Methodology for the Modeling and Simulation of Microsystems

155 Pages·1998·5.022 MB·English

by  Bartlomiej F. Romanowicz (auth.)

METHODOLOGY FOR THE
MODELING AND SIMULATION
OF MICROSYSTEMS
MICRO SYSTEMS
Series Editor
Stephen D. Senturia
Massachusetts Institute o/Technology
Editorial Board
Roger T. Howe, University ofC alifornia, Berkeley
D. Jed Harrison, University ofA lberta
Hiroyuki Fujita, University of Tokyo
Jan-Ake Schweitz, Uppsala University
METHODOLOGYFORTHE
MODELING AND SIMULATION
OF MICROSYSTEMS
by
Bartlomiej F. Romanowicz
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
ISBN 978-1-4613-7572-2 ISBN 978-1-4615-5621-3 (eBook)
DOI 10.1007/978-1-4615-5621-3
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available
from the Library of Congress.
Copyright © 1998 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint of the hardcover 1s t edition 1998
AlI rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transrnÎtted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC
Printed on acid-free paper.
Contents
List of Figures vii
List of Tables XI
Contributing Authors XIII
Editors Preface XVII
Foreword XIX
Preface XXI
1
In trod uction 1
1.1 Modeling and Simulation of Microsystems 1
1.2 Overview 4
1.3 State of the Art 6
1.4 Contributions 8
2
Data exchange formats 11
2.1 Overview 11
2.2 Data exchange standards and STEP 12
2.3 VHDL 1076.1 13
2.4 Towards a microsystem application protocol 14
2.5 An investigation in data exchange 16
2.6 Conclusions 22
3
Energy-based macro-models 23
3.1 Overview 23
3.2 Generalized variables 24
3.3 Deriving HDL-ATM models of transducers 28
vi METHODOLOGY FOR THE MODELING AND SIMULATION OF MICROSYSTEMS
3.4 Comparison of equivalent circuit and HDL models 31
3.5 Conclusions 33
4
Physical parameter extraction 37
4.1 Overview 37
4.2 Field solvers 37
4.3 The finite element method 38
4.4 Analogies between FE and SPICE analysis domains 40
4.5 Extraction of generalized variables 41
4.6 Extraction of physical macro parameters 45
4.7 The PXT physical parameter extractor 51
4.8 Conclusions 57
5
Analog HDL modeling techniques 61
5.1 Overview 61
5.2 Modeling principles 62
5.3 Conservative systems 64
5.4 Piecewise linear models 71
5.5 Signal flow models 71
5.6 Piecewise defined behavior 78
5.7 Conclusions 84
6
Simulation examples 89
6.1 Overview 89
6.2 Wobble electrostatic micromotor 89
6.3 Electro-magnetic displacement sensor 100
6.4 Vertical Hall Device 106
7
Conclusions 115
Appendix: A Glossary of Abbreviations 118
Appendix: B Glossary of VH DL 1076.1 Syntax 121
References 123
Index 135
List of Figures
1.1 Schematic representation of a microsystem showing the interac-
tions between components (sensors, actuators and electronics)
and the environment. Various modeling and simulation levels
are also displayed. 2
1.2 Proposed micro system simulation data flow. 5
2.1 Domains of application of VHDL. 14
2.2 Proposed schema for data exchange between CAD, FE and VR
based on a common STEP data base. 17
2.3 Implemented schema for data exchange between CAD, FE and
VR based on a common STEP data base. 18
2.4 a) Microsystem assembly station with microscope and mobile
robot. b) VR view of robot below microscope. c) Mobile micro-
assembly robot with three feet and micro-gripper. 19
2.5 VR view of micro-gripper assembling micromotor components. 20
2.6 Different gripper designs investigated. Screen dumps are from
Pro/ENGINEER©. 20
2.7 At left, design of gripper that was selected. At right, mesh of
gripper for data exchan~ with the FE tool. Both screen dumps
from Pro/ENGINEER c . 21
2.8 At left, deformed and undeformed shape of micro-gripper in
ANSYS© FE simulator, at right, Von Mises stress in gripper
simulated using FE. 21
3.1 Schema of a general dynamic system. 24
3.2 Electromechanical transducers studied 30
3.3 System composed of electrostatic transducer coupled to a me-
chanical resonator. 32
3.4 Electrostatic transducer coupled to mechanical resonator. 33
viii METHODOLOGY FOR THE MODELING AND SIMULATION OF MICROSYSTEMS
3.5 Simulation comparing linear lumped parameter electrostatic
transducer and behavioral HDL-ATM (mathematical) model.
Exciting voltage pulses of 5, 10 and 15 V are displayed above.
Displacements (represented by voltages D and DT respectively)
for the HDL-ATM and linearized systems are visible below. 34
4.1 Coupled field capabilities of ANSYS© 39
4.2 Schema of device interface flow variable density integration 43
4.3 Capacitances between conducting objects 48
4.4 Graphical user interface of PXT. 51
4.5 Finite element model of a parallel plate capacitor as seen in the
ANSYSTM postprocessor. Contours represent voltages. No
fringing fields are medeled in this example 52
4.6 PXT available parameter extraction methods window. 55
4.7 PXT ANSYS© element type window. 56
4.8 PXT selected element list window. 56
4.9 PXT selected node list window. 57
4.10 PXT HDL-ATM model generation window. 58
4.11 PXT SIMULINK™ model generation window. 58
5.1 Vibrating gyroscope mechanical model. 66
5.2 Schematic of gyroscope model. 67
5.3 Cross section of piezoelectric pressure sensor. 68
5.4 Finite element model of pressure sensor simulated in ANSYS™.
Displacements (in m) are shown for a 5 bar pressure. 69
5.5 Experimental, FEM (both used for PWL model) and analytical
(used for conservative model) membrane response to pressure. 72
5.6 SEM photograph of the accelerometer. The device was manu
factured by Gerold Schr6pfer of the Laboratoire de Physique et
de Metrologie des Oscillateurs, Universite de Franche-Comte,
25000 Besan<.;on, France . 75
5.7 Finite element model of the accelerometer submitted to a con
stant acceleration. Contours represent vertical displacements.
FE modeling and simulation of the device were performed by
Yannick Ansel of IMS-DMT-EPFL. 75
5.8 Calculated temperature dependent displacement spectrum of
the accelerometer. 76
5.9 Calculated length dependent displacement spectrum of the ac-
celerometer. 78
5.10 Schema of micro-relay device. 79
5.11 Detail of 1/4 symmetry FE model used magneto-static analysis
of micro-relay. Coils, substrate, keeper, poles and surrounding
air are visible. 80
5.12 Vertical force on keeper as a function of the gap and the mag-
netic circuit thickness H. 81
LIST OF FIGURES lX
5.13 FE simulation results: a) Detail of magnetic flux density in
polar gap. b) Detail of scalar magnetic potential in polar gap. 81
5.14 Electrical schema of micro-relay system showing VHDL-AMS
models and SPICE devices. 82
6.1 Calculation model of the planar electrostatic wobble motor. 90
6.2 FEM results (stars) are reported together with analytical re
sults (lines) for the torques of the macroscopic wobble motor.
The torques are functions of the phase angle between contact
point and the center of the activated electrode. a) shows the
drive torques for different rotor inclination angles (5.7°, 10° and
20°) while b) shows the adherence torques for the same angles.
The highest torques correspond to the smallest tilt angles. 92
6.3 Drive and adherence torques around the z axis for two values of
the dielectric thickness: di=0.34 mm (dotted lines) and di=0.05
mm (continuous lines), for the micromotor as given in table 6.1,
=
and for a phase width of 90°, with J.ts 1. 95
6.4 Block diagram of the wobble electrostatic micromotor showing
drive electronics and transducer models. 97
6.5 Transient simulation example of wobble electrostatic motor
ASIC system. Successive electrode drive potentials (ELi) are
visible in the upper graph. The wavy stepped response below
(ROT) represents the angle swept by the rotor as it oscillates
from one electrode to the next. 98
6.6 Transient simulation example of wobble motor-ASIC system
showing stochastic behavior. Successive electrode drive poten
tials (ELi) are visible in the upper graph. An overlap of 1/2
is defined for the rectangular drive voltages. ROT is the an
gle swept by the rotor as it oscillates from one electrode to the
next. As the fourth electrode (EL3) is activated, the motor
loses synchronization with the rotating electrostatic field and
spins the wrong way. This happens because electrode (ELI)
is grounded at the same moment (the rotor's position being
directly above it). 99
6.7 Photograph of sensor above toothed ferromagnetic substrate.
Source: Yves de Coulon, CSEM S.A., Rue Jaquet-Droz 1, P.O.
Box 41, CH-2007 Neuchatel, Switzerland. 101
6.8 Schema of displacement sensor used to elaborate FE model for
harmonic (AC) simulations. 101
6.9 Simulated flux lines between transducer coils and an aluminum
target at a frequency of 500 kHz showing concentration at teeth
extremities due to eddy currents 103
6.10 Simulated in phase current (i) in pick-up coil as a function of
displacement (dx) and operating frequency (f) for a steel target 104
x METHODOLOGY FOR THE MODELING AND SIMULATION OF MICROSYSTEMS
6.11 Simulated in phase current (i) in pick-up coil as a function of
displacement (dx) and operating frequency (f) for an aluminum
target 104
6.12 Simulated voltages in primary (VI) and secondary (V2) coils
of inductive displacement sensor. A 10 mA harmonic current
is used to drive the primary coil at a frequency of 60 kHz. The
modulation of the envelope of the secondary coil is created by
the sensor-toothed substrate displacement. 107
6.13 a) Mask used to manufacture vertical Hall devices with different
contact lengths a. b) Photograph of vertical Hall device glued
and wire bonded to a ceramic substrate. 108
6.14 Detail of FE model used to simulate vertical Hall device. The
trench cut into the silicon wafer is the insulating junction around
the active region. The five contacts are visible in the center of
the model. 109
6.15 Cut through FE model showing contour plot of simulated elec-
tric equipotential lines. Random contour colors are used to
aid in viewing the potential distribution. The automatic mesh
refinement is not displayed for reasons of clarity. 110
6.16 Simulated Hall voltage as a function of the magnetic flux den-
sity and the width of the Hall contacts. 110
6.17 Simulated input voltage at the IC current terminal as a function
of magnetic flux density and the width of the Hall contacts for
an input current of 1 mAo 111
6.18 Schematic diagram of vertical Hall device behavioral model for
circuit simulators. 112