Fast Simulation of Electro-Thermal MEMS: Efficient Dynamic Compact Models

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Springer Science & Business Media, Nov 1, 2006 - Technology & Engineering - 180 pages
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Fast Simulation of Electro-Thermal MEMS provides the reader with a complete methodology and software environment for creating efficient dynamic compact models for electro-thermal MEMS devices. It supplies the basic knowledge and understanding for using model order reduction at the engineering level. Emphasis is placed on the application of the Arnoldi method for effective order reduction of thermal systems. This tutorial is written for MEMS engineers and is enriched with many case studies which equip readers with the know-how to facilitate the simulation of a specific problem.

 

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Contents

Introduction
1
11 MEMS Compact Modeling and Model Order Reduction
2
12 MEMS and Electrothermal Simulation
4
13 Thematic Outline
5
Dynamic Electrothermal Simulation of Microsystems
7
21 Overview of Coupled Electrothermal and Thermoelectric Effects
8
22 Joule Heating in Microsystems
10
23 Physical Model Heat Transfer Equation
13
532 Reduction of Systems with Nonlinear Input Functions
82
533 SystemLevel Simulation
84
534 Computational Efficiency
86
54 Arnoldi versus Guyan versus Control Theory Methods
88
55 Inverse Thermal Problem via Model Order Reduction
91
56 Summary
96
Advanced Development
97
611 Convergence of Relative Error
99

24 Decoupling the Heat Transfer Equation from Other Physical Domains
15
25 Solving the Heat Transfer Partial Differential Equation
17
251 Linearization
18
253 Numerical Methods
19
26 Dynamic Compact Thermal Modeling
21
262 Modal Approaches
23
263 Model Order Reduction
24
27 Summary
28
Overview of Linear Model Order Reduction
31
311 Balanced Truncation Approximation
32
312 Singular Perturbation Approximation
35
314 Comparison of Methods
36
321 Lanczos Algorithm
39
322 Arnoldi Process
41
323 Arnoldi versus Lanczos
43
33 Guyan Reduction
45
332 Dynamic Matrix Condensation
46
34 Summary
48
Selected Model Reduction Software
50
41 SLICOT Library
52
43 Using Package Post4MOR and Mathlink Interface to SLICOT in Mathematica
57
44 Summary
59
Application of Model Reduction to Electrothermal MEMS
61
51 MEMS Case Studies
62
512 Tunable Optical Filter
65
513 Microhotplate Gas Sensor
67
52 Preparation for Automatic Model Order Reduction
70
53 Model Reduction of Thermal MEMS via the Arnoldi Algorithm
74
531 Approximation of the Complete Output
81
612 Convergence of Hankel Singular Values
107
613 Sequential Model Order Reduction
112
614 Advantages and Disadvantages of the Proposed Strategies
115
62 Order Reduction of Interconnected Thermal MEMS Models
116
621 Microhotplate Array
118
622 Block Arnoldi
120
623 Coupling of Reduced Order Models via Substructuring
127
624 Coupling of Reduced Order Models in the General Case
131
625 Overview of Proposed Strategies
137
631 Parametric Model Reduction
138
632 Model Reduction for SecondOrder Systems
140
64 Summary
141
References
142
Appendix
157
811 Basic Theory
158
812 Preparing ANSYS files
159
813 Performing Model Reduction
162
814 Advanced Options
163
Summary
164
816 References
165
82 Post4MOR
166
822 SimulationResult
169
823 Functions for Transient and Harmonic Simulation
172
83 Mathlink interface to SLICOT
173
831 How to Compile the Interface
174
833 How to Call SLICOT
175
Index
176
Copyright

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About the author (2006)

Tamara Bechtold earned her Dipl.-Ing. degree in electrical engineering and microsystem technology at the University of Bremen, Germany in 2000 and her Dr. Ing. in microsystem simulation at the Institute of Microsystem Technology (IMTEK) in Freiburg, Germany in 2005. Currently, she is working at IMTEK as a post-doctoral researcher. Her research interests include the application of model order reduction to MEMS problems and their efficient system-level simulation.

Evgenii B. Rudnyi graduated from Moscow State University (MSU), Department of Chemistry in 1981, diploma (equiv. M.Sc.) in Chemistry. He received the Candidate of Science (equiv. Ph.D.) degree in physical chemistry in 1985. Dr. Rudnyi was a Research worker, Assistant Professor, and Associated Professor at the Chemistry Department of MSU from 1985 to 2000 and a guest scientist at the National Institute of Standards and Technology (USA) in 1991. Currently, he is working at the Institute of Microsystem Technology (IMTEK) in Freiburg, Germany, as a senior scientist. He is actively involved in the application of model reduction to MEMS problems. He is an author of software mor4ansys that performs model reduction directly for ANSYS models.

Jan G. Korvink earned his Master of Science in computational mechanics at the University of Cape Town, South Africa and read his doctorate at the Swiss Federal Institute of Technology (ETH) in Zurich (Dr. sc. techn. in applied computer science). After he had built up and lead the Microsystem Modeling Group at the Physical Electronics Laboratory, Institute for Quantum Electronics at the ETH he was called upon to join IMTEK (Institute for Microsystem Technology) at the Albert Ludwig University of Freiburg, Germany to hold the Chair of Microsystem Simulation. He is now a vice-dean and chairman of the examination board at the Faculty of Applied Sciences to which IMTEK belongs. Prof. Korvink is author or co-author of more than 130 publications in the field of microsystems and joint-editor of "Advanced Micro and Nanosystems" [http://www.wiley-vch.de/books/info/amn]. Prof. Korvink is a member of the technical programe committees of several conferences and is a member of ASME. He has been visiting professor at the ETH Zurich, the Ritsumeikan University of Kusatsu, Japan and visiting scientist at the Kyoto University in Kyoto, Japan. His research activities focus on the development of ultra low-cost methods of MEMS production and the modeling for and simulation of micro- and nanosystems.

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