Antonio Arnau (Ed.)

Piezoelectric Transducers and Applications

Springer-Verlag Berlin Heidelberg GmbH

Antonio Arnau (Ed.)

Piezoelectric Transducers and Applications

With 112 Figures

' Springer

Prof. Dr. Antonio Arnau Vives Departamento de Ingenieria Electr6nica Universidad Politecnica de Valencia Camino de Vera s/n E - 46022 Valencia Spain aarnau@eln. upv.es

ISBN 978-3-662-05363-8 ISBN 978-3-662-05361-4 (eBook) DOI 10.1007/978-3-662-05361-4

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Foreword

One of the most valuable aids to those beginning to investigate a new area of study is a source which will guide them from beginning principles, through detailed implementation and applications. Even for seasoned in­vestigators, it is useful to have a reasonably detailed discussion of closely related topics in a single volume to which one can refer. This is often diffi­cult for many emerging areas of studies because they are so multi­disciplinary. The subject matter of the principles, techniques and applica­tions of piezoelectric transducers certainly fits into this category. The host of emerging new uses of piezoelectric devices that are being commercial­ized as well as the growing number of potential applications ensures that this field will encompass more and more disciplines with passing time. It is extremely fortunate and timely that this volume becomes available to the student at this time.

Piezoelectricity is a classical discipline traced to the original work of Jacques and Pierre Curie around 1880. This phenomenon describes the re­lations between mechanical strains on a solid and its resulting electrical behavior resulting from changes in the electric polarization. One can create an electrical output from a solid resulting from mechanical strains, or can create a mechanical distortion resulting from the application of an electri­cal perturbation. In the former case, the unit acts as a receiver of mechani­cal variations, converting it into electrical output, as in the case of a micro­phone. In the latter case, the unit can act as a transmitter converting the electrical signal into a mechanical wave. The piezoelectric units can be used both in narrow-band or resonant modes, and under broad-band re­gimes for detection and imaging applications. One of the remarkable prop­erties of these devices is the ability to use them in a viscous medium, such as a liquid. When excited sinusoidally, these devices can generate waves in the immersing medium. Typically, as a result of the physical size of these devices, the waves are in the ultrasonic regime. From this classical disci­pline, an astounding number of applications are developing. From its use as a frequency generating standard in the earlier part of the 201h century, additional uses have seen these devices used as highly sensitive mass bal­ances for use both in vacuum deposition and in electrochemical applica­tions, as well as chemical specific sensors, as Doppler devices for fluid ve­locity measurements and for ultrasonic imagery. There are many other emerging applications in the bio-sciences for example. The number of ap­plications is astounding.

VI

It is clear that the discipline is inter-disciplinary. The authors of the con­tents of this book are a select group who has all been challenged by the in­tellectual diversity of the field. To successfully pass on such diverse in­formation, intellectual competence is only a beginning. A devotion to, and love of clear communication is also required. These authors are members of the PETRA organization, (Piezoelectric Transducers and Applications) sponsored by the European Union, devoted to the collection and dissemi­nation of knowledge and skills in the piezoelectric arts to students among the participating universities in Europe and Latin America. I have person­ally observed many of the authors interacting with students and have been very impressed by their care and mentoring. Contributions from such dedi­cated and seasoned teachers are now available to the student in this vol­ume. This book fills a real need for a unified source for information on piezoelectric devices, ranging from broadband applications to resonant ap­plications and will serve both experienced researchers and beginning stu­dents well.

Kay Keiji Kanazawa Technical Director, Emeritus

CPIMA Stanford University Stanford, CA 94305

Preface

This book is one of the results from the PETRA network (PiezoElectric TRansducers and Applications) following the execution of the project PETRA I co-financed by the European Union in the framework of the ALFA Program (America Latina Formaci6n Academica). It is not the ob­jective of the book to give a complete and detailed treatment of all the fac­ets related to piezoelectricity, piezoelectric transducers and their applica­tions, which would be completely impossible in a single-volume work, but to provide a guide for doctoral degree students and for researchers going into this complex and multidisciplinary issue, at least in those topics in which the members of the network carry out their research.

The book covers, in 16 chapters and two appendices, aspects related to piezoelectric transducers and their applications. Some of the chapters focus on the more basic concepts of the different disciplines involved and are presented in a didactic way, while others go deeper into complex aspects of the specific field of research that they treat, following a similar structure to that of a scientific article. Chapters 1, 11 and Appendices A and B pre­sent, respectively, basic concepts of piezoelectricity, electrochemistry, electrostatics and physical properties of crystals. Chapters 4, 6, 13 and 16 delve more deeply into resonant sensors, especially bulk acoustic wave thickness shear mode resonators and their applications as quartz microbal­ance sensors, their fundamentals and models (Chap. 4), electronic inter­faces and associated problems (Chap. 6), the problems associated with the analysis and interpretation of the experimental data (Chap. 16), and com­plementary techniques (Chap. 13). Chapters 3, 5 and 14 deal with broad­band ultrasonic systems, introducing basic aspects and different models of piezoelectric transducers (Chap. 3), electronic interfaces used in broadband configurations (Chap. 5) and ultrasonic schemes and electronic implemen­tations for non-destructive testing industrial applications (Chap. 14). Chap­ters 8 and 15 introduce specific applications of ultrasonic waves in differ­ent disciplines - sonoelectrochemistry (Chap. 8) and hyperthermia (Chap. 15).

Finally, Chapters 2, 7, 9, 10 and 12 present overviews concerning spe­cific or related aspects of resonant sensors and their applications. Chapter 2 is an overview of acoustic sensors, and Chapter 7 provides a guide to the important subject of modification of piezoelectric surfaces in piezoelectric transducers for sensor applications. Chapter 9 provides an overview of chemical sensors, which is of great interest for establishing the differences between chemical sensors based on piezoelectric transducers and those

'1111 Preface

based on other techniques, such as electrochemical, optical, calorimetric and magnetic techniques, and in consequence to facilitate the interpretation of the different data. Chapter 10 treats the specific topic of biosensors from a biological point of view; this treatment is especially useful to understand the mechanism of biological recognition and its potential use for the de­velopment of biosensors and, specifically, for piezoelectric biosensors, which is a field of much current interest. Finally, Chapter 12 introduces the concept of viscoelasticity and describes in depth the physical properties of polymers, an aspect of great importance in resonant sensor applications.

The present volume is the result of the effort of a work group that began to be formed nearly 4 years ago and that I have had the honour of coordi­nating. I will always be in debt to my colleagues, eminent professors and now dear friends that gave me, at that time, the opportunity and the re­sponsibility of creating something, maybe different, and therefore giving sense to life, since, as Gregorio Marafi6n, a famous Spanish doctor in medicine and writer said: to live is not only to exist, but to exist and to cre­ate, to know how to enjoy and suffer and not to sleep without dreaming, to rest is to begin to die. Any effort would have been useless without the work and dedication of all of those that carried out the important labour of writing each of the chapters and who reviewed and patiently corrected the different versions of the chapters. Theirs is all the merit, the defects only belong to me, but if the work that is presented can facilitate the study of and the access to this multidisciplinary topic, it will have been worth it. They say that the bad things come without being called while the good things have to be carried out with great effort. I hope this effort has pro­vided something good that helps others. Very recently, the project PETRA II, the second phase of PETRA I, was approved by the European Union for development during the next three years. The project will include 28 re­search training projects and the creation of a joint course of multidiscipli­nary training by the 14 members of the network. Undoubtedly, it will re­quire much effort, but it will allow us to create something more, new and different that will help us to continue giving sense to our lives.

Antonio Arnau Vives

December 2003

Contents

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

1 Fundamentals on Piezoelectricity ................................................ ! 1.1 Introduction .......................................................................... ! 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 ........... .............. ? 1.8 Natural Vibrating Frequencies ........................................... 12

1.8.1 Natural Vibrating Frequencies Neglecting Losses ...... l2 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 l.A ................................................ .................. ......... 29 The Butterworth Van-Dyke Model for a Piezoelectric Resonator ................................................................................. 29

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

References .......................................................... ... ................... 3 7

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

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 Circuits ..................................... ............... ........ 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.l 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

5.1 Introduction .................................................... ................. 101 5.2 General Interface Schemes for an Efficient Coupling of Broadband Piezoelectric Transducers ................................... 102

Contents XI

5.3 Electronic Circuits Used for the Generation of High Voltage Driving Pulses and Signal Reception in Broadband Piezoelectric Applications ..................................................... 1 04

5.3.1 Some Classical Circuits to Drive Ultrasonic Transducers ........................................................................ 1 04 5.3.2 Electronic System Developed for the Efficient Pulsed Driving ofHigh Frequency Transducers ............................ l06 5.3.3 Electronic Circuits in Broadband Signal Reception .. I 09

References .............................................................................. 11 0

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

6.1 Introduction ...................................................................... lll 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 ............................................................ ...... ........... 115

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 ...................................................................... l33 Appendix 6 .A ......................................................................... 134 Critical Frequencies of a Resonator Modeled as a BVD Circuit .................................................................................... 134

6.A.l 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 VacuumMethods ........................ .............. ................ l42 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 ofUltrasound ................................. 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......................................... ..... .. ............................. 1 71

10 Biosensors. Natural Systems and Machines ......................... 173 10.1 Introduction ............................ ....................................... 173 10.2 General Principle of Cell Signaling .............................. 173

Contents XIII

10.3 Biosensors .......... ......... ........................ ... ........................ 177 10.3.1 Molecular Transistor .................. .. ........................... 181 10.3.2 Analogy and Difference of Biological System and Piezoelectric Device ....... ........ ... .... ..................................... 181

References .............................................................................. 183

11 Fundamentals of Electrochemistry ........................................ 185 11.1 Introduction .................. ........... ............................... .. ...... 185 11.2 What is an Electrode Reaction? ......... ... ............. .... ........ 185 11.3 Electrode Potentials ....................................................... 187 11.4 The Rates of Electrode Reactions .................... .............. 188 11.5 How to Investigate Electrode Reactions Experimentally ....................................................................... 189 11.6 Electrochemical Techniques and Combination with Non-Electrochemical Techniques .................................................. 191 11.7 Applications ......................................... .... ................. ..... 192 11.8 Bibliography .................................................................. 193 11.9 Glossary of Symbols ...................................................... 193 References .............................................................................. 194

12 Viscoelastic Properties of Macromolecules ........................... 195 12.1 Introduction .......................... .. ... ... ........ .......................... 195 12.2 Molecular Background of Viscoelasticity of Polymers .196 12.3 Shear Modulus, Shear Compliance and Viscosity ......... 199 12.4 The Temperature-Frequency Equivalence ..................... 205 12.5 Conclusions .................................................................... 210 References .............................................................................. 211

13 Combination of Quartz Crystal Microbalance with other Techniques .................................................................................... 213

13.1 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 ofPulse-Echo Transceivers for Beam Focusing and Scanning Purposes. 233 14.4.2 Electronic Sequential Scanning ofUltrasonic Beams for Fast Operation in NDT .......... ....... ................ ..... .......... 235

References ..................................................................... ........ 23 7

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 15.4.3 Attenuation .............................. ...................... ...... ... 247

15.5 Ultrasonic Hyperthermia ............................................... 248 15.6 Focusing Ultrasonic Transducers ... ............................ ... 249

15.6.1 Spherically Curved Transducers ............................ 250 15.6.2 Ultrasonic Lenses ................... ................................ 250 15.6.3 Electrical Focusing ................................................. 250 15.6.4 Transducer Arrays ....... .... ....... .. .............. ....... .. ....... 251 15.6.5 Interstitial Transducers ........................................... 251

15.7 Trends .......................................... ....................... .......... 253 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 ofthe Simple Cases ..................................... .269

16.3 The General Case. The Problem of Data Analysis and Interpretation .......................................................................... 27 5

16.3.1 Different Strategies to Face the Problem ............... .276 16.3 .2 Additional Considerations. Calibration .................. .283 16.3.3. Other Effects. TheN-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 Hooke's Law ........... 306

B.3 Dielectric Properties ........................................................ 31 0 B.4 Coefficients ofThermal Expansion ................................. 311 B.5 Piezoelectric Properties ................................................... 311

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

Associated Editors and Contributors

Amau,A. Departamento de Ingenieria Electr6nica, Universidad Politecnica de Valencia Camino de Vera s/n, Valencia E-46022 Spain

Brett, C. Departamento de Quimica, Faculdade de Ciencias e Tecnologia, Universidade de Coimbra Rua Larga, Coimbra-3004-535 Portugal

Calvo, E. Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabellon 2, Ciudad Universitaria, AR-1428 Argentina

Ferrari, V. Dipartamento di Electr6nica per 1 'Automazione, Universita' degli Studi di Brescia Via Branze 38, Brescia 1-25123 Italy

Gonzalez, G. Departamento de Ingenieria Electrica, Centro de Investigaci6n y Estudios A vanzados Avda. Instituto Politecnico Nacional No 2508, San Pedro Zacatenco, Mexico, D.F. 07360 Mexico, D.F.

Jimenez, Y. Departamento de Ingenieria Electr6nica, Universidad Politecnica de Valencia. Camino de Vera s/n, Valencia E-46022 Spain

XVIII Associated Editors and Contributors

Kanazawa, K. Center of Polymer Interfaces and Macromolecular Assemblies, Stanford University Stanford University, North-South Mall381, Stanford, CA 94305-5025 USA

Leija, L. Departamento de Ingenieria Electrica, Centro de Investigaci6n y Estudios A vanzados Avda. Instituto Politecnico Nacional N° 2508, San Pedro Zacatenco, Mexico, D.F. 07360 Mexico, D.F.

Lucklum, R. Institute for Micro and Sensor Systems, Otto-Von-Giiericke UniversiHit Magdeburg UniversiUitsplatz 2, Magdeburg D-39016 Germany

Mufioz, R. Departamento de Ingenieria Electrica, Centro de Investigaci6n y Estudios A vanzados A vda. Instituto Politecnico Nacional no 2508, San Pedro Zacatenco, Mexico, D.F. 07360 Mexico, D.F.

Otero, M. Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires. Pabellon 2, Ciudad Universitaria, AR-1428 Argentina

Perrot, H. Laboratoire Interface et Systemes Electrochimiques, Universite P. et M. Curie Place Jussieu 4, Paris 75252 France

Ramos, A. Departamento de Sefiales, Sistemas y Tecnologias Ultras6nicas. Instituto de Acustica. Consejo Superior de Investigaciones Cientificas. Serrano 144, Madrid 28006 Spain

Associated Editors and Contributors XIX

San Emeterio, J.L. Departamento de Sefiales, Sistemas y Tecnologias Ultras6nicas. Instituto de Acustica. Consejo Superior de Investigaciones Cientificas. Serrano 144, Madrid 28006 Spain

Soares, D. Instituto de Fisica, Departamento de Fisica Aplicada, Universidade Estadual de Campinas Caixa Postal6165, Campinas 13083-970 Brasil

Sogorb, T. Departamento de Ingenieria Electr6nica, Universidad Politecnica de Valencia Camino de Vera s/n, Valencia E-46022 Spain

Stipek, S. Institute of Medical Biochemistry, First Faculty of Medicine, Charles University in Prague Katerinska 32. Prague CZ-121 08 Czech Republic