Antonio Arnau (Ed.)

Piezoelectric Transducers and Applications

With 112 Figures

Springer

Contents

Associated Editors and Contributors ...................................... XVII

1 ~~ndamentals on Piezoelectricity ................................................. 1.1 Introduction .......................................................................... 1

....................................................... 1.2 The Piezoelectric Effect 2 1.3 Mathematical Formulation of the Piezoelectric Effect . A

........................................................................... First Approach 4 1.4 Piezoelectric Contribution to Elastic Constants ................... 5

.............. 1.5 Piezoelectric Contribution to Dielectric Constants 5

.............. 1.6 The Electric Displacement and the Internal Stress 6 1.7 Basic Model of Electric Impedance for a Piezoelectric Material Subjected to a Variable Electric Field ......................... 7

........................................... 1.8 Natural Vibrating Frequencies 12 ...... 1.8.1 Natural Vibrating Frequencies Neglecting Losses l 2

1.8.2 Natural Vibrating Frequencies with Losses ................ 16 1.8.3 Forced Vibrations with Losses . Resonant

......................................................................... Frequencies -20 1.9 Introduction to the Microgravimetric Sensor ..................... 26

......................................................................... Appendix 1 .A. -29 The Butterworth Van-Dyke Model for a Piezoelectric

................................................................................ Resonator -29 1 .A. 1 Rigorous Obtaining of the Electrical Admittance of a

...... Piezoelectric Resonator . Application to AT Cut Quartz 29 1 . A.2 Expression for the Quality Factor as a Function of Equivalent Electrical Parameters ......................................... 36

................................................................................ References 37

2 Overview of Acoustic-Wave Microsensors ................................ 39 ........................................................................ 2.1 Introduction 39

............................................................... 2.2 General Concepts 40 ...................................................................... 2.3 Sensor Types 42

2.3.1 Quartz Crystal Thickness Shear Mode Sensors .......... 42 ...... 2.3.2 Thin-Film Thickness Longitudinal Mode Sensors 44

.................................. 2.3.3 Surface Acoustic Wave Sensors 44 ......... 2.3.4 Shear-Horizontal Acoustic Plate Mode Sensors 47

X Contents 1

2.3.5 Surface Transverse Wave Sensors ............................. 47 2.3.6 Love Wave Sensors ................................................... 48

...................................... 2.3.7 Flexural Plate Wave Sensors 48 2.4 Operating Modes ............................................................... 49 ! ......................................................................... 2.5 Sensitivity 51

............................................................................... References 53

3 Models for Piezoelectric Transducers Used in Broadband Ultrasonic Applications ................................................................. 55

3.1 Introduction ...................................................................... 55 3.2 The Electromechanical Impedance Matrix ....................... 56 . . 3.3 Equivalent Circults ............................................................ 60 3.4 Broadband Piezoelectric Transducers as Two-Port Networks . Transfer Functions .............................................. 63 References ............................................................................... 67

4 Models for Resonant Sensors .................................................... 69 4.1 Introduction ..................................................................... 69

............................................ 4.2 The Resonance Phenomenon 69 ................ 4.3 Concepts of Piezoelectric Resonator Modeling 70

..... 4.4 The Equivalent Circuit of a Quartz Crystal Resonator 75 ............................................. 4.5 Four Important Conclusions 78

4.5.1 The Sauerbrey Equation ............................................ 78 4.5.2 Kanazawa's Equation ................................................. 79

................................................. 4.5.3 Resonant Frequencies 79 ................................................... 4.5.4 Motional Resistance 80

.......................................................................... Appendix 4.A 80 4.A.1 Introduction ............................................................... 80 4.A.2 The Coated Piezoelectric Quartz Crystal . Analytical

............................................................................... Solution 81 .................................. 4.A.3 The Transmission Line Model 85

............................................................. 4.A.4 Special Cases 91 References ............................................................................... 99

5 Interface Electronic Systems for Broadband Ultrasonic Applications .................................................................................. 101 l

..................................................................... 5.1 Introduction 1 01 5.2 General Interface Schemes for an Efficient Coupling of

................................... Broadband Piezoelectric Transducers 102 l

Contents XI

5.3 Electronic Circuits Used for the Generation of High Voltage Driving Pulses and Signal Reception in Broadband

..................................................... piezoelectric Applications 104 5.3.1 Some Classical Circuits to Drive Ultrasonic

........................................................................ Transducers 104 5.3.2 Electronic System Developed for the Efficient Pulsed

............................ Driving of High Frequency Transducers 106 5.3.3 Electronic Circuits in Broadband Signal Reception .. l09

............................................................................. References 110

6 Interface Electronic Systems for AT Quartz Crystal .................................................................. Microbalance Sensors 111

6.1 Introduction ................................................................... 111 6.2 A Suitable Model for Including a QCMS as Additional

...................................... Component in an Electronic Circuit 112 .......... 6.3 Critical Parameters for Characterizing the QCMS 113

6.4 Systems for Measuring Sensor Parameters and their ........................................................................... Limitations 1 1 5

............................... 6.4.1 Impedance or Network Analysis 116 6.4.2 Decay and Impulse Excitation Methods ................... 117 6.4.3 Oscillators ................................................................. 121 6.4.4 Parallel Capacitance Compensation Techniques ...... 130

................................. 6.4.5 The Transfer Function Method 132 ..................................................................... 6.5 Conclusions 133

......................................................................... Appendix 6 .A 134 Critical Frequencies of a Resonator Modeled as a BVD

.................................................................................... Circuit 134 6.A. 1 Equations of Admittance and Impedance ................. 134

................................................. 6.A.2 Critical Frequencies -136 ........................................ 6.A.3 The Admittance Diagram 138

............................................................................. References 140

............................................... 7 Modified Piezoelectric Surfaces 141 ...................................................................... 7.1 Introduction 141 . . .......................................................... 7.2 Metallic Deposition 141

...................................................... 7.2.1 Vacuum Methods 142 .................................................. 7.3 Electrochemical Method 143

XII Contents

7.3.1 Technique Based on Glued Solid Foil (Nickel. Iron. .............................................................. ... Stainless Steel ) 145

......................................... 7.3.2 Organic Film Preparation 146 .............................................. 7.3.3 Monolayer assemblies 146 ............................................. 7.4 Biochemical Modifications 149

7.4.1 Direct Immobilization of Biomolecules (Adsorption. ............................................................ Covalent Bonding) 149

7.4.2 Entrapping of Biomolecules (Electrogenerated Polymers: Enzyme. Antibodies. Antigens ... ) ................... 150

............................................... 7.4.3 DNA Immobilization 150 ............................................................................. References 151

8 Sonoelectrochemistry ............................................................... 153 ..................................................................... 8.1 Introduction 153

................................. 8.2 Basic Consequences of Ultrasound 154 ........................................... 8.3 Experimental Arrangements 154

.................................................................... 8.4 Applications 156 .................................................. 8.4.1 Sonoelectroanalysis 157 ................................................ 8.4.2 Sonoelectrosynthesis 157

8.4.3 Ultrasound and Bioelectrochemistry ........................ 157 8.4.4 Corrosion, Electrodeposition and Nanopowders ...... 158

............................... 8.4.5 Waste Treatment and Digestion 159 ...................................... 8.4.6 Multi-frequency Insonation 159

................................................................ 8.5. Final Remarks 159 ............................................................................. References 159

9 Chemical Sensors ...................................................................... 161 ................................. 9.1 Introduction ............................ 161

................................................. 9.2 Electrochemical Sensors 163 .................................................... 9.3 Potentiometric Sensors 164 .................................................... 9.4 Amperometric Sensors 166

............................................................... 9.5 Optical Sensors 168 9.6 Acoustic Chemical Sensors ............................................. 170

....................................................... 9.7 Calorimetric Sensors 171 ............................................................................. References 171

10 Biosensors . Natural Systems and Machines ......................... 173 I

................................................................... 10.1 Introduction 173 .............................. 1 0.2 General Principle of Cell Signaling 173

Contents XI1

...................................................................... 10.3 Biosensors 177 .............................................. 10.3.1 Molecular Transistor 1 8 1

10.3.2 Analogy and Difference of Biological System and ........................................................... Piezoelectric Device 181

.......................................................................... References 1 8 3

11 ~ ~ ~ d a r n e n t a l s of Electrochemistry ........................................ 185 ............................................................... 1 1 . 1 Introduction 1 8 5

..................................... 1 1.2 What is an Electrode Reaction? 185 ....................................................... 1 1.3 Electrode Potentials 187

.................................. 1 1.4 The Rates of Electrode Reactions 188 1 1.5 How to Investigate Electrode Reactions

....................................................................... Experimentally 189 1 1.6 Electrochemical Techniques and Combination with Non-

.................................................. Electrochemical Techniques -191 ................................................................... 1 1.7 Applications 192 .................................................................. 1 1.8 Bibliography 193

...................................................... 1 1.9 Glossary of Symbols 193 ............................................................................ References 1 9 4

........................... 12 Viscoelastic Properties of Macromolecules 195 .................................................................... 12.1 Introduction 195

12.2 Molecular Background of Viscoelasticity of Polymers . l96 ......... 12.3 Shear Modulus, Shear Compliance and Viscosity l99

..................... 12.4 The Temperature-Frequency Equivalence 205 .................................................................... 12.5 Conclusions 210

......................................................................... References 2 1 1

13 Combination of Quartz Crystal ~icrobalance with other Techniques .................................................................................... 213

................................................................... 1 3.1 Introduction -213 13.2 Electrochemical Quartz Crystal Microbalance and other

............................................................................ Techniques -214 .............................................................................. References 222

14 Ultrasonic Systems for Non-Destructive Testing Using Piezoelectric Transducers ............................................................ 225

............................... 14.1 Generalities about Ultrasonic NDT 225

XIV Contents

14.1.1 Some Requirements for the Ultrasonic Responses in ............................................................. NDT Applications 226

14.2 Through-Transmission and Pulse-Echo Piezoelectric .................. Configurations in NDT Ultrasonic Transceivers 227

14.3 Analysis in the Frequency and Time Domains of Ultrasonic Transceivers in Non-Destructive Testing

............................................................................... Processes 229 14.4 Multi-Channel Schemes in Ultrasonic NDT Applications for High Resolution and Fast Operation ............................... 232

14.4.1 Parallel Multi-Channel Control of Pulse-Echo Transceivers for Beam Focusing and Scanning Purposes . 233 14.4.2 Electronic Sequential Scanning of Ultrasonic Beams

................................................ for Fast Operation in NDT 235 References .......................................................................... 237

15 Ultrasonic Hyperthermia ....................................................... 241 ................................................................... 15.1 Introduction 241

........................................................... 15.2 Ultrasonic Fields 241 ................................................... 15.3 Ultrasonic Generation 243

............................................. 15.3.1 Piezoelectric Material 244 ........................................ 15.3.2 The Therapy Transducer 244

................................. 15.3.3 Additional Quality Indicators 245 .................................. 15.3.4 Beam Non Uniformity Ratio 245

............................ 15 .3.5 Effective Radiating Area (ERA) 246 ......................................... 15.4 Wave Propagation in Tissue 246

.............................................. 15.4.1 Propagation Velocity 246 ............................................... 15.4.2 Acoustic Impedance 246

............................................................. 1 5.4.3 Attenuation 247 ............................................... 15.5 Ultrasonic Hyperthermia 248

15.6 Focusing Ultrasonic Transducers ............................. 249 I

15.6.1 Spherically Curved Transducers ............................ 250 l

................................................... 15.6.2 Ultrasonic Lenses 250 ................................................. 15.6.3 Electrical Focusing 250 .................................................. 1 5.6.4 Transducer Arrays 251

........................................... 15.6.5 Interstitial Transducers 251 ........................................................................... 15.7 Trends 253 I

............................................................................. References 253

Contents XV

16 Data analysis and Interpretation in Bulk Acoustic Wave . ................................................... Thickness Shear Mode Sensors 255

.................................................................. . 16.1 Introduction -255 16.2. Transmission Line Model, Experimental Data and

.......................................................................... Interpretation 256 16.2.1. Experimental Parameters for Sensor

................................................................ Characterization -258 16.2.2 Interpretation of Simple Cases ................................ 262 6.3.2. Limits of the Simple Cases ...................................... 269

16.3 The General Case . The Problem of Data Analysis and .......................................................................... Interpretation 275

16.3.1 Different Strategies to Face the Problem ................ 276 16.3.2 Additional Considerations . Calibration ................... 283 16.3.3. Other Effects . The N-layer Model ......................... 284

.............................................................................. References 285

Appendix A Fundamentals of Electrostatics .............................. 287 .............................................. A . 1 Principles of Electrostatics 287

A.2 The Electric Field ............................................................ 288 .............................................. A.3 The Electrostatic Potential 289

........................ A.4 Fundamental Equations of Electrostatics 290 A.5 The Electric Field in Matter . Polarization and Electric

......................................................................... Displacement -291

.............................. Appendix B Physical Properties of Crystals 299 ..................................................................... B . 1 Introduction 299

............................................................. B.2 Elastic Properties 299 B.2.1 Stresses and Strains .................................................. 300 B . 2.2 Elastic Constants . Generalized ~ o o k e ' s Law ........... 306

B.3 Dielectric Properties ........................................................ 310 B.4 Coefficients of Thermal Expansion ................................. 311 B.5 Piezoelectric Properties ................................................... 311

Index .............................................................................................. 315

Index

Acoustic Impedance, 246 Acoustic impedance matching, 64,

65 acoustic load approximation, 26 1 acoustic load impedance, 74,257,

260 acoustic wave, 40

Bleustein-Gulyaev, 42 bulk, 40 flexural plate, 41 Lamb, 41,226 Longitudinal, 226 Love, 41,226 Plate, 4 1 Rayleigh, 4 1,226 Shear horizontal, 41 surface, 40 surface skimming bulk, 42 surface transverse, 41 transverse (shear), 226

Acoustic-wave microsensors, 39 characteristics, 52 Flexural Plate, 47 General Concepts, 40 Love, 47 Operating Modes, 48 Sensitivity, 50 Shear-Horizontal Acoustic Plate

Mode, 46 Surface, 44 Surface Transverse, 46 Thin-Film Thickness

Longitudinal Mode, 43 Admittance, 133

conductance G, 259 Diagram, 137 Equations, 133 susceptance B, 259

AT cut crystal, 26 Attenuation, 247

attenuation coefficients, 248

Beam Non uniformity Ratio, 245 Biochemical Modification, 149 Biosensors, 173

Cell Signaling, 173 enzyme electrode, 178 membrane receptors, 174 Molecular Transistor, 18 1 selectivity, 178 sensitivity, 179

Broadband Models, 55 Broadband Signal Reception, 109

Cavitation, 154

characteristic frequencies, 25 Chemical Sensors, 16 1

Selectivity, 163 Sensitivity, 163 Stability, 163

clamped capacitance, 59, 103, 108 complex compliance, 200 complex viscosity, 200 compliance coefficient, 5 Coulomb's law, 288 Crystals, 299

Dielectric Properties, 3 10 Elastic Proper-ties, 299 Piezoelectric Properties, 3 11 thermal expansion coefficients,

311

dielectric constant, 5 displacement vector, 296 dissipation, 77

effective dielectric constant, 6 Effective Radiating Area, 246 Efficient Coupling, 102 Elastic Constants, 306 Electric Displacement, 6

316- Index

Electric Field, 288 Electric Impedance, 7

Basic Model, 7 Electrical Admittance, 28

of a Piezoelectric Resonator, 28 electrical impedance matching, 64,

103,229 electrochemical impedance, 192,

214 Electrochemical Techniques, 19 1 Electrochemistry, 185

electrochemical cell, 189 electrode reactions, 185, 188 Electrode reactions, 185 oxidation, 185, 186 reduction, 185, 186

Electrode Potentials, 187 electromechanical coupling factor,

63,259 Electromechanical Impedance

Matrix, 56, 59 Electronic Circuits, 104 electronic focusing, 233,235 electronic nose, 162 Electronic Scanning, 235,237 electropolymerisation, 146 Electrostatic Potential, 289 Electrostatics, 287

free charges, 291 linked charges, 292 polarization, 293 principle of charge conservation,

287 principle of charge quantization,

288 Ellipsometry, 277 Entrapping, 150 Equivalent Circuits, 60

Butterworth Van-Dyke, 28 KLM, 61 Mason, 60 Modified Butterworth-Van Dyke,

90 Redwood, 61

Faraday constant, 164

Faraday law, 278 Fermi energy level, 186 film resonance, 262 Fraunhofer zone, 242 frequency constant, 26 Fresnel zone, 242

galvanostat, 190 Gauss' law, 290 Generation of Driving Pulses, 104

half power spectrum of the resonance, 76,26 1

High Voltage Driving, 104 Hooke's Law, 306

Immobilization, 149 DNA, 150

Impedance, 133 Equations, 63, 133

Interface Electronic Systems, 10 1, 103,109 high-voltage ramp generator, 102,

106 matching, 102, 103,227 pulsed transmitter, 103 I selective damping, 106, 108,228 spike generator, 106

Kanazawa Equation, 78, 95 Kanazawa' s extended equation, 267

l

Lanbert-Beer law, 168 Langrnuir-Blodgett, 147 loss tangent, 204

Macromolecules, 195 Isomers, 197 morphology, 197 polymers, 197

Martin's Equation, 96 matching circuits, 103,227,229,

232 matching layers, 56, 65 Maxwell Equation, 298

rrr r I I I r I ~ - r ~ - ~ - r r r r r r r CI

Index 317

Maxwell model, 201 mechanical transmission lines, 6 1,

65 Metallic Deposition, 141 Microbalance and other Techniques,

214 atomic force microscopy, 2 15 calorimetry, 2 16 Ellipsometry, 2 16 impedance spectroscopy, 214 scanning electrochemical

microscope, 220 scanning tunnelling microscopy,

215 surface plasmon resonance, 2 15,

218 Microbalance Sensors, 11 1

Critical Frequencies, 133 Critical Parameters, 113 Electrochemical Quartz Crystal,

214 Interface Electronic Systems, 11 1 Measuring Sensor par-meters,

115 Microgravimetric Sensor, 11,25 Models for Piezoelectric

Transducers, 55 Broadband, 55 Electromechanical Impedance

Matrix, 56 Equivalent Circuits, 60 KLM, 62 Mason, 60 Redwood, 61 transmission line analogy, 62

Monolayer assemblies, 146 motional, 33

impedance, 33,258 Resistance, 79 series resonant frequency, 34

Nernst equation, 187 Newtonian Liquid, 264

Newtonian behavior, 264 Non-Destructive Testing, 225

Beam Focusing, 233

dynamic focusing, 233,236 Electronic Sequential Scanning,

235 High Resolution, 232 high-voltage Mux-Dmux, 236 Multichannel schemes, 225,232,

234,236 pulse-echo, 227,228 rapid-scan, 237 Through-Transmission, 227,228 Ultrasonic Response, 225 Ultrasonic transceivers, 227,228

optrode, 168 Oscillators, 121

automatic gain control, 129 Motional Resistance

Determination, 129 MSRF Determination, 127 Oscillating Conditions, 123 Parallel Mode Crystal, 124 Series Mode Crystal, 125

Parallel Capacitance Compensation, 130

parasitic capacitance, 257 partition coefficient, 170 Phase-Zero frequencies, 135 Piezoelectric Effect, 2

Dielectric Constants, 5 Elastic Constants, 5 Mathematical Formulation, 4 piezoelectric'polarization, 5

piezoelectric strain coefficient, 4 piezoelectric stress constant, 5 piezoelectrically stiffened constant,

5 Piezoelectricity, 2 Poisson coefficient, 306 Poisson's Equation, 29 1 Poisson's ratio, 202 polarization vector, 295 Polymer Electrogeneration, 146 Polymers, 198

dynamic glass transition, 209 entanglement coupling, 198

318 Index

glass-rubber transition, 202 loss tangent, 204 Macromolecules, 195 modified WLF-equation, 209 Shear Modulus, 199 Temperature-Frequency

Equivalence, 204 Viscoelastic properties, 198 Viscoelastic solids, 203 viscosity, 198 WLF equation, 206

potentiostat, 190 propagation speed, 15 pulse-echo applications, 65 Pulser, 106,228,237

multichannel, 234 PZT, 244

quality factor, 19

Receiver, 229,237 Resonant Frequencies, 20

Series and parallel, 135 Resonant Sensors, 69

Acoustic Load, 88 Acoustic Load Concept, 92 Calibration, 264,282 Kanazawa Equation, 95 Martin's Equation, 96 Modeling, 70 Modified Butterworth-Van Dyke

Circuit, 90 Sauerbrey Equation, 94 Small phase shift approximation,

97 Transmission Line Model, 85,

256

Sauerbrey condition, 263 Sauerbrey Equation, 78

Sauerbrey Equation, 94 Sensitivity, 50

nominal, 5 1 usable, 5 1

Sensor Characterization, 258 Experimental Parameters, 258

Sensors, 161 Acoustic Chemical, 169 Amperometric, 166 Calorimetric, 170 Chemical, 16 1 Electrochemical, 163 Optical, 168 Potentiometric, 164

shear loss modulus, 199 Shear Modulus

frequency dependence, 200 shear storage modulus, 199 Signal Reception, 109,228 small surface load impedance

condition, 260,274 Sonoelectroanalysis, 157 Sonoelectrochemistry, 153

Bioelectrochemistry, 157 Corrosion, 158 Electrodeposition, 158 Waste treatment, 159

Sonoelectrosynthesis, 157 Sputtering, 142 static capacitance, 257 Stationary waves, 18 Surface plasmon resonance, 169

Tafel relation, 189 thickness extensional transducer, 57,

60,62 thickness shear mode, 8 time constant, 1 18 Transfer Functions, 63,66,229 Transmission Line Model, 6 1

Ultrasonic Application, 55, 10 1,225 ultrasonic array, 233,235,237 Ultrasonic Hyperthermia, 241,248

Focusing, 249,250 Ultrasonic System, 225 Ultrasonic Transceiver, 227,229

Analysis in the Frequency Domain, 229

ultrasonic transducers, 66, 104,234 Coupling, 102, 103,108 damping, 106,108,228

Index 319

Driving, 104 matching, 103,227 pulse-echo, 65,228 Transfer Functions, 63 tuning, 227,228,230

Vibrating Frequencies, 12 fundamental frequency, 15 inharmonic modes, 15 with Losses, 15

viscoelastic contribution, 273,278 Viscoelastic Medium, 265 Viscoelasticity, 196

viscosity, 9 viscous phenomenon, 9 Voigt model, 201 voltammetry, 190

wave length, 14 wave number, 14 wave propagation speed, 18 WLF equation, 206

Young's modulus, 306