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Resonant MEMS: Fundamentals, Implementation, and Application

Oliver Brand (Editor), Isabelle Dufour (Editor), Stephen Heinrich (Editor), Fabien Josse (Editor), Gary K. Fedder (Series Editor), Christofer Hierold (Series Editor), Jan G. Korvink (Series Editor), Osamu Tabata (Series Editor)
ISBN: 978-3-527-33545-9
512 pages
June 2015
Resonant MEMS: Fundamentals, Implementation, and Application (3527335455) cover image

Description

Part of the AMN book series, this book covers the principles, modeling and implementation as well as applications of resonant MEMS from a unified viewpoint. It starts out with the fundamental equations and phenomena that govern the behavior of resonant MEMS and then gives a detailed overview of their implementation in capacitive, piezoelectric, thermal and organic devices, complemented by chapters addressing the packaging of the devices and their stability. The last part of the book is devoted to the cutting-edge applications of resonant MEMS such as inertial, chemical and biosensors, fluid properties sensors, timing devices and energy harvesting systems.

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Table of Contents

Series editor’s preface XV

Preface XVII

About the Volume Editors IX

List of Contributors XXI

Part I: Fundamentals 1

1 Fundamental Theory of Resonant MEMS Devices 3
Stephen M. Heinrich and Isabelle Dufour

1.1 Introduction 3

1.2 Nomenclature 4

1.3 Single-Degree-of-Freedom (SDOF) Systems 5

1.3.1 Free Vibration 6

1.3.2 Harmonically Forced Vibration 8

1.3.3 Contributions to Quality Factor from Multiple Sources 13

1.4 Continuous Systems Modeling: Microcantilever Beam Example 14

1.4.1 Modeling Assumptions 15

1.4.2 Boundary Value Problem for a Vibrating Microcantilever 16

1.4.3 Free-Vibration Response of Microcantilever 17

1.4.4 Steady-State Response of a Harmonically Excited Microcantilever 19

1.5 Formulas for Undamped Natural Frequencies 22

1.5.1 Simple Deformations (Axial, Bending, Twisting) of 1D Structural Members: Cantilevers and Doubly Clamped Members (“Bridges”) 23

1.5.1.1 Axial Vibrations (Along x-Axis) 23

1.5.1.2 Torsional Vibrations (Based on h ⪡ b) (Twist About x-Axis) 24

1.5.1.3 Flexural (Bending) Vibrations 24

1.5.2 Transverse Deflection of 2D Structures: Circular and Square Plates with Free and Clamped Supports 25

1.5.3 Transverse Deflection of 1D Membrane Structures (“Strings”) 25

1.5.4 Transverse Deflection of 2D Membrane Structures: Circular and Square Membranes under Uniform Tension and Supported along Periphery 26

1.5.5 In-Plane Deformation of Slender Circular Rings 26

1.5.5.1 Extensional Modes 26

1.5.5.2 In-Plane Bending Modes 26

1.6 Summary 27

Acknowledgment 27

References 27

2 Frequency Response of Cantilever Beams Immersed in Viscous Fluids 29
Cornelis Anthony van Eysden and John Elie Sader

2.1 Introduction 29

2.2 Low Order Modes 30

2.2.1 Flexural Oscillation 30

2.2.2 Torsional Oscillation 36

2.2.3 In-Plane Flexural Oscillation 37

2.2.4 Extensional Oscillation 37

2.3 Arbitrary Mode Order 38

2.3.1 Incompressible Flows 38

2.3.2 Compressible Flows 46

2.3.2.1 Scaling Analysis 47

2.3.2.2 Numerical Results 48

References 51

3 Damping in Resonant MEMS 55
Shirin Ghaffari and Thomas William Kenny

3.1 Introduction 55

3.2 Air Damping 56

3.3 Surface Damping 59

3.4 Anchor Damping 61

3.5 Electrical Damping 63

3.6 Thermoelastic Dissipation (TED) 64

3.7 Akhiezer Effect (AKE) 66

References 69

4 Parametrically Excited Micro- and Nanosystems 73
Jeffrey F. Rhoads, Congzhong Guo, and Gary K. Fedder

4.1 Introduction 73

4.2 Sources of Parametric Excitation in MEMS and NEMS 74

4.2.1 Parametric Excitation via Electrostatic Transduction 75

4.2.2 Other Sources of Parametric Excitation 77

4.3 Modeling the Underlying Dynamics–Variants of the Mathieu Equation 77

4.4 Perturbation Analysis 79

4.5 Linear, Steady-State Behaviors 80

4.6 Sources of Nonlinearity and Nonlinear Steady-State Behaviors 81

4.7 Complex Dynamics in Parametrically Excited Micro/Nanosystems 84

4.8 Combined Parametric and Direct Excitations 85

4.9 Select Applications 85

4.9.1 Resonant Mass Sensing 85

4.9.2 Inertial Sensing 86

4.9.3 Micromirror Actuation 87

4.9.4 Bifurcation Control 88

4.10 Some Parting Thoughts 89

Acknowledgment 89

References 89

5 Finite ElementModeling of Resonators 97
Reza Abdolvand, Jonathan Gonzales, and Gavin Ho

5.1 Introduction to Finite Element Analysis 97

5.1.1 Mathematical Fundamentals 97

5.1.1.1 Static Problems 98

5.1.1.2 Dynamic Problems (Modal Analysis) 100

5.1.2 Practical Implementation 101

5.1.2.1 Set Up 102

5.1.2.2 Processing 103

5.1.2.3 Post-processing 103

5.2 Application of FEA in MEMS Resonator Design 104

5.2.1 Modal Analysis 104

5.2.1.1 Mode Shape Analysis for Design Optimization 104

5.2.1.2 Modeling Process-Induced Variation 108

5.2.2 Loss Analysis 110

5.2.2.1 Anchor Loss 110

5.2.2.2 Thermoelastic Damping 112

5.2.3 Frequency Response Analysis 113

5.2.3.1 Spurious Mode Identification and Rejection 113

5.2.3.2 Filter Design 115

5.3 Summary 116

References 116

Part II: Implementation 119

6 Capacitive Resonators 121
Gary K. Fedder

6.1 Introduction 121

6.2 Capacitive Transduction 122

6.3 Electromechanical Actuation 123

6.3.1 Electromechanical Force Derivation 123

6.3.2 Voltage Dependent Force Components 124

6.4 Capacitive Sensing and Motional Capacitor Topologies 127

6.4.1 Parallel-Moving Plates 127

6.4.2 Perpendicular Moving Plates 129

6.4.3 Electrostatic Spring Softening and Snap-In 132

6.4.4 Angular Moving Plates 134

6.5 Electrical Isolation 135

6.6 Capacitive Resonator Circuit Models 136

6.7 Capacitive Interfaces 138

6.7.1 Transimpedance Amplifier 138

6.7.2 High-Impedance Voltage Detection 142

6.7.3 Switched-Capacitor Detection 142

6.8 Conclusion 143

Acknowledgment 144

References 144

7 Piezoelectric Resonant MEMS 147
Gianluca Piazza

7.1 Introduction to Piezoelectric Resonant MEMS 147

7.2 Fundamentals of Piezoelectricity and Piezoelectric Resonators 149

7.3 Thin Film Piezoelectric Materials for Resonant MEMS 152

7.4 Equivalent Electrical Circuit of Piezoelectric Resonant MEMS 153

7.4.1 One-Port Piezoelectric Resonators 156

7.4.2 Two-Port Piezoelectric Resonators 157

7.4.3 Resonator Figure of Merit 158

7.5 Examples of Piezoelectric Resonant MEMS: Vibrations in Beams, Membranes, and Plates 158

7.5.1 Flexural Vibrations 159

7.5.2 Width-Extensional Vibrations 163

7.5.3 Thickness-Extensional and Shear Vibrations 166

7.6 Conclusions 168

References 169

8 Electrothermal Excitation of Resonant MEMS 173
Oliver Brand and Siavash Pourkamali

8.1 Basic Principles 173

8.1.1 Fundamental Equations for Electro-Thermo-Mechanical Transduction 173

8.1.2 Time Constants and Frequency Dependencies 175

8.2 Actuator Implementations 178

8.2.1 Thin-Film/Surface Actuators 179

8.2.2 Bulk Actuators 184

8.3 Piezoresistive Sensing 185

8.3.1 Fundamental Equations for Piezoresistive Sensing 185

8.3.2 Piezoresistor Implementations 187

8.3.3 Self-SustainedThermal-Piezoresistive Oscillators 189

8.4 Modeling and Optimization of Single-Port Thermal-Piezoresistive Resonators 193

8.4.1 Thermo-Electro-Mechanical Modeling 193

8.4.2 Resonator Equivalent Electrical Circuit and Optimization 195

8.5 Examples ofThermally Actuated Resonant MEMS 197

References 199

9 Nanoelectromechanical Systems (NEMS) 203
Liviu Nicu, Vaida Auzelyte, Luis Guillermo Villanueva, Nuria Barniol, Francesc Perez-Murano,Warner J. Venstra, Herre S. J. van der Zant, Gabriel Abadal, Veronica Savu, and Jürgen Brugger

9.1 Introduction 203

9.1.1 Fundamental Studies 203

9.1.2 Transduction at the Nanoscale 206

9.1.3 Materials, Fabrication, and System Integration 208

9.1.4 Electronics 211

9.1.5 Nonlinear MEMS/NEMS Applications 212

9.2 Carbon-Based NEMS 215

9.3 Toward Functional Bio-NEMS 219

9.3.1 NEMS-Based Energy Harvesting: an Emerging Field 220

9.4 Summary and Outlook 222

References 224

10 Organic Resonant MEMS Devices 233
Sylvan Schmid

10.1 Introduction 233

10.2 Device Designs 235

10.2.1 Conductive Polymer with Electrostatic Actuation 235

10.2.2 Dielectric Polymer with Polarization Force Actuation 236

10.2.3 Superparamagnetic Nanoparticle Composite with Magnetic Actuation 238

10.2.4 Metallized Polymer with Lorentz Force Actuation 239

10.3 Quality Factor of Polymeric Micromechanical Resonators 242

10.3.1 Quality Factor in Viscous Environment 242

10.3.2 Quality Factor of Relaxed Resonators in Vacuum 242

10.3.3 Quality Factor of Unrelaxed Resonators in Vacuum 243

10.4 Applications 247

10.4.1 Humidity Sensor 247

10.4.2 Vibrational Energy Harvesting 252

10.4.3 Artificial Cochlea 253

References 256

11 Devices with Embedded Channels 261
Thomas P. Burg

11.1 Introduction 261

11.2 Theory 263

11.2.1 Effects of Fluid Density and Flow 263

11.2.2 Effects of Viscosity on the Quality Factor 267

11.2.3 Effect of Surface Reactions 269

11.2.4 Single Particle Measurements 271

11.3 Device Technology 273

11.3.1 Fabrication 273

11.3.2 Packaging Considerations 275

11.4 Applications 279

11.4.1 Measurements of Fluid Density and Mass Flow 279

11.4.2 Single Particle and Single Cell Measurements 279

11.4.3 Surface-Based Measurements 280

11.5 Conclusion 282

References 283

12 Hermetic Packaging for Resonant MEMS 287
Matthew William Messana, Andrew Bradley Graham, and Thomas William Kenny

12.1 Introduction 287

12.2 Overview of Packaging Types 289

12.3 Die-Level Vacuum-Can Packaging 291

12.4 Wafer Bonding for Device Packaging 293

12.5 Thin Film Encapsulation-Based Packaging 296

12.6 Getters 298

12.7 The “Stanford epi-Seal Process” for Packaging of MEMS Resonators 299

12.8 Conclusion 302

References 302

13 Compensation, Tuning, and Trimming of MEMS Resonators 305
Roozbeh Tabrizian and Farrokh Ayazi

13.1 Introduction 306

13.2 Compensation Techniques in MEMS Resonators 306

13.2.1 Compensation for Thermal Effects 306

13.2.1.1 Engineering the Geometry 307

13.2.1.2 Doping 307

13.2.1.3 Composite Resonators 309

13.2.2 Compensation for Manufacturing Uncertainties 313

13.2.3 Compensation and Control of Quality Factor 315

13.2.4 Compensation for Polarization Voltage 317

13.3 Tuning Methods in MEMS Resonators 317

13.3.1 Device Level Tuning 317

13.3.1.1 Electrostatic Tuning 318

13.3.1.2 Thermal Tuning 318

13.3.1.3 Piezoelectric Tuning 319

13.3.2 System-Level Tuning 320

13.4 Trimming Methods 321

References 322

Part III: Application 327

14 MEMS Inertial Sensors 329
Diego Emilio Serrano and Farrokh Ayazi

14.1 Introduction 329

14.2 Accelerometers 329

14.2.1 Principles of Operation 330

14.2.2 Quasi-Static Accelerometers 331

14.2.2.1 Squeeze-Film Damping 332

14.2.2.2 Electromechanical Transduction in Accelerometers 333

14.2.2.3 Mechanical Noise in Accelerometers 334

14.2.3 Resonant Accelerometers 334

14.2.3.1 Electrostatic Spring-Softening 335

14.2.3.2 Acceleration Sensitivity in Resonant Accelerometers 336

14.3 Gyroscopes 336

14.3.1 Principles of Operation 337

14.3.1.1 Vibratory Gyroscopes 337

14.3.1.2 Mode-Split versus Mode-Matched Gyroscopes 339

14.3.2 Bulk-AcousticWave (BAW) Gyroscopes 341

14.3.2.1 Angular Gain 342

14.3.2.2 Zero-Rate Output 343

14.3.2.3 ZRO Cancelation 345

14.3.2.4 Electromechanical Transduction in Gyroscopes 345

14.3.2.5 Electrostatic Mode Matching and Mode Alignment 346

14.3.3 Mechanical Noise in Mode-Matched Gyroscopes 347

14.4 Multi-degree-of-Freedom Inertial Measurement Units 348

14.4.1 System-in-Package IMUs 348

14.4.2 Single-Die IMUs 349

14.4.3 Future Trends in Sensor Integration 351

References 352

15 Resonant MEMS Chemical Sensors 355
Luke A. Beardslee, Oliver Brand, and Fabien Josse

15.1 Introduction 355

15.2 Modeling of Resonant Microcantilever Chemical Sensors 357

15.2.1 Generalized Resonant Frequency 360

15.3 Effects of Chemical Analyte Sorption into the Coating 361

15.3.1 Resonant Frequency 361

15.3.2 Quality Factor 363

15.4 Figures of Merit 364

15.5 Chemically Sensitive Layers 368

15.6 Packaging 371

15.7 Gas-Phase Chemical Sensors 374

15.8 Liquid-Phase Chemical Sensors 377

15.8.1 Cantilevers 379

15.8.2 Microdisk Resonators 380

15.8.3 AcousticWave Sensors 381

15.8.4 Resonators with Encapsulated Channels 383

References 383

16 Biosensors 391
Blake N. Johnson and Raj Mutharasan

16.1 Introduction 391

16.2 Design Considerations: Length Scale, Geometry, and Materials 392

16.2.1 Fabrication Materials 392

16.2.2 Single-Layer Geometry 402

16.2.3 Multi-Layer Geometry 403

16.2.4 Length Scales 403

16.3 Surface Functionalization: Preparation, Passivation, and Bio-recognition 404

16.3.1 Antibody-Based Bio-recognition 405

16.3.2 Nucleic Acid-Based Bio-recognition 405

16.3.3 Alternative Bio-recognition Agents 407

16.4 Biosensing Application Formats 408

16.4.1 Dip-Dry-Measure Method 408

16.4.2 Continuous Flow Method 408

16.5 Application Case Studies 409

16.5.1 Whole Cells: Pathogens and Parasites 409

16.5.1.1 Foodborne Pathogen: Escherichia coli O157:H7 409

16.5.1.2 Foodborne Pathogen: Listeria monocytogenes 411

16.5.1.3 Waterborne Parasite: Cryptosporidium parvum 413

16.5.1.4 Waterborne Parasite: Giardia lamblia 413

16.5.2 Proteins: Biomarkers and Toxins 414

16.5.2.1 Prostate Cancer Biomarker: Prostate Specific Antigen 414

16.5.2.2 Prostate Cancer Biomarker: Alpha-methylacyl-CoA Racemase (AMACR) 414

16.5.2.3 Toxin in SourceWater: Microcystin 415

16.5.2.4 Toxin in Food Matrices: Staphylococcal enterotoxin B 415

16.5.3 Virus 416

16.5.4 Nucleic Acids: Biomarkers and Genes Associated with Toxin Production 416

16.5.4.1 RNA-Based Biomarkers: MicroRNA 416

16.5.4.2 Gene Signature of a Virus 417

16.5.4.3 Toxin-Associated Genes for Pathogen Detection without DNA Amplification 417

16.6 Conclusions and Future Trends 418

Acknowledgment 419

References 419

17 Fluid Property Sensors 427
Erwin K. Reichel, Martin Heinisch, and Bernhard Jakoby

17.1 Introduction 427

17.2 Definition of Fluid Properties 429

17.2.1 Rheological Properties 429

17.2.2 Time-Harmonic Deformation 431

17.2.3 Classical Methods for Measuring Fluid Properties 431

17.2.4 Miniaturized Rheometers 432

17.3 Resonator Sensors 433

17.3.1 Excitation and Readout 433

17.3.2 Eigenmode Decomposition 433

17.3.3 Electrical Equivalent Circuit 434

17.3.4 Damping 435

17.3.5 Fluid-Structure Interaction 436

17.4 Examples of Resonant Sensors for Fluid Properties 438

17.4.1 Microacoustic Devices 440

17.4.2 MEMS Devices 441

17.4.2.1 Cantilever Devices 441

17.4.2.2 U-Shaped Cantilevers 445

17.4.2.3 Tuning Forks 445

17.4.2.4 Doubly-Clamped Beam Devices 445

17.4.2.5 In-Plane Resonators 445

17.4.2.6 Other Principles 445

17.4.3 Comparison 446

17.5 Conclusions 446

References 446

18 Energy Harvesting Devices 451
Stephen P. Beeby

18.1 Introduction 451

18.2 Generic Harvester Structures 452

18.2.1 Inertial Energy Harvesters 453

18.2.2 Direct Force Energy Harvesters 456

18.2.3 Broadband Energy Harvesters 457

18.2.4 Frequency Conversion 460

18.3 MEMS Energy Harvester Transduction Mechanisms 461

18.3.1 Piezoelectric Transduction 462

18.3.2 Electromagnetic Transduction 464

18.3.3 Electrostatic Transduction 465

18.3.4 Other Transducer Materials 467

18.4 Review and Comparison of MEMS Energy Harvesting Devices 468

18.5 Conclusions 471

References 472

Index 475

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Author Information

Oliver Brand is Professor of Bioengineering and Microelectronics/Microsystems at Georgia Institute of Technology, Atlanta, USA. He received his diploma degree in Physics from Technical University Karlsruhe, Germany, in 1990, and his PhD from ETH Zurich, Switzerland, in 1994. Between 1995 and 2002, he held research and teaching positions at the Georgia Institute of Technology (1995-1997) and ETH Zurich (1997-2002). Oliver Brand's research interest lies in the areas of CMOS-based micro- and nanosystems, MEMS fabrication technologies, and microsystem packaging.

Isabelle Dufour is Professor of Electrical Engineering at the University of Bordeaux, France. She received the PhD and habilitation degrees in Engineering Sciences from the University of Paris-Sud, Orsay, France, in 1993 and 2000, respectively. Isabelle Dufour was a CNRS research fellow from 1994 to 2007, first in Cachan working on the modeling of electrostatic actuators such as micromotors and micropumps and after 2000 in Bordeaux working on microcantilever-based chemical sensors. Her research interests are mainly in the areas of sensors for chemical detection, rheological measurements and materials characterization.

Stephen M. Heinrich is Professor of Civil Engineering at Marquette University, Wisconsin, USA. He earned his MSc and PhD degrees from the University of Illinois after which he joined the faculty at Marquette University. Stephen Heinrich's research is focused on structural mechanics applications in microelectronics packaging and the development of new analytical models for predicting and enhancing the performance of cantilever-based chemical sensors. The work performed by Stephen Heinrich and his colleagues has resulted in over 100 publications and presentations and three best-paper awards from IEEE and ASME.

Fabien Josse is Professor in the Department of Electrical and Computer Engineering and the Department of Biomedical Engineering at Marquette University, Wisconsin, USA. He received the MSc and PhD degrees in Electrical Engineering from the University of Maine, and belongs to the Marquette University faculty since 1982. His research interests include solid state sensors, acoustic wave sensors and MEMS devices for liquid-phase biochemical sensor applications, investigation of novel sensor platforms, and smart sensor systems.
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