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System-level Modeling of MEMS

Tamara Bechtold (Volume Editor), Gabriele Schrag (Volume Editor), Lihong Feng (Volume Editor), Oliver Brand (Editor), Gary K. Fedder (Editor), Christofer Hierold (Editor), Jan G. Korvink (Editor), Osamu Tabata (Editor)
ISBN: 978-3-527-31903-9
562 pages
March 2013
System-level Modeling of MEMS (3527319034) cover image


System-level modeling of MEMS - microelectromechanical systems - comprises integrated approaches to simulate, understand, and optimize the performance of sensors, actuators, and microsystems, taking into account the intricacies of the interplay between mechanical and electrical properties, circuitry, packaging, and design considerations. Thereby, system-level modeling overcomes the limitations inherent to methods that focus only on one of these aspects and do not incorporate their mutual dependencies.

The book addresses the two most important approaches of system-level modeling, namely physics-based modeling with lumped elements and mathematical modeling employing model order reduction methods, with an emphasis on combining single device models to entire systems. At a clearly understandable and sufficiently detailed level the readers are made familiar with the physical and mathematical underpinnings of MEMS modeling. This enables them to choose the adequate methods for the respective application needs.

This work is an invaluable resource for all materials scientists, electrical engineers, scientists working in the semiconductor and/or sensor
industry, physicists, and physical chemists.
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Table of Contents

About the Editors XIX

Series Editor Preface XXI

Volume Editors Preface XXIII

List of Contributors XXVII

Part I Physical and Mathematical Fundamentals 1

1 Introduction: Issues in Microsystems Modeling 3
Gary K. Fedder and Tamal Mukherjee

1.1 The Need for System-Level Models for Microsystems 3

1.2 Coupled Multiphysics Microsystems 4

1.3 Multiscale Modeling and Simulation 6

1.4 System-Level Model Terminology 7

1.5 Automated Model Order Reduction Methods 9

1.6 Handling Complexity: Following the VLSI Paradigm 10

1.7 Analog Hardware Description Languages 11

1.8 General Attributes of System-Level Models 12

1.9 AHDL Simulation Capabilities 13

1.10 Composable Model Libraries 14

1.11 Parameter Extraction, Model Verification, and Model Validation 15

1.12 Conclusions 16

References 17

2 System-Level Modeling of MEMS Using Generalized Kirchhoffian Networks – Basic Principles 19
Gabriele Schrag and Gerhard Wachutka

2.1 Introduction and Motivation 19

2.2 Generalized Kirchhoffian Networks for the Tailored System-Level Modeling of Microsystems 20

2.3 Application 1: Physics-Based Electrofluidic Compact Model of an Electrostatically Actuated Micropump 32

2.4 Application 2: Electrostatically Actuated RF MEMS Switch 41

References 48

3 System-Level Modeling of MEMS by Means of Model Order Reduction (Mathematical Approximations) – Mathematical Background 53
Lihong Feng, Peter Benner, and Jan G. Korvink

3.1 Introduction 53

3.2 Brief Overview 55

3.3 Mathematical Preliminaries 56

3.4 Numerical Algorithms 63

3.5 Linear System Theory 66

3.6 Basic Idea of Model Order Reduction 71

3.7 Moment-Matching Model Order Reduction 73

3.8 Gramian-Based Model Order Reduction 77

3.9 Stability, Passivity, and Error Estimation of the Reduced Model 84

3.10 Dealing with Nonzero Initial Condition 85

3.11 MOR for Second-Order, Nonlinear, Parametric systems 86

3.12 Conclusion and Outlook 86

References 87

4 Algorithmic Approaches for System-Level Simulation of MEMS and Aspects of Cosimulation 95
Peter Schneider, Christoph Clauß, Ulrich Donath, G¨unter Elst, Olaf Enge-Rosenblatt, and Thomas Uhle

4.1 Introduction 95

4.2 Mathematical Structure of MEMS Models 96

4.3 General Approaches for System-Level Model Description 104

4.4 Numerical Methods for System-Level Simulation 107

4.5 Emerging Problems and Advanced Simulation Techniques 113

4.6 Conclusion 118

References 118

Part II Lumped Element Modeling Method for MEMS Devices 123

5 System-Level Modeling of Surface Micromachined Beamlike Electrothermal Microactuators 125
Ren-Gang Li and Qing-An Huang

5.1 Introduction 125

5.2 Classification and Problem Description 127

5.3 Modeling 131

5.4 Solving 136

5.5 Case Study 139

5.6 Conclusion and Outlook 142

References 143

6 System-Level Modeling of Packaging Effects of MEMS Devices 147
Jing Song and Qing-An Huang

6.1 Introduction 147

6.2 Packaging Effects of MEMS and Their Impact on Typical MEMS Devices 148

6.3 System-Level Modeling 150

6.4 Conclusion and Outlook 160

References 160

7 Mixed-Level Approach for the Modeling of Distributed Effects in Microsystems 163
Martin Niessner and Gabriele Schrag

7.1 General Concept of Finite Networks and Mixed-Level Models 163

7.2 Approaches for the Modeling of Squeeze Film Damping in MEMS 165

7.3 Mixed-Level Modeling of Squeeze Film Damping in MEMS 169

7.4 Evaluation 179

7.5 Conclusion 186

References 187

8 Compact Modeling of RF-MEMS Devices 191
Jacopo Iannacci

8.1 Introduction 191

8.2 Brief Description of the MEMS Compact Modeling Approach 192

8.3 RF-MEMS Multistate Attenuator Parallel Section 194

8.4 RF-MEMS Multistate Attenuator Series Section 202

8.5 Whole RF-MEMS Multistate Attenuator Network 205

8.6 Conclusions 207

References 208

Part III Mathematical Model Order Reduction for MEMS Devices 211

9 Moment-Matching-Based Linear Model Order Reduction for Nonparametric and Parametric Electrothermal MEMS Models 213
Tamara Bechtold, Dennis Hohlfeld, Evgenii B. Rudnyi, and Jan G. Korvink

9.1 Introduction 213

9.2 Methodology for Applying Model Order Reduction to Electrothermal MEMS Models: Review of Achieved Results and Open Issues 213

9.3 MEMS Case Study – Silicon-Based Microhotplate 220

9.4 Application of the Reduced-Order Model for the Parameterization of the Controller 223

9.5 Application of Parametric Reduced-Order Model to the Extraction of Thin-Film Thermal Parameters 227

9.6 Conclusion and Outlook 232

References 234

10 Projection-Based Nonlinear Model Order Reduction 237
Amit Hochman, Dmitry M. Vasilyev, Michał J. Rewiénski, and Jacob K. White

10.1 Introduction 237

10.2 Problem Specification 238

10.3 Projection Principle and Evaluation Cost for Nonlinear Systems 239

10.4 Taylor Series Expansions 240

10.5 Trajectory Piecewise-Linear Method 245

10.6 Discrete Empirical Interpolation method 250

10.7 A Comparative Case Study of an MEMS Switch 255

10.8 Summary and Outlook 260

Acknowledgment 260

References 261

11 Linear and Nonlinear Model Order Reduction for MEMS Electrostatic Actuators 263
Jan Lienemann, Emanuele Bertarelli, Andreas Greiner, and Jan G. Korvink

11.1 Introduction 263

11.2 The Variable Gap Parallel Plate Capacitor 264

11.3 Model Order Reduction Methods 269

11.4 Example 1: IBM Scanning-Probe Data Storage Device 275

11.5 Example 2: Electrostatic Micropump Diaphragm 281

11.6 Results and Discussion 285

11.7 Conclusions 286

Acknowledgments 287

References 287

12 Modal-Superposition-Based Nonlinear Model Order Reduction for MEMS Gyroscopes 291
Jan Mehner

12.1 Introduction 291

12.2 Model Order Reduction via Modal Superposition 292

12.3 MEMS Testcase: Vibratory Gyroscope 293

12.4 Flow Chart of the Nonlinear Model Order Reduction Procedure 294

12.5 Theoretical Background of Modal Superposition Technologies 295

12.6 Specific Algorithms of the Reduced Order Model Generation Pass 299

12.7 System Simulations of MEMS Based on Modal Superposition 304

12.8 Conclusion and Outlook 307

References 308

Part IV Modeling of Entire Microsystems 311

13 Towards System-Level Simulation of Energy Harvesting Modules 313
Dennis Hohlfeld, Tamara Bechtold, Evgenii B. Rudnyi, Bert Op het Veld, and Rob van Schaijk

13.1 Introduction 313

13.2 Design and Fabrication of the Piezoelectric Generator 317

13.3 Experimental Results 318

13.4 Modeling and Simulation 318

13.5 Maximum Power Point for the Piezoelectric Harvester 327

13.6 Conclusions and Outlook 332

References 333

14 Application of Reduced Order Models in Circuit-Level Design for RF MEMS Devices 335
Laura Del Tin, Evgenii B. Rudnyi, and Jan G. Korvink

14.1 Model Equations for RF MEMS Devices 337

14.2 Extraction of the Reduced Order Model 340

14.3 Application Examples 345

14.4 Conclusion and Outlook 354

References 355

15 SystemC AMS and Cosimulation Aspects 357
François Pêcheux, Marie-Minerve Louërat, and Karsten Einwich

15.1 Introduction 357

15.2 Heterogeneous Modeling with SystemC AMS 358

15.3 Case Study: Detection of Seismic Perturbations Using the Accelerometer 363

15.4 Conclusion 370

Appendix 371

References 374

16 System Level Modeling of Electromechanical Sigma–Delta Modulators for Inertial MEMS Sensors 377
Michael Kraft

16.1 Introduction and Motivation 377

16.2 Second Order Electromechanical ΣΔM for a MEMS Accelerometer 380

16.3 Higher Order Electromechanical ΣΔM for MEMS Accelerometer 391

16.4 Higher Order Electromechanical ΣΔM for MEMS Gyroscopes 397

16.5 Concluding Remarks 400

References 401

Part V Software Implementations 405

17 3D Parametric-Library-Based MEMS/IC Design 407
Gunar Lorenz and Gerold Schröpfer

17.1 About Schematic-Driven MEMS Modeling 407

17.2 A 3D Parametric Library for MEMS Design–MEMS+® 409

17.3 Toward Manufacturable MEMS Designs 415

17.4 Micromirror Array Design Example 419

17.5 Conclusions 422

References 423

18 MOR for ANSYS 425
Evgenii B. Rudnyi

18.1 Introduction 425

18.2 Practice-Oriented Research during the Development of MOR for ANSYS 426

18.3 Programming Issues 429

18.4 Open Problems 432

18.5 Conclusion 436

References 437

19 SUGAR: A SPICE for MEMS 439
Jason V. Clark

19.1 Introduction 439

19.2 SUGAR 439

19.3 SUGAR-Based Applications 444

19.4 Integration of SUGAR + COMSOL + SPICE + SIMULINK 454

19.5 Conclusion 457

References 458

20 Model Order Reduction Implementations in Commercial MEMS Design Environment 461

Sandeep Akkaraju
20.1 Introduction 461

20.2 IntelliSense’s Design Methodology 467

20.3 Implementation of System Model Extraction in IntelliSuite 470

20.4 Benchmarks 474

20.5 Summary 480

References 481

21 Reduced Order Modeling of MEMS and IC Systems – A Practical Approach 483
Sebastien Cases and Mary-Ann Maher

21.1 Introduction 483

21.2 The MEMS Development Environment 484

21.3 Modeling Requirements and Implementation within SoftMEMS Simulation Environment 485

21.4 Applications 494

21.5 Conclusions and Outlook 498

References 498

22 A Web-Based Community for Modeling and Design of MEMS 501
Peter J. Gilgunn, Jason V. Clark, Narayan Aluru, Tamal Mukherjee, and Gary K. Fedder

22.1 Introduction 501

22.2 The MEMS Modeling and Design Landscape 501

22.3 Leveraging Web-Based Communities 502

22.4 MEMS Modeling and Design Online 505

22.5 Encoding MEMS Behavioral Models 508

22.6 Conclusions and Outlook 515

References 515

Index 519

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Author Information

Tamara Bechtold is post-doctoral researcher at Philips/NXP Research Laboratories in the Netherlands. She obtained her PhD from the University of Freiburg, Germany, with a thesis on microsystems simulation conducted at the Institute of Microsystems Technology in the group of Jan Korvink. She is the author of one book and many scientific publications. As of 2009, Tamara Bechtold has more than ten years of experience in modeling and simulation of MEMS.

Gabriele Schrag heads a research group in the field of MEMS modeling with a focus on methodologies for the virtual prototyping of microdevices and microsystems at the Technical University of Munich, Germany. In her diploma and doctoral studies she worked on modeling methods for electromechanical microdevices and microsystems with an emphasis on fluid-structure interaction and viscous damping effects, including coupled effects on the device and system level.

Lihong Feng is a team leader in the research group of Computational Methods in Systems and Control theory headed by Professor Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Germany. After her PhD from Fudan University in Shanghai, China, she joined the faculty of the State Key Laboratory of Application-Specific Integrated Circuits (ASIC) & System, Fudan University, Shanghai, China. From 2007 to 2008 she was a Humboldt research fellow in the working group of Mathematics in Industry and Technology at the Technical University of Chemnitz, Germany. In 2009-2010, she worked in the Laboratory for Microsystem Simulation, Department of Microsystems Engineering, University of Freiburg, Germany. Her research interests are in the field of reduced order modelling and fast numerical algorithms for control and optimization in Chemical Engineering, MEMS simulation, and circuit simulation.
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