequency Resonance in change 2 0.2

1 0.1 3 4 5 6 7 8 910 20 30 40 50 6070 100 200 molecular weight (amu)

Figure 5.4: Change in resonance frequency and quality factor plotted as function of molecular (or atomic) weight of the adsorbate. The dashed lines are fit to the data and show a characteristic ~m0.5 relationship for change in resonance frequency and quality factor as a function of molecular weight (or atomic weight) of the adsorbate. 206

atmospheric pressure. As can be seen from the Table 5.1, the penetration depth of

shear waves is of the order of a few hundred nanometers which makes changes in this

layer manifest themselves as changes in frequency and quality factor of the oscillating

QCM.

The expression for change in the resonance frequency of an oscillating QCM as a

function of viscous drag of the ambient gas was given in detail by Stockbridge et al.

[237] in 1966. The analysis is adapted for the current case and is presented below. Let us define three mutually orthogonal axis with the x-axes parallel to the direction of motion of surface of the QCM, and z-axes being perpendicular to the surface of the

QCM surface. The classical equation of motion for the fluid may be written as

∂v ∂2v ρ x = η x (5.3) g ∂t g ∂z 2

where ηg is the viscosity of the gas, and ρg is the density of the gas in question, and vx

is the velocity of the particle motion in the x-direction. A solution to this equation was

given by Stokes in 1858, which can be expressed as

⎡ ⎛ 1 α ⎞⎤ ⎜ s ⎟ ψ x = Aexp⎢ jωt − jωz⎜ + ⎟⎥ (5.4) ⎣ ⎝Vs jω ⎠⎦

In this formula, ψx represents a wave traveling in the z-direction in the gas with

velocity Vs of wavelength λs with attenuation αs. Substitution of equation 5.4 into equation 5.3 yields

2 ⎛ 1 α ⎞ 2 ⎜ s ⎟ jωρg = −ηgω ⎜ + ⎟ (5.5) ⎝Vs jω ⎠ 207

Equating the real and imaginary parts of the above equation, we get

2ηgω 2ηg ρgω Vs = and λs = 2π and α s = . (5.6) ρg ρgω 2ηg

The classical shear impedance of the gas (Zgc) is given by

−1 ⎛ 1 α ⎞ ⎜ s ⎟ Z gc = Rgc + jX gc = ρg ⎜ + ⎟ = (1+ j) πfρgηg . (5.7) ⎝Vs jω ⎠

The above expressions are valid for purely viscous regime. During the processes of

“fill in” and “evacuation”, the QCM goes through a range of pressure when the time constant between collisions in the ambient gas is approximately equal to the time period of the oscillations of the QCM. In such a case, the gas should be considered as viscoelastic fluid (as a Maxwell Fluid). Then the viscosity of gas has an imaginary part to it which causes the classical impedance of the gas (Zgc) not to be equal to the impedance of the gas. But since such an effect is transitionary and our pumping speed relatively fast, we do not observe such an effect for our measurements. At very low pressure of 10-6 torr, the regime is molecular and hence there is little viscous damping of the QCM due to the ambient gas molecules. Hence for the current measurements, it will suffice just to calculate the difference in viscous drag at ambient and in low vacuum in order to calculate the change in resonance frequency. Since the viscous drag at low pressures is negligible as compared to viscous drag in ambient, we can say that the difference between the two is equal to the value of the viscous drag present in the ambient conditions of NTP. The expression in equation 5.7 is valid only if the oscillations of the quartz crystal are purely shear. In case of flexural vibrations in the 208 z-direction, contributions are towards frequency change are expected due to decreased viscous loading on the flexural mode of vibration of the quartz crystal.

Mason in 1947 [238] proved that the increase in virtual reactance of the electrode of the QCM is equal to the ratio of the change in mechanical reactance of the resonator and the imaginary part of the shear wave loading per unit area. In effect he showed that

Δm jΔX = jω . (5.8) m A

Now the value of Δm/A is given by the Sauerbrey equation and the value of ΔXm is equal to Xgc. Substituting for the two values in the above equation, we get

− Δf0 μq ρq πf0ηg ρ g = 2πf0 2 (5.9) 2 f0

Rearranging the above equation we get

3 / 2 − f0 ηg ρg Δf0 = . (5.10) πμq ρq

The above equation is called as Kanazawa-Gordon equation [239], since they were the first one to present this equation for viscous loading of QCM by liquids in 1985. Table

5.2 presents the value of the observed change in resonance frequency and the one calculated from the above equation 5.10 for the four gases. The predicted frequency change using the Gordan-Kanazawa equation are nearly 80% of the measured frequency changes indicating the predominant effect in the resonator performance at ambient conditions in various gas environments as arising from viscous damping. The 209

~20% mismatch between the two values, is thought to arise due to the following factors

(a) The viscous loading is more in case when random roughness is presented on

the metal electrode of the QCM [240-243]. We suspect that in the present case,

since the

rms surface roughness of the metal electrodes of the QCM was not equal to zero,

the change in resonance frequency due to viscous damping is larger than that

predicted by Kanazawa equation. The Kanazawa equation is valid only when the

surface is perfectly flat and atomically smooth.

(b) The contribution from a small and reversible adsorption of gas molecules on

the gold coated surface of the QCM is expected which is further likely to

account for the difference.

Coming back to equation 5.10, the change in resonance frequency due to viscous damping is primarily due to the change in the density of the gas with change in pressure. All other parameters are approximately constant with ambient pressure of gases, even the viscosity of the gas is primarily dependent on the temperature and not the pressure near atmospheric conditions. Writing the ideal gas law, we have

PV = nRT (5.11) where P is the ambient pressure, V is the volume, n is the number of moles of gas present in the volume V, R is the gas constant and T is the temperature. We can express the ideal gas law in terms of density of the gas as follows 210

Table 5.2 Listing of calculated change in resonance frequency as given by the Kanazawa

− f 0 ωρη 2 equation ( Δf 0 = ). THe value of Rq in this expression is given as πRq 6 -2 -1 Rq = μq ρq = 8.83×10 kg m s . There is a small difference between the calculated and experimentally obtained values of resonance frequency which can be attributed to the non zero surface roughness of gold electrode and also to the physisorption of gases on gold at room temperature.

3 ρ (kg/m ) η x 10-6 Theoretically Experimetnally

(at an overpressure -2 Obtained Δf Measured Δf of 5 psi) (N-s m ) 0 0

Helium 0.219 18.6 20.66 27

Nitrogen 1.533 16.7 51.79 70

Argon 2.19 22.17 71.33 84

SF6 7.9935 16.1 116.14 155

Table 5.3 Listing of calculated change in quality factor and the experimentally observed change in quality factor for bare quartz surface with gold electrode.

3 ρ (kg/m ) η x 10-6 ΔQ ΔQ (at an overpressure -2 RL theoretical exp erimental of 5 psi) (N-s m )

Helium 0.219 18.6 9.59 1.65 1.6

Nitrogen 1.533 16.7 24.04 4.13 4

Argon 2.19 22.17 33.10 5.69 5

SF6 7.9935 16.1 53.90 9.27 10

211

mRT m (MW )P ∂ρ MW PV = ⇒ ρ = = ⇒ = (5.12) MW V RT ∂P RT where MW is the molecular or atomic weight of the gas in question, m is the mass of the gas enclosed in a volume V. Hence the change in density with pressure is proportional to the molecular weight (or atomic weight) of the gas in question.

According to equation 5.10, the absolute change in resonance frequency due to viscous damping is proportional to square root of density of gas. Hence, the absolute change in resonance frequency due to viscous damping with change in pressure is proportional to square root of molecular (or atomic) weight of the gas in question. This is why we observe the MW0.5 relationship for change in resonance frequency as depicted in

Figure 5.4.

The observed changes in quality factor of the resonator during the events of “fill in” and “evacuation” can be similarly explained. As mentioned in previous chapters, the quartz resonator can be expressed in terms of an equivalent circuit called as

Butterworth Van Dyke equivalent circuit. In case of viscous loading, the gas expresses itself in the form of a resistance (RL) and an inductance (LL) in series with the motional parameters. Martin et al. [244] have derived the values of the load resistance and load inductance due to viscous damping by gas in terms of material parameters of quartz, the gas and the resonance frequency as

1/ 2 π ⎛ ρ gη g ⎞ R = ⎜ ⎟ (5.13) L 2 ⎜ ⎟ 4K C0 ⎝ 2ω0 μ q ρ q ⎠

RL and LL ≅ . (5.14) ω0 212

Where K2 is the electromechanical coupling coefficient of quartz (=7.74x10-3),

-13 ω0=2πf0, and C0 is the static capacitance of quartz (=1.2x10 Farads in the current case). All other parameters have already been defined in the text. As evident from the above equation, for a given change in load resistance due to viscous damping the change in the load inductance is insignificant (since ω0 is typically a very large number). We can then write the quality factor of the resonator as

ω (L + L ) ω L Q = 0 q L ≈ 0 q , (5.15) Rq + RL Rq + RL

where Lq and Rq are the motional inductance and capacitance for the quartz, and LL and

RL are terms due to viscous damping from the gas and since LL << Lq.

During the event of the “fill in” and “evacuation”, only the values of RL changes which means

−ω0 Lq ∂Q = 2 ∂RL . (5.16) ()Rq + RL

The value of change in load resistance can be obtained from equation 5.13, and then substituting that value in equation 5.16, we can obtain the value of the change in quality factor as:

− ω0 Lq ∂Q = ∂RL (5.17) 1/ 2 2 ⎛ π ⎛ ρ η ⎞ ⎞ ⎜ R + ⎜ g g ⎟ ⎟ ⎜ q 4K 2C ⎜ 2ω μ ρ ⎟ ⎟ ⎝ 0 ⎝ 0 q q ⎠ ⎠ 213

The value of Lq and Rq were obtained from Labview as fit to the resonance data (in high vacuum conditions). Table 5.3 shows the value of expected change in quality factor and the obtained change in quality factor.

Again, we observe in Figure 5.4 that the variation in quality factor for bare quartz for both the “fill in” and “evacuation” steps follows ~MW0.5 relationship. This is because the change in RL according to equation 5.13 is dependent on square root of density of gas which was shown in equation 5.12 to be proportional to molecular (or atomic weight) of the gas in question. Hence using simple kinetic theory of gases, the ~MW0.5 relationship observed for change in resonance frequency and quality factor during the

“fill in” and “evacuation” event in the case of bare gold coated quartz surface can be explained with relative ease.

5.3.2 Addition of Carbon Nanotubes to Bare Gold Coated Surface Of Quartz

As mentioned in the section on experimental details, the QCM was then loaded with

“nominally” open ended isolated Single Walled Carbon Nanotubes (SWNTs). The weight of the deposited nanotubes as already mentioned in the experimental section was approximately 40 ng. The SWNT coated surface of quartz was subjected to the processes of “fill in” and “evacuation”, and the change in resonance frequency and quality factor during the two events is as shown in Figure 5.5. In this case also, the change in resonance frequency and quality factor shows a characteristic ~MW0.5 relationship, where MW is the molecular (or atomic) weight of the adsorbate, as shown in Figure 5.6. When the carbon nanotubes are present on the surface of the resonator, apart from events of desorption and adsorption of gas molecules from the carbon nanotubes, there is additional viscous drag generated due to the enhanced 214 random surface roughness generated by the presence of the carbon nanotubes. Daikhin et al. [240, 241, 243, 245-248] have conducted detailed theoretical and experimental studies on the influence of the random roughness on the surface of the QCM and its influence on the resonance frequency and the quality factor of the resonator. Several other researchers have found experimental and theoretical results which agree within first order of magnitude of the expressions as derived by Daikhin and co workers.

Some of the notable works include that by Bund et al. [249, 250], Yang et al. [251], and by Martin et al. [244]. The surface roughness created by presence of carbon nanotubes on the surface of the resonator can be characterized as slight roughness.

Daikhin and co workers gave the expression for the change in the resonance frequency and width of resonance spectrum in presence of random surface roughness on the resonator as

2 2 f0 ρgδ ⎡ h ⎤ Δf = − ⎢1+ 2 F()l δ ⎥ (5.18) ()μq ρq ⎣ l ⎦

2 2 2 f0 ρgδ ⎡ h ⎤ FWHM = ⎢1+ 2 Φ()l δ ⎥ (5.19) ()μq ρq ⎣ l ⎦

In the above expression, δ is the velocity decay length in the ambient gas, and is given by equation 5.2. The first term within brackets for the above expressions is the

Kanazawa equation which has already been derived and discussed earlier in the text.

The result of the presence of the random surface roughness due to SWNTs is to introduce a scaling factor given by the second term within brackets in the above expressions. h in the above equations represents the rms height of the random surface roughness and l is the measure of correlation of the random surface roughness. The 215

fill in Isolated SWNTs resonance frequency 200 y=-288.5+153.3e-17.55x +103.6e-1.019x y=-736.6+462.6e-17.55x +233.9e-1.799x 0 y=-861.3+559.8e-17.53x +280.9e-2.066x y=-1540+737.7e-11.11x +433.8e-1.7x

-200

-400

-600

-800

-1000

-1200 Change in Resonance Frequency (Hz) Frequency Resonance in Change -1400 (a)

-1600 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) evacuation Isolated SWNTs resonance frequency 1800 y=269.2-139.9e-15.62x -108.8e-1.637x y=717.9-449.4e-14.84x -230e-0.5053x 1600 y=866.7-429.5e-14.84x -359.2e-0.6959x y=1615-1220e-11.95x -357.4e-0.5553x 1400

1200

1000

800

600

400

200 Change in Resonance Frequency (Hz) Frequency Resonance in Change

0 (b)

-200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) fill in Isolated SWNTs Quality Factor 216 5 y=-5.504+5.78e-8.813x -0.3696e-17.55x y=-13.92+10.9e-16.42x +2.711e-3.571x y=-16.94+16.71e-17.55x +0.4709e-2.835x 0 y=-53.09+34.04e-17.55x +20.02e-0.0138x

-5 He

-10

N2 -15 Argon

-20 Change in Quality Factor Quality in Change -25

-30 (c)

SF6 -35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) evacuation Isolated SWNTs Quality Factor 45 y=5.63-2.794e-14.44x -2.663e-1.077x y=13.94-12.16e-9.178x -1.032e-3.717x 40 y=16.92-15.12e-17.55x -2.013e-2.458x y=36.45-33.42e-10.62x -3.416e0.004679x 35 SF6 30

20 Ar

15 N2

10 Change in Quality Factor Quality in Change

He 5

0 (d) -5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) Figure 5.5: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for quartz coated with partially open ended isolated SWNTs. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question. 217

isolated SWNTs 10000 10000 "evacuation" resonance frequency 5000 "fill in" resonance frequency 5000 "evacuation" quality factor 3000 "fill in" quality factor 3000 2000 log10 (y)=2.126+0.4979log10 (x) 2000 log10 (y)=2.184+0.4699log10 (x) 1000 log10 (y)=0.4261+0.5026log10 (x) 1000 log10 (y)=0.3845+0.5283log10 (x) 500 500 300 300 200 200 100 100 50 50 30 30 20 20 change in Quality Factor Quality in change 10 10

change in Resonance Frequency (Hz) Frequency Resonance in change 5 5 3 3 2 2 1 1 2 3 4 5 6 7 8 910 20 30 40 50 70 100 200 molecular weight (amu) Figure 5.6: Change in resonance frequency and quality factor plotted as function of molecular (or atomic) weight of the adsorbate for the QCM coated with partially open isolated SWNTs. The dashed lines are fit to the data and show a characteristic ~m0.5 relationship for change in resonance frequency and quality factor as a function of molecular weight (or atomic weight) of the adsorbate.

218

Table 5.4 Listing of change in resonance frequency and quality factor obtained experimentally for partially open ended isolated SWNTs when compared with calcualted values of resonance frequency and quality factor. As can be seen, the values of quality factor obtained from experiment and from theory match within experimental errors. However, the change in resonance frequency due to surface roughness created on surface of QCM by presence of SWNTs is much less than experimentally obtained value of change in resonance frequency. This suggests that the remaining change in resonance frequency is due to physisorption on carbon nanotubes, which does not cause change in the quality factor of the QCM.

3 -6 ρ (kg/m ) η x 10 Calculated Experimentally Qcalculated Qexp-obtained (at an overpressure -2 Δf0 Obtained Δf0 of 5 psi) (N-s m )

Helium 0.219 18.6 20.8 270 5.6 5.4

Nitrogen 1.533 16.7 52.9 667 14.1 14

Argon 2.19 22.17 73 860 19.4 17

SF6 7.9935 16.1 122 1614 31.5 33

l ⎡ α2δ ⎤ F()l /δ = ⎢α1 + ⎥,when()l >> δ (5.20) δ ⎣ l ⎦

l ⎡ β2l ⎤ F()l /δ = β1 + ,when()l << δ (5.21) δ ⎣⎢ δ ⎦⎥

Φ(l /δ ) = γ 1, when(l >> δ ) (5.22)

2 Φ(l /δ ) = (l /δ ) γ 2 ,when(l << δ ). (5.23)

(R −1)l 2 (R −1)l 2 Where α = π , α = , β = 3 π , β = −2 , γ = , and γ = 2 . For 1 2 h2 1 2 1 h2 2

Gaussian random surface roughness, we have

2h2 R = 1+ . (5.24) l 2

The asymptotic behavior of the above expressions was pictorially depicted by Daikhin and coworkers which is being reproduced here for convenience in Figure 5.7 [240]. As can be seen from the figure, the convergence between the actual solution and simplified asymptotic expressions is excellent except when l ≈ δ.

We can easily convert the change in width of resonance spectrum to Q-factor using the following expression

f Q = 0 . (5.25) FWHM

Differentiating the above expression for the change in full width at half maximum, we get the expression 220

− f dQ = 0 d(FWHM ) . (5.26) FWHM 2

In the current case, it was found that the value of δ (values given in Table 5.1) was much larger than l. Since these are isolated SWNTs with diameter of 1.4 nm, we take h to be equal to 1.4 nm. The value of l has been arbitrarily chosen to be 10 nm within reasonable physical distribution of SWNT. This is because for AFM studies on similar nanotube samples, one of the coworkers (Mr. Awnish Gupta) has observed l to be approximately 10 nm. Additionally, looking at Figure 5.8, we observe that the change in resonance frequency and quality factor as a function of l and h does not vary much, even when their values are varied by a couple of orders of magnitude. Hence, in the calculation of values of l and h, it is reasonable to assume that the value of h is 1.4 nm, which is the value of the diameter of the nanotube, and the value of the l was assumed to be 10 nm within assumption of reasonable distribution of carbon nanotubes on the surface of the resonator. Hence, plugging in the values of l (~10 nm) and h (~1.4 nm), the values of change in Q-factor and the resonance frequency due to surface roughness generated due to presence of isolated open ended SWNTs is shown in Table 5.4 and compared to the values obtained experimentally. As can be seen from table 5.4, the values of Q-factor match within experimental errors. However, the calculated change in resonance frequency does not conform to the experimentally obtained value. This effect can be attributed to the fact that the gas molecules which are physically adsorbed on the carbon nanotubes do not cause a change in the Q-factor of the resonator during the process of “fill in” or “evacuation”. They only cause a change in resonance frequency and not in Q-factor. The difference in the values of the calculated and experimentally obtained resonance frequency should represent the gas molecules 221

(a)

(b)

Figure 5.8: Variation of (a) change in quality factor, and (b) change in resonance frequency, for variation of values of l and h. The values in this case have been generated for the case of Helium for QCM coated with isolated SWNTs. As can be seen from the figure, the variation in change in resonance frequency and quality factor is insignificant even when we vary the values of l and h by an order of magnitude. Hence in this case it is reasonable to assume that the value of h is 1.4 nm, which is the value of diameter of the nanotube, and that the value of l is 10 nm, which is what one of the coworkers observed using AFM for similar samples on Mica substrates. 222 actually physically interacting with carbon nanotubes by way of physical adsorption, etc. Also, as can be seen from table 5.4, the change in resonance frequency due to viscous damping by gas molecules is very small as compared to the observed change in the resonance frequency. Hence we can conclude that the change in resonance frequency is primarily due to gas molecules physically adsorbed on, near or within carbon nanotubes.

5.3.3 Coating with bundled close ended SWNTs

As indicated in the experimental section, the “nominally” isolated open ended SWNTs were subsequently removed from the surface of the resonator using oxygen plasma and the resonator was subsequently loaded with bundled “nominally” close ended

SWNTs (90 ng). The change in resonance frequency and quality factor in this case for the events of “fill in” and “evacuation” are given in Figure 5.9.

Similar analysis as in the last section was performed. Table 5.5 compares the observed changes in resonance frequency and quality factor to the calculated change in the resonance frequency and quality factor for values of l (~100 nm) and h (~140 nm). As can be inferred from the table 5.5, the viscous damping due to surface roughness created by the presence of carbon nanotubes can explain the change in the Q-factor observed but cannot explain the change in the resonance frequency change observed.

In the case the nanotubes were nominally closed bundled SWNTs, the frequency change in due to adsorption in the interstitial sites, grooves and the outer surface of

SWNTs which are present in bundles.

223

5.3.4 Adsorption of Gases in Carbon nanotubes

From the analysis presented in the previous sections, the change in resonance frequency and Q-factor for the case of bare quartz gold coated surface can be explained in terms of Gordon-Kanazawa equation. In the case when the QCM is coated with either “nominally” open ended isolated SWNTs or “nominally” closed ended bundled SWNTs, the change in Q-factor can be reasonably explained within experimental errors as arising from viscous damping and an additional correction term due to the rms surface roughness created by the presence of the SWNTs on the surface. Further, using the modified viscous damping model, the MW0.5 functional dependence of the Q-factor can also be accounted. However, the change in resonance frequency due to this additional surface roughness is much less than the experimentally obtained values of resonance frequency. In this section, an attempt to account the source of this additional frequency change during events of “fill in” and

“evacuation” due to the gas molecules or atoms being physically adsorbed on the internal and external surface of the nanotube will be explored. Carbon atoms constituting the carbon nanotubes are known to generate an attractive potential for the gas molecules causing their density to be larger near the walls of the nanotubes than that of ambient. In the case of open tubes, the distribution of these gas molecules can be schematically represented as in Figure 5.11. For the case of the “nominally” closed nanotube bundles, the presence of the gas molecules inside the nanotubes is ruled out.

As seen in the figure 5.11, looking at the cross section of the nanotube, the regions of enhanced density of molecules is in the form of a cylinder, with two characteristic radii (r0ext and r0int) wherein the potential is most attractive and hence the number of 224

fill in bundled SWNTs resonance frequency 2000 He y=-1836+845.9e-11.22x +1005e-1.506x N2 y=-5148+3600e-8.494x +1528e-0.82x Argon y=-5929+2141e-11.78x +3893e-3.207x 0 SF6 y=-1.009×104+8616e-7.014x +1884e-1.493x

-2000

-4000

-6000

-8000

Change in Resonance Frequency (Hz) Frequency Resonance in Change -10000 (a)

-12000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) evacuation Bundled SWNTs resonance frequency 15000 He y=1932-472.1e-17.76x -1459e-1.628x 13500 N2 y=5095-3542e-12.49x -1668e-0.7449x Ar y=6070-2345e-15.9x -3786e-3.08x 12000 SF6 y=9859-9567e-7.389x -625.6e-0.5798x

10500

9000

7500

6000

4500

3000

1500

Change in Resonance Frequency (Hz) Frequency Resonance in Change 0

-1500 (b)

-3000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (hrs) fill in bundled SWNTs quality factor 225 20 Helium y=-23.61+15.65e-17.99x +7.523e-1.26x Nitrogen y=-73.24+46.44e-17.59x +27.28e-2.126x Argon y=-80.03+51.55e-17.59x +26.87e-1.55x 0 -17.68x -1.454x SF6 y=-145.3+114.5e +36.15e

-20

-40

-60

-80

-100 Change in Quality Factor Quality in Change -120

-140 (c)

-160 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 55.5 Time (hrs) evacuation bundled SWNTs quality factor 160 He y=23.62-13.99e-17.76x -9.288e-0.8612x Nitrogen y=68.86-44.34e-17.76x -24.31e-1.753x Ar y=73.92-46.24e-17.76x -27.64e-2.06x 140 -17.76x -1.274x SF6 y=150.8-94.65e -55e

120

100

40 Change in Quality Factor Quality in Change 20

0 (d)

-20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (hrs) Figure 5.9: Change in (a) resonance frequency during the process of fill in, (b) resonance frequency during the process of evacuation, (c) quality factor during the process of fill in, and (d) quality factor during the process of evacuation, for quartz coated with bundled close ended SWNTs. The dashed lines are fit to the data. The fit equations are also shown in the figure. Due to variability of the manual fill in and evacuation process, no trend can be observed for the four gases in question. 226

Table 5.5

Listing of change in resonance frequency and quality factor obtained experimentally for close ended bundled SWNTs when compared with calcualted values of resonance frequency and quality factor. As can be seen, the values of quality factor obtained from experiment and from theory match within experimental errors. However, the change in resonance frequency due to surface roughness created on surface of QCM by presence of SWNTs is much less than experimentally obtained value of change in resonance frequency. This suggests that the remaining change in resonance frequency is due to physisorption on carbon nanotubes, which does not cause change in the quality factor of the QCM.

3 -6 Experimentall ρ (kg/m ) Calcualted η x 10 y Obtained (at an overpressure -2 Δf Qcalcualted Qexp-obtained 0 Δf of 5 psi) (N-s m ) 0

Helium 0.219 18.6 109 1964 27.6 25

Nitrogen 1.533 16.7 307 5123 69.1 75

Argon 2.19 22.17 426 6174 95.3 80

SF6 7.9935 16.1 845 9963 155 150

20000 200 "evacuation" resonance frequency "fill in" resonance frequency "evacuation" quality factor "fill in" quality factor log10 (y)=3.034+0.4564log10 (x) log (y)=2.992+0.4804log (x) 10000 10 10 100 log10 (y)=1.07+0.526log10 (x) log10 (y)=1.11+0.5097log10 (x) 8000 80 7000 70 6000 60 5000 50 4000 40

3000 30 Change in Quality Factor 2000 20 Change in Resonance Frequency (Hz) Frequency Resonance in Change

1000 10 2 3 4 5 6 7 8 910 20 30 40 50 6070 100 200 Molecular Weight (amu)

gas molecules is the maximum. The r0C is the radius of the carbon nanotube and is 0.7 nm in the current case. The values of r0ext and r0int are given in Table 5.6.

The values of these characteristic radii and the value of the attractive potential experienced by gas atoms and molecules near the inner and outer surface of SWNTs has been calculated by Dr. Milton Cole, who is one of the collaborators on this project. The attractive potential of walls of SWNTs causes a very small number of gas molecules to be physisorbed near the walls of SWNTs, i.e. the coverage is low enough that intermolecular interactions can be ignored. This implies that the density at distance r from the center of a nanotube is given by the barometric formula

n(r) = n(∞)exp[−V (r) / kT] (5.27) where n(r) is the density of gas molecules at a distance r from the center of the nanotube, n(∞) is the density of gas molecules far away from the surface of the nanotube at standard temperature and pressure, V(r) is the attractive potential experienced by the gas atoms or molecules as a function of distance r from the center of the nanotubes, k is the Boltzmann’s constant and T is the ambient temperature

(300K). The ideal gas formula yields the asymptotic density at standard temperature and pressure as given by

n(∞) = P / kT = 3×1019 / cc = 3×1026 / m3 (5.28)

The potential V(r) was calculated by assuming that adsorption potential can be expressed as a sum of Lennard-Jones (LJ) two body interactions the host C atom and the adsorbate. This calculation is based on several simplifying assumptions which

228

Table 5.6

Listing of values of radii where the potential is most attractive inside (r0int) and outside of the nanotube (r0ext). The values of rm, which is a measure of nearest neighbor distance for gas molecules for different gases are also listed.

r0int r0ext

He 4.4467 9.5558

N2 3.9404 10.065

Ar 4.0891 9.9154

SF6 3.3057 10.707

(a)

r0C r0int

r0ext

(b)

(b) (a)

Figure 5.13: Schematic diagram of longitudinal density of adsorbates ((a) Helium, (b) Nitrogen, (c) Argon, and (d) SF6) along the inside and outside surface of carbon nanotubes as a function of distance from the center of the nanotube. The nanotube was assumed to have a diameter of 0.7 nm. 230 yield a maximum uncertainty of 25% in the calculations. Some of these simplifying assumptions are

• The potential has distance and energy parameters obtained with semi-

empirical combining rules from the LJ parameters of the carbon atom and

the adsorbate.

• Many body interactions were ignored in the current calculations. This is

because in the case of adsorption on graphite, ignoring the many body

interactions resulted in a maximum error of 15%. In the current case, since

the effective coordination number is larger than that of graphite, the many

body effects will be smaller in magnitude.

• Another assumption was that the pair potential between carbon atom and

the adsorbate is isotropic and of LJ form, i.e. of the form

12 6 ⎡⎛σ ⎞ ⎛σ ⎞ ⎤ U (x) = 4ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥ (5.29) ⎣⎢⎝ x ⎠ ⎝ x ⎠ ⎦⎥

Here, U(x) is the potential energy, σ is the distance wherein the potential is

no longer repulsive, ε the value of the potential for two body interaction,

and x = r< /r>, and r<(>) are the smaller (greater) of r and R.

• Finally, the potential used was azimuthally and longitudinally averaged.

Under such assumptions, which introduce a maximum uncertainty of 25% in the calculated values, result in the potential to be of the form

10 4 2 ⎡ 21⎛σ ⎞ ⎛σ ⎞ ⎤ V (r; R) = 3πθεσ ⎢ ⎜ ⎟ f11(x)M11(x) − ⎜ ⎟ f5 (x)M 5 (x)⎥ (5.30) ⎣⎢32 ⎝ R ⎠ ⎝ R ⎠ ⎦⎥ 231

20000 Δfexp 10000 Δfext-cal-using barometric formula log10 (y)=2.09+0.4984log10 (x) 5000 log10 (y)=-0.9226+2.316log10 (x) 3000 2000

1000 500 300 200

100

50 30 20

Change in Resonance Frequency (Hz) Frequency Resonance in Change 10

5 3 2 2E+0 3E+0 5E+0 7E+0 1E+1 2E+1 3E+1 5E+1 7E+1 1E+2 2E+2 Molecular Mass (amu) Figure 5.14: Data showing the experimental obtained change in resonance frequency, and the theoretically expected change in resonance frequency as given by using the barometric formula and by using a simple “filling” theory.

Table 5.7

Table listing of the density of adsorbates, at the points of maximum attractive potential at the inside and outside surface of SWNTs. For SF6, a very high value of adsorption is obtained inside the nanotube, which is probably wrong.

λint (atoms/Å) λext (atoms/Å) Total Γ(atoms/Å)

He 0.001253 0.00205 0.003307

N2 0.05287 0.0247 0.07761

Ar 0.04884 0.0243 0.073162

SF6 55.525 0.3730 55.898 (or 0.3730)

232 where θ = 0.38 Å-2 is the surface density of C atoms and R is the radius of the carbon nanotube cylinder. Here, x = r< /r>, and r<(>) are the smaller (greater) of r and R. The

n function f n(x) is defined as 1 for rR, where n is a positive integer.

Mn(x) is given by the following integral

π 1 M (x) = dϕ . (5.31) n ∫ 2 n / 2 0 ()1+ x − 2xcosϕ

The calculated potentials using the above expressions are shown in Figure 5.12 for the four gases used in the current experiments. The reader is encouraged to read these references for further information [252-259].

The potentials were then used to calculate the density of gas molecules physisorbed both inside and outside of the SWNT and the net physisorption inside and outside of the nanotube. The results are expressed in one-dimensional density, Γ, expressed in atoms/molecules per Å of nanotube and are shown in Figure 5.13. For comparison, note that a monolayer coverage corresponds to

λmonolayer = 2πθr0ext (5.32)

2 where θ is the monolayer density on graphite (typically θ= 0.1/ Å ) and r0ext is the radius of the surface containing the admolecules, say r0ext ~10 Å for the external gas.

Hence monolayer coverage corresponds to about λ monolayer ~ 6 molecules per Å of nanotube.

The key conclusions are these: 233

a. The lighter gases show such low coverage that the model is ok. He

adsorbs Γ~0.003, less than 0.1% of a monolayer. Ar and N2 adsorb about

1% of a monolayer. SF6 adsorbs many layers, according to the model.

b. Only He adsorbs more gas outside than inside. Ar and N2 have roughly 2/3

inside. SF6 has virtually all outside.

The absolute values of Гmonolayer calculated are shown in Table 5.7. Hence, using these values for inside and outside of the tube, we can calculate the total number of gas molecules present on the surface of the nanotube. The results for the four gases are plotted in Figure 5.14. Using the physisorption model as discussed above, a characteristic ~MW2.5 relationship is obtained for the change is resonance frequency as compared to ~MW0.5 relationship obtained experimentally.

5.4 Conclusions

In this chapter, the property of carbon nanotube to physically adsorb gases has been studied using a miniaturized QCM. The change in resonance frequency and Q-factor were studied for bare gold coated quartz surface, the gold coated surface covered with

“nominally” isolated open ended single walled carbon nanotubes and “nominally” close ended bundled SWNTs. In all the three cases, the change in resonance frequency and Q- factor was found to have a characteristic ~MW0.5 relationship, wherein MW is the molecular/atomic mass of the gas in question. In the case of bare quartz covered with gold electrode, the absolute change in resonance frequency and Q-factor and the characteristic ~MW0.5 relationship, was explained on the basis on Gordon-Kanazawa 234 equation. In the case of SWNT coated resonators, the change in Q-factor and its

~MW0.5 relationship was explained by modified Gordon-Kanazawa equation with an additional correction term to account for the enhanced surface roughness created by the presence of SWNTs. However, in both the cases wherein the SWNTs were present, the change in resonance frequency obtained from modified Gordon-Kanazawa equation was much less than that experimentally obtained values. The remaining change in resonance frequency was then explained on the assumption of physical adsorption of gases on the inside and outside surface of SWNTs. However, the proposed model could not explain the observed characteristic dependence of ~MW0.5.

Instead it yielded a dependence of ~MW2.5. In summary, the developed miniaturized

QCM hence presents itself as a useful tool to study phenomena at the nanoscale.

235

Chapter 6

CONCLUSIONS AND FUTURE WORK

6.1 Conclusions

A miniaturized Quartz Crystal Microbalance (QCM) has been fabricated and tested.

Miniaturization of the QCM allowed its fabrication in an array format, with the capability of individually addressing each pixel. This allows for true temporal and spatial mass sensing. Through optimal design, fabrication, and miniaturization the mass sensitivity of the sensors was increased by more than four orders of magnitude to less than 1 pg/Hz as compared to 17 ng/Hz for commercially available 5 MHz bulk resonators. The etching process for fabricating miniaturized QCMs was thoroughly studied using formal statistical techniques such as Design of Experiment (DOE) method. Additionally, direct correlation between the deliverables of the etching process namely etch rate and rms surface roughness were quantitatively correlated to the process parameters namely the ICP power, substrate power, flow rate of etch gases, operating pressure, distance of substrate holder from source, and temperature of the substrate holder. The fabricated resonators were tested for operation in air and water and a high quality factor of 7500 and ~2000 was obtained respectively.

The QCMs were integrated with carbon nanotubes using a simple spray-on technique.

It was found that the addition of carbon nanotubes onto the electroded surface of the resonator increased its Q-factor by as much as 100%. It was proposed that the carbon nanotubes due to their high stiffness suppress the out of plane flexural vibrations in 236 the QCMs thereby suppressing an energy loss channel and hence causing an increase in the Q-factor. Measurement of out of plane vibrations of the quartz crystals using a laser based optical vibrometer revealed that the out-of-plane vibrations of QCM increase from 13 pm to 26 pm when carbon nanotubes are removed from the surface of the resonator – directly confirming the suppression of the out-of-plane motion on the resonator surface by carbon nanotubes.

Additionally, the QCMs were used to study the gas adsorption and desorption behavior of nominally “open-ended” isolated and nominally “close-ended” bundled

SWNTs. Using the ultrasensitive QCM, we were able to probe gas storage properties of carbon nanotubes. It was found that carbon nanotubes can adsorb large amount of gas molecules not only in the cylindrical pore that they enclose, but also on their external surface. Four different gases were tested, namely Helium, Nitrogen, Argon, and SF6. It was found that the change in resonance frequency and quality factor for the “fill in” and “evacuation” of gases from carbon nanotubes exhibited a characteristic ~ MW relationship, where MW is the atomic/molecular weight of gas species adsorbed. Such a behavior was consistently observed both for change in resonance frequency and Q-factor during the events of “fill in” and “evacuation” in the case of bare quartz with gold electrode, gold electrode covered with isolated

“open-ended” SWNTs, and gold electrode with bundled “close-ended” SWNTs. In the case of bare quartz with gold electrode, the observed change in resonance frequency and Q-factor and their characteristic ~ MW relationship can be explained on the basis of the viscoelastic dissipation arising in gas ambient through the Gordon-

Kanazawa equation. In the case of QCM with carbon nanotubes, the change in Q- 237 factor and its characteristic ~ MW relationship could be explained on the basis of enhanced viscoelastic dissipation arising due to surface roughness or modified

Gordon Kanazawa equation. However, for the case of frequency change in the presence of carbon nanotubes, the characteristic ~m0.5 relationship and the observed change in magnitude of resonance frequency was explained in terms of physical adsorption of gas molecules near the inside and outside walls of carbon nanotubes, in regions where the potential due to the carbon atoms for gas atoms and molecules is attractive.

To conclude, the fabricated ultrasensitive QCM offers a versatile gravimetric sensor platform for real world applications involving measurement in air as well as fluid environments.

238

Publications from this work in Peer Reviewed Journals:

1. A. Goyal, V. Hood, S. Tadigadapa, “High Speed Anisotropic Etching of

Glass for Microsystems Applications”, Journal of Non-Crystalline Solids,

352, 2006, p 667-663..

2. A. Goyal, S. Tadigadapa, A. Gupta, P.C. Eklund, “Use of Single Wall

Carbon Nanotubes (SWNTs) to Increase the Quality Factor of an AT-cut

micromachined Quartz Resonator”, Applied Physics Letters, Nov 07, 2005.

This article also appeared in Virtual Journal of Nanoscale Science and

Technology, November 21, 2005.

3. J. Cheong, A. Goyal, S. Tadigadapa, C. Rahn, “Fabrication and

performance of a PZT flextensional actuator”, Journal of Micromechanics

and Microengineering, v 15, n. 10, October 2005, p 1947-1955.

4. A. Goyal, J. Cheong, S. Tadigadapa, “Tin-based solder bonding for MEMS

fabrication and packaging applications”, Journal of Micromechanics and

Microengineering, v 14, n 6, June 2004, p 819-25.

Publications from this work in Conference Proceedings:

1. A. Goyal, S. Subasinghe, V. Hood, and S. Tadigadapa, “High-speed

anisotropic etching of glass and piezoceramics for microsystem

applications” Proceedings of the Solid-State Sensors, Actuators, and

Microsystems Workshop, Hilton Head Island, SC, June 2006.

2. S.S. Subasinghe, A. Goyal, S. Tadigadapa, “High aspect ratio etching for

bulk lead zirconate titanate”, Proceedings of SPIE – The International 239

Society of Optical Engineering, Micromachining and Microfabrication

Process Technology XI, Jan. 2006, San Francisco.

3. P. Joshi, A. Goyal, A. Gupta, S. Tadigadapa, P.C. Eklund, “Stiffness

modification of micromachined silicon beams using carbon nanotubes”,

Proceedings of SPIE – The International Society of Optical Engineering,

Reliability, Packaging, Testing and characterization of MEMS/MOEMS V,

Jan. 2006, San Francisco, California.

4. A. Goyal, V. Hood, S. Tadigadapa, “High speed anisotropic dielectric

(SiO2) etch process for MEMS fabrication and packaging applications

using Inductively Coupled Plasma Reactive Ion Etching system

employing SF6/C4F8/Ar/O2/CH4 based chemistry”, Proceedings of SPIE –

The International Society of Optical Engineering, Reliability, Packaging,

Testing and characterization of MEMS/MOEMS V, Jan. 2006, San Francisco,

California.

5. A. Goyal, S. Tadigadapa, A. Gupta, P.C. Eklund, “Micromachined Quartz

Resonator Functionalized with Single Wall Carbon Nanotubes (SWNTs)

for Sensing Applications”, Proceedings of IEEE Sensors 2005, the 4th IEEE

Conference on Sensors, Oct. 31- Nov. 3, 2005, Irvine, California.

6. A. Goyal, Y. Zhang, S. Tadigadapa, “Micromachined Quartz Resonator

based Calorimetric Biosensor”, Proceedings of IEEE Sensors 2005, the 4th

IEEE Conference on Sensors, Oct. 31- Nov. 3, 2005, Irvine, California.

7. A. Goyal, S. Tadigadapa, A. Gupta, P.C. Eklund, “Improvement in Q-

factor of AT-Cut Quartz Crystal Resonators using Single Wall Carbon 240

Nanotubes (SWNTs)”, to appear in Proceedings of 2005 IEEE International

Ultrasonics Symposium, Sep. 18-21, 2005, Rotterdam, Netherlands.

8. P. Joshi, N. Duarte, A. Goyal, A. Gupta, S. Tadigadapa, P.C. Eklund,

“Improvement of the elastic modulus of micromachined structures using

carbon nanotubes”, MRS Proceedings, Volume 875, O1.5, MRS Spring

Meeting, San Francisco, March 28 – April 1, 2005, USA.

9. J. Cheong, A. Goyal, S. Tadigadapa, C. Rahn, “Reliable bonding using

indium based solders”, Proceedings of the SPIE - The International Society

for Optical Engineering, v 5343, n 1, 2003, p 114-20 .

10. A. Goyal, S. Tadigadapa, R. Islam, “Solder bonding for

microelectromechanical (MEMS) fabrication and packaging

applications”, Proceedings of the SPIE - The International Society for

Optical Engineering, v 4980, 2003, p 281-8.

Patents Filed:

1. Goyal, S. Tadigadapa, P.C. Eklund, “Carbon Nanotube-Quartz Resonator

With Femtogram Resolution For (Bio)Chemical Sensor Applications”,

PSURF No. 2004-2927, provisional patent granted, patent application filed,

decision pending.

241

6.2 Future Work

6.2.1 Quartz Calorimeter

Calorimetry is a powerful and effective investigative tool for analyzing biochemical reactions [260]. Thermal sensors based on the measurement of the heat of reaction

(enthalpy) and the thermal properties of biological molecules suspended in solutions can be the basis of versatile calorimetric biosensors [261]. Specificity to identify or perform a selective assay can be achieved by coating the calorimeter with specific catalysts such as enzymes, and antibodies [262]. When the analyte is exposed to such immobilized enzymes or antibodies on the sensor active area, the biochemical reaction begins and its evolution in terms of total amount of heat generated and kinetics is proportional to the concentration of the reactants and the rate constants of the reaction.

Also, it is desirable to miniaturize these calorimetric biosensors so that small quantities of samples can be analyzed, thus offering low cost, ease of use, fast response time, and good operational stability. With reduction is sample volumes achieving high molar sensitivities can only be possible if a sensing element with high phenomenological sensitivity is used.

The phenomenological temperature sensitivity of Y-cut quartz of ~10-6°C represents 2-

3 orders of magnitude improvement in temperature sensitivity as compared to other temperature dependent phenomena such as Seebeck effect on which a thermopile device is based [263]. This temperature sensitivity along with the low noise performance that can be achieved in quartz crystal oscillators is the principle motivation behind their use as sensing elements in calorimetric (bio)chemical sensors. 242

The temperature profile of the Y-cut resonator pixel can be modeled as a circular membrane (pixel) of radius a, and of uniform thickness d. The electrode (resonator) area will be smaller than the pixel area for energy confinement and Q-factor reasons.

Neglecting radiation and convection heat losses and assuming uniform heat generation

Q& per unit time per unit area over the whole pixel area, the radial temperature profile of the quartz membrane can be modeled by the two dimensional heat conduction equations. If the boundaries of the circular quartz membrane are clamped at ambient temperature, the solution of the heat conduction equation can be written as [264],

Q&(a2 − r 2 ) ΔT(r) = (6.1) Membrane 4κ||d where ΔT(r) is the temperature difference between the pixel membrane at radius r and

the rim of the membrane and κ|| is the planar thermal conductivity for the membrane material. The average temperature over the electrode area which covers the membrane

ΔT (r) = 11Q&a2 48κ d κ from r=0 to r=a/2 can be given by avg || , where || for Y-cut quartz is

1.38 Wm-1K-1. Assuming the heat generated on the surface of the membrane is due to an enzymatic reaction, the heat generated per unit time per unit area can be calculated

using the expression Q& = ΔH.M.dc τ , where ΔH is the enthalpy of the reaction in J/mol,

M is the molarity of the reactant in moles/liter, dc is the depth of the reaction chamber, and τ is the time, in seconds, required to refresh the entire volume of the reaction chamber which in turn depends on the flow rate used in the experiment. For the case of catalytic hydrolysis of urea molecules using urease, 1 M solution of urea will generate a total heat of 6.1x107 J/m3 of heat when completely reacted. For the typical flow rates 243 used in the enzymatic testing, τ = 0.27 s. Using the depth of the reaction chamber of 30

μm, the heat generated per unit area per second on the membrane can be estimated to

3 2 Q& ΔT (r) be 6.8x10 W/m . Using this value of , the average temperature, avg , was calculated and plotted as a function of membrane thickness for different pixel diameters and is shown in Fig. 6.1. From this it can be concluded that for a 25 μm thick quartz pixel of 1 mm diameter (with electrode diameter of 500 µm), the average increase in the temperature of the quartz membrane is ~10°C for completely reacted

1 M urea solution. Assuming a temperature resolution of 10-5°C using the quartz resonator, the expected sensitivity of the device is ~1 μM (25 femtomoles) for a

500 FEM Simulation (a=2mm) 200 FEM Simulation (a=1mm) FEM Simulation (a=0.5mm) 100 FEM Simulation (a=0.1mm)

T (K) Analytic Solution (a=2m m )

Δ 50 Analytic Solution (a=1m m ) Analytic Solution (a=0.5mm) 20 Analytic Solution (a=0.1mm) 10 5

2 1 0.5

0.2 0.1

Average Temperature Difference 0.05

0.02 5 10 15 20 25 30 35 40 45 50 Membrane Thickness (μm) Figure 6.1: Average electrode temperature increase for different membrane diameter and thickness for hydrolysis of 1M urea. 244 sample volume of ~25 nl. Using a thermopile device in our earlier work we were able to achieve ~2 mM sensitivity for 15 nl sample volumes [265]. The proposed technique clearly represents at least 3 orders of sensitivity improvement.

In order to demonstrate the concept, a 3×3 array of resonators were fabricated on a one inch diameter quartz plate (~125 µm thick), by defining large one millimeter diameter overlapping electrodes on the opposite faces of the disc. Conventionally, for reasons of energy trapping and drive efficiency, such resonator arrays are fabricated in inverted

MESA structures defined by dry anisotropic etching steps. Without the energy trapping advantages of an inverted MESA structure, the quality factors obtained were not high, with a maximum Q of 30,000 with insufficient phase rotation of ~15°, against a Q-factor of ~75000 with a large phase rotation for conventional resonators.

High quality factors of the resonator are necessary to ensure low frequency noise, thus ensuring high temperature sensitivity. The fabricated resonator array was enclosed in a wall made of PDMS, which formed an open reaction chamber on top of the pixels.

The resonance frequency of the resonator was ~15.7 MHz with higher overtones at

46.8 and 78.2 MHz respectively. The crystal was driven at resonance using an Agilent

4294A impedance analyzer and the magnitude and phase of the impedance were monitored and recorded using a Labview® based program implemented on a personal computer. A program was then written in Mathematica to fit the resonance curve with a Lorentzian line shape to obtain the values of the resonance frequency. 245

300 First Overtone Third Overtone Fifth Overtone 250

200

150 Slope = 100 ppm/°C

100

50 Change in Resonance Frequency (kHz) Frequency Resonance in Change

0 20 25 30 35 40 45 50 55 60 65 Temperature (°C)

Figure 6.2: Calibration curve for first, third and fifth overtone modes of Y-cut quartz calorimeter. As can be seen from the graph, the temperature sensitivity of the device is linear at room The fabricated resonator was then calibrated for temperature sensitivity at the first, third, and fifth overtones as shown in Figure 6.2. The resonator was housed in a

Faraday cage in an oven. The temperature inside the oven was monitored using two thermocouples, one mounted on the walls of the oven and the other located in close proximity to the resonator in the center of the oven. Calibration was performed over the temperature range of room temperature to ~60°C. Frequency calibration at higher temperatures was not investigated because, for the intended applications, the calorimeter is expected to monitor reactions which produce small amounts of heat and the overall temperature of the resonator is not expected to go beyond ~60°C.

Additionally, the present resonator was packaged using adhesives and materials that were incompatible for use at temperatures above ~60°C. The temperature of the oven 246

was fixed at ~60°C, and then the heating was turned off. The oven then slowly

returned to room temperature over several hours thereby giving an accurate estimate of

temperature sensitivity of the device. Under such equilibrium condition, the

temperature at the two thermocouples and the quartz resonator is almost the same,

thereby allowing calibration of device. The device was found to be non-linear at

temperatures greater than ~45°C [266, 267]. It has been proposed to use different cuts

of quartz crystal which can yield linear temperature characteristics. However, use of

such crystal cuts causes reduction in sensitivity to ~45 ppm/°C.

The Y-cut quartz resonator based calorimeter was tested for functionality in liquid

environments. Stable resonances with a quality factor of ~1000 were obtained in liquid

15.69

15.688

15.686

15.684 Air 15.682

15.68 In NH4OH 15.678 HCl + NH4OH Resonance Frequency (MHz) 15.676 0 1 2 3 4 5 6 7 89 Time (min)

Figure 6.3: Actual time evolution of the resonance frequency during the reaction with 1.08 M HCl. The reduction is frequency at the end of the reaction is due to increase in density of the solution due to formation of NH4Cl which has a density of 1.537 g/cc as compared to ~1 g/cc for all other 247 environments. The fabricated sensor was used to monitor heat of reaction of acid-base neutralization reaction. In the current experiment, neutralization reaction between HCl and NH4OH was monitored. 100 µl of NH4OH (molarity ~ 0.66 M) was poured in the

PDMS well formed on top of the resonating crystal arrays, and the crystal was allowed to stabilize. As seen from Fig 6.3, the resonance frequency decreases and then stabilized after addition of NH4OH on the resonator. This was followed by introduction of 100 µl of HCl (molarity ~ 1.08 M) into the cell. The neutralization reaction can be written as

ΔH o =−70.6kJ / mol HCl + NH 4OH ⎯⎯→⎯⎯⎯⎯ NH 4Cl + H 2O , (6.2) where, ΔHo is the heat of reaction and the negative sign indicates an exothermic reaction. The addition of HCl causes release of heat which causes the resonance frequency of the oscillator to increase. After the spike in frequency due to generation of heat, the heat is ultimately dissipated and the resonance frequency decreases because the density of the reaction product is 1.537 g/cc (for concentrated NH4Cl solution), which is much higher as compared to 0.8 for NH4OH, 1.05 for HCl, and 1 g/cc for water. However, errors are introduced due to indeterminate NH4Cl solution density. The error introduced in the frequency due to indeterminate density can be calculated using the Kanazawa equation

3 2 −1 2 Δf = − fo (πρq μq ) η1ρ1 , (6.3) 248

Where, fo is the center resonance frequency, ρq is the density of quartz, μq is the shear viscosity of quartz, η1 and ρ1 are the viscosity and density of fluid on top of quartz.

Taking logarithms and then partial differentials both side, we get

∂(Δf ) Δf = 0.5∂(ρ1) ρ1 (6.4)

Hence, 50% indeterminacy in density is expected to introduce an error of as much as

25% in the reading of the frequency.

Since this work was performed, the resonators in form of inverted mesa structures like

QCM arrays developed in this thesis have been fabricated. Measurements using such arrayed Y-cut quartz resonators is expected to significantly improve the accuracy of the measurement by using differential measurement techniques and by use of PDMS channels integrated on top of the resonators to maximize the energy dissipation in the quartz rather than the environment. The Y-cut based calorimeters and temperature sensors which can operate in water offer a versatile sensitive platform which can be used for several (bio) chemical sensing applications.

6.2.2 Functionalization using Self Assembled Monolayers

Even though the mass sensitivity of the fabricated QCM have been theoretically calculated to be in the sub-picogram range, there has been no direct evidence for the same. Functionalization using carbon nanotubes does not reveal the true mass sensitivity of the QCM since the system is self referenced and there has been little work in the past to estimate the desorption of gases from carbon nanotubes. Such theoretical models, even if developed, would not be good at predicting the desorption 249 rate from carbon nanotubes given rather lack of control over the properties of carbon nanotubes in terms of percentage of carbon nanotubes that appear with open ends and the level of agglomeration during the deposition process. Hence, a system which has been widely studied needs to be used to calibrate the mass sensitivity of the QCMs. In this respect, use of self assembled monolayers (SAMS) of conventional alkanethiol molecules present an attractive alternative.

Alkanethiols consist of long alkyl chains terminating using two different functional groups. One of the ends terminates in a Sulfur atom, which forms a covalent but slightly polar bond with the gold and hence “sticks” to the surface. The other end can be chosen to terminate in a variety of end groups, for example carboxyl group (-

COOH), amino group (-NH2), or the methyl group (-CH3), etc. These different end groups terminating the alkyl chain, which is attached to the gold surface using Sulfur atom, can be used to preferentially bind different molecules to the alkyl chain, for example proteins, antibodies, etc. This arrangement makes SAMS excellent candidates for functionalization and sensitivity calibration of QCM whose electrodes are made out of gold. These alkanethiols systems have been extensively studied in the past [268-273] and hence accurate information is available about the spectral density of the films growing on gold surface. This information along with molecular mass of these molecules and data on frequency change of the QCM can hence be used for accurate calibration of the mass sensitivity of these devices. Additionally it is estimated that study of SAMs using such a sensitive technique might reveal presence of hitherto undiscovered phenomena. Possible experiments that can be accomplished using the quartz resonator array include 250

• Recording adsorption isotherm for hexadecanethiol.

• Recording adsorption isotherm of different proteins, for example, albumin

on the SAM of hexadecanethiol.

• Use of multiple alkanethiol with different end termination groups for SAM

growth and study of selectivity of different proteins to these groups using

the ultrasensitive QCM.

• Functionalization of each pixel of the QCM using different SAMs by

integrating the QCM array with microfluidic channels thereby enabling

different SAMs solution to be used for different pixels of the array.

The work on SAMs functionalization of QCM has been initiated and the preliminary technical issues concerning growth of SAMs on the small electrodes of the QCM have been resolved. Some of these issues and their resolution can be summarized as follows –

• Conventional SAMs growth is accomplished over large surface area in the

form of 2” silicon wafers coated with gold. Hence, in order to characterize

the growth of SAMs on small gold electrodes of QCM, analytical

techniques such as microIR, XPS, etc. were used to compare the SAMs

quality for small electrodes as compared to SAMs growth over large areas.

Under identical conditions of SAMs growth, the quality of the monolayers

over large and small area were found to be the same.

• Since the QCMs for SAMs growth studies involve reuse of the same

device several times, it was critical that an effective cleaning process after 251

each test run was developed and thoroughly characterized for its efficacy.

Several techniques were investigated, for example, cleaning with piranha

solution (1:1 H2O:H2SO4), oxygen plasma clean, UV clean in ozone, etc.

Ultimately it was determined that a thorough clean in an alcohol based

solvent followed by a UV clean in ozone suffices to clean the surface of

the QCM.

• There were other issues regarding contamination of the samples from

Sulfur, Copper, etc. It was thought that the source of these contaminations

arise from the e-beam evaporator being used in the microfabrication

facility. However, use of a different evaporator since has resolved the

issue. 252

6.2.3 Preliminary data

In order to prove the ability of the device to make liquid based measurements, we

generated preliminary data on adsorption of lysine on the electrodes of the QCM.

Three different concentrations of lysine solution were prepared, namely 10 μM, 30

μM, and 50 μM. The change in resonance frequency for the three different

concentrations of the solution was recorded and is shown in Figure 6.4. The

adsorption of lysine on gold electrode of the QCM is non-specific. However, the

present result proves that the present resonator can be used for measurements in

aqueous solution. However, the accuracy and precision of the measurements still

needs to be verified.

102.369 Air Air Air 102.366

102.363

102.36

102.357

102.354 10 μM 50 μM Resonance Frequency (MHz) Frequency Resonance 102.351 30 μM

102.348 0 5 10 15 20 25 30 35 40 45 Time (min)

Figure 6.4: Non-specific adsorption of lysine on gold electrode of the QCM. Due to enhanced sensitivity of the QCM, we could resolve lysine solutions varying in concentration by 20 μM. 253

Preliminary experiments were also conducted to demonstrate the ability of the device to measure SAMs adsorption on gold electrode followed by adsorption of proteins on the SAMs layer. In this experiment which was conducted in conjunction with Dr.

102.5 SAMs growth of hexadecanethiol 102.498

102.496

102.494 Introduction of protein solution 102.492

102.49 Protein adsorption onto SAMs

Resonance Frequency (MHz) 102.488

102.486 0 20 40 60 80 100 120 140 160 180 Time (min)

Figure 6.5: Specific adsorption of protein Human Serum Albumin (HAS) on SAM of hexadecanethiol.

Allara’s group, solution of hexadecanethiol was poured on top of one of the electrodes of the QCM. As can be seen from Figure 6.5, slow growth of SAMs of hexadecanethiol on the gold electrode over a period of twenty minutes can be seen.

The hexadecanethiol solution had IPA as the solvent, which evaporated over time.

When most of the solvent had evaporated we added a protein solution (Human Serum

Albumin) on top of the electrode having SAMs film on it. As can be seen from Figure

6.5, there is slow adsorption of the protein on SAMs of hexadecanethiol over a period of couple of hours, after which the resonance frequency saturates to a constant value. 254

These two experiments show the versatility of the miniaturized QCM for measurements in aqueous solution.

6.3 Automatic Gain Control Oscillator Circuit

6.3.1 Introduction

The miniaturized Quartz Crystal Microbalance (QCM) described in the previous chapters of this thesis is expected to find a large number of applications in area for

(bio) chemical sensing etc. as outlined in Chapter 1. Currently we are using an impedance analyzer for capturing the impedance spectrum of the resonating crystal.

However, the impedance analyzer is expensive, bulky (weighs several tens of pounds) and hence is not readily portable. Additionally, the time lapsed between two readings for an impedance analyzer is of the order of several tens of seconds. Some of the (bio) chemical phenomena that can be probed with the enhanced sensitivity of the fabricated QCM last only a fraction of that time [274]. Hence there is a need to develop oscillator circuits based on the resonating crystal for real time monitoring of the frequency of the crystal. There are numerous circuits currently available which can perform this function, for example, the Clapps, Colpitts [275-277], Pierce

Oscillator [278, 279], etc. In such circuits, the frequency of the oscillator can be calibrated directly to read the effective mass loading of the quartz crystal whereas the amplitude of the oscillations can be calibrated to directly read the viscoelastic damping [280-282]. However, for (bio) chemical sensing applications, where fluid environments are involved, these measurements are accompanied by a significant change in the viscoelastic properties of the medium on top of the QCM electrode 255

[283-285]. Viscoelastic damping of the crystal by the ambient fluid often results in a significant loss in the closed loop gain of the circuit and can result in either a reduction or a complete loss in the amplitude of the oscillator circuit. Hence an oscillator circuit with dynamic feedback is required that can quickly adapt to changing viscous and viscoelastic loading on the electrode of the QCM to maintain the overall closed loop gain constant [281, 286, 287].

To summarize, the required oscillation circuit should be able to –

(1) Oscillate at a resonance frequency determined primarily the natural

resonance frequency of the quartz crystal.

(2) The circuit should have feedback that can dynamically change the gain of

the circuit to compensate for the changes occurring at the surface of the

crystal, so that the amplitude of the sinusoidal output of the circuit remains

constant.

(3) The magnitude of the gain used to maintain a constant amplitude of

oscillation can then be directly calibrated to read the quality factor (or

viscoelastic damping) of the resonating crystal. The larger the gain setting,

Figure 6.6: Schematic depicting the basic feedback topology of an oscillator. 256

the smaller is the quality factor of the resonating crystal.

In this section, the concept of an oscillator circuit with feedback is presented to

accomplish the goals listed above.

6.3.2 Conventional circuits without dynamic feedback

There are numerous oscillator circuits that have been developed for quartz,

particularly for applications in frequency control, timing, and clock generation. This

section discusses two of the more widely used configurations, namely Pierce

Oscillator and the Colpitts Oscillator. The fundamental components of an oscillator

circuit include an amplifier and a feedback network, which are illustrated in Figure

6.6. Two main criteria exist that must be met so that a circuit can freely oscillate:

1 The feedback must be positive (i.e. it must aid the original input signal).

2 The Barkhausen criterion [288, 289] for oscillation must be met. This

basically states that the gain of the amplifier multiplied by the feedback

factor of the feedback network must be greater than or equal to unity.

Figure 6.7: A generalized circuit diagram showing the principle of operation of oscillator circuits with feedback. 257

Once both these conditions are met, oscillation of the circuit can be sustained. Several circuit designs have been readily developed to be used with a quartz crystal oscillator, e.g. the Clapp, Colpitts and Pierce oscillator circuits. A simplified circuit schematic that is applicable to all three can be seen in Figure 6.7. With the proper values of CA and CB it can be ensured that the loop gain of the circuit will be unity or greater for satisfying the Barkhausen criterion and allowing oscillation to be self sustaining.

Even though these oscillators show adequate stability, high frequency operation and ease of implementation, they are not suitable for the applications for which the miniaturized resonators are designed. Even though the gain of the these oscillators can be changed with changing dissipation (Q-factor) of the quartz crystal using variable capacitors, the overall dynamic range is expected to be limited. Let us say that the experiment is being designed for operation in water. We can then choose transistor gain so that the overall loop-gain of the circuit is greater than one and then use a variable resistor to adjust the gain till it is one. As long as the change in the quality factor of the quartz is not substantial, the circuit will continue to operate and cause vibrations in quartz. However, suppose we suddenly inject glycerine into water causing a substantial drop in the Q-factor of the crystal. Now since the overall dynamic range of the oscillator circuit is limited and there is enhanced attenuation in the crystal, the circuit will cease to oscillate until the gain is again manually adjusted.

Such a situation is not desirable particularly when due to the nature of experiments; the value of the Q-factor of the crystal exhibits large fluctuations. Hence, a circuit is needed that can sense the oscillator signal amplitude and be capable of automatically adjusting the gain of the circuit so that the amplitude of the signal remains constant. 258

Operational Amplifier with Adjustable Gain To frequency Buffer Circuit counter Operational Amplifier

Half Wave Rectifier

Averaging circuit To multi meter (Quality Factor Indicator)

This also ensures operation of the circuit even when the crystal is loaded with highly

dissipative viscous fluids. Ideally, we would like that the circuit can operate for the

largest range of change of Q-factor of the crystal, from let’s say 1 million to less than

1. In the subsequent sections, such a circuit is proposed.

6.3.3 Proposed Circuit with dynamic feedback

Several circuit topologies were considered to accomplish the above mentioned design

goals [290-301]. The basic functional blocks and the operation of the circuit with

dynamic feedback are schematically illustrated in Figure 6.8 [302]. The quartz crystal

determines the resonance frequency of the circuit. The sinusoidal signal coming off

from the quartz crystal is amplified by the operational amplifier whose gain is 259 adjusted by the feedback loop. The signal then passes through another constant gain operational amplifier stage for further amplification. This signal is fed back into the quartz crystal through a buffer circuit, and is also picked by the half wave rectifier which then feeds the signal to the averaging circuit. The averaging circuit senses the amplitude of the signal coming off from the rectifier and provides an output DC signal to the variable gain operational amplifier, to adjust its gain.

Conventionally, the oscillator circuits for the quartz crystal do not have separate automatic gain control feedback path to maintain the proper value of the loop gain in the event of reduced quality factor of the crystal. Further, the oscillator circuits typically use bipolar transistors since they provide high gain along with large current drives which makes designing the circuits easier. However, in the current project, the aim was to design the entire circuit to be implemented on a single chip using CMOS technology, in a commercial foundry using the MOSIS integrated circuit fabrication service. Analog circuits based on CMOS technology are less widespread and are an active area of research. Additionally, it was required to design the circuit to have a frequency bandwidth of 100 MHz (since the typical operating frequency of miniaturized resonators can be as high as 100 MHz).

Initially, it was attempted to realize the proposed circuits on an evaluation board using off the shelf circuit components. The picture of the fabricated circuit is as shown in Figure 6.9. In one of the earlier attempts to build out of discrete components, the maximum operating frequency that could be achieved was 20 MHz.

As part of future work on this circuit, it is proposed to use Cadence design tools 260 modified by MOSIS™ to design, evaluate and determine the functionality of the circuit components and the circuit as a whole.

(a)

(b)

Figure 6.9: (a) Photograph of the set up used to monitor the resonance frequency of the oscillator circuit with dynamic feedback, (b) the circuit realized on an evaluation board.

261

APPENDIX A

This is the Mathematica program used to fit the resonance curves.

SetDirectory["D:\\mathematica\\"] (*Sets the data directory*) fitfn=a0+A*((f/fo)*Cos[phi]+(1-(f/fo)^2)* Q* Sin[phi])/((f/fo)^2+(1-

(f/fo)^2)^2*Q^2)

(*Defines the fitting function*) datfiles=[303]

(*Defines a list of data files to fit, performs the fit on each of the data files. Reports time required, fitted parameter values (fo and Q), and fit statistics. Results are written to a text file.*) paraml={};

(*defines an arbitary parameter for output of the results*)

Do[Print[s1"working on:"]; data=Drop[ReadList[StringJoin[ToString[s1],".dat"],Real,RecordLists→True],1 peakfit=Timing[{BestFit,BestFitParameters,ANOVATable}/.NonlinearRegress[data,f itfn,f,{{a0,450},{fo,19591375},[304],{Q,4000},[305]},RegressionReport→{BestFit,

BestFitParameters,ANOVATable}]];

Export[StringJoin[ToString[s1],".mprm"],peakfit[[2,2]],"Table"]; 262 datafit=Show[{Plot[peakfit[[2,1]],{f,data[[1,1]],Last[data][[1]]},PlotStyle RGBColo r[1,0,0],DisplayFunction→Identity],ListPlot[data[[All,{1,2}]],Prolog→AbsolutePoint

Size[1],DisplayFunction→Identity,PlotJoined→True]},GridLines→None,PlotRange

→All,PlotLabel→ToString[s1],Axes→False,Prolog→AbsolutePointSize[0.2],Displa yFunction→$DisplayFunction];

Print[peakfit[[1,1]]"Seconds Required"];

Print[NumberForm[peakfit[[2,2,2]],7]];

Print[peakfit[[2,2,4]]]; paraml=Append[paraml,{datfiles[[j]],NumberForm[fo/10^6,7]/.peakfit[[2,2,2]],Numb erForm[Abs[Q],5]/.peakfit[[2,2,4]]}];,{j,1,Length[datfiles]}];

Export["mdata.txt",paraml,"Table"];

Export["freqs.dat",paraml,"Table"];

Print[TableForm[paraml]]

263

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VITA

Abhijat received his bachelors degree from Indian Institute of Technology, Chennai in

Materials and Metallurgical Engineering in 2001. He then joined Penn State as a Master’s student in Electrical Engineering. He went on to complete his PhD degree from Penn

State in 2006. He has worked on several interdisciplinary projects during his short research career. During the past five years, he has been working in the general area of

MEMS and nanotechnology. He has developed ultrasensitive gravimetric and thermal sensors based on quartz resonators and has also investigated the integration of carbon nanotubes to the sensor platforms for specificity and added functionality. He is a member of MRS, IEEE, APS, and SPIE.