Understanding MEMS E-Book

Luis Castaner

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 347

Veröffentlichungsjahr: 2015

Beschreibung

The continued advancement of MEMS (micro-electro-mechanical systems) complexity, performance, commercial exploitation and market size requires an ever-expanding graduate population with state-of-the-art expertise.

Understanding MEMS: Principles and Applications provides a comprehensive introduction to this complex and multidisciplinary technology that is accessible to senior undergraduate and graduate students from a range of engineering and physical sciences backgrounds.

Fully self-contained, this textbook is designed to help students grasp the key principles and operation of MEMS devices and to inspire advanced study or a career in this field.

Moreover, with the increasing application areas, product categories and functionality of MEMS, industry professionals will also benefit from this consolidated overview, source of relevant equations and extensive solutions to problems.

Key features:

• Details the fundamentals of MEMS, enabling readers to understand the basic governing equations and know how they apply at the micron scale.
• Strong pedagogical emphasis enabling students to understand the fundamentals of MEMS devices.
• Self-contained study aid featuring problems and solutions.
• Book companion website hosts Matlab and PSpice codes and viewgraphs.

Leseprobe

UNDERSTANDING MEMS

PRINCIPLES AND APPLICATIONS

Luis Castañer

Department of Electronic Engineering Universitat Politécnica de Cataluña, Spain

This edition first published 2016 © 2016 John Wiley & Sons Ltd

Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

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The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom.

MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book's use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.

PSpice is a registered trademark of Cadence Design System, Inc.

Library of Congress Cataloging-in-Publication Data

Castañer, Luis, author.    Understanding MEMS : principles and applications / Luis Castañer.       pages cm    Includes bibliographical references and index.    ISBN 978-1-119-05542-6 (cloth)  1. Microelectromechanical systems.   I. Title.    TK7875.C37 2015    621.381–dc23

2015024280

A catalogue record for this book is available from the British Library.

ISBN: 9781119055426

To my wife Pamen, daughters Maya and Olga, grandsons Teo, Raul and Marc-Eric and granddaughter Claudia

CONTENTS

Preface

About the Companion Website

1 Scaling of Forces

1.1 Scaling of Forces Model

1.2 Weight

1.3 Elastic Force

1.4 Electrostatic Force

1.5 Capillary Force

1.6 Piezoelectric Force

1.7 Magnetic Force

1.8 Dielectrophoretic Force

1.9 Summary

Problems

Notes

2 Elasticity

2.1 Stress

2.2 Strain

2.3 Stress–strain Relationship

2.4 Strain–stress Relationship in Anisotropic Materials

2.5 Miller Indices

2.6 Angles of Crystallographic Planes

2.7 Compliance and Stiffness Matrices for Single-Crystal Silicon

2.8 Orthogonal Transformation

2.9 Transformation of the Stress State

2.10 Orthogonal Transformation of the Stiffness Matrix

2.11 Elastic Properties of Selected MEMS Materials

Problems

3 Bending of Microstructures

3.1 Static Equilibrium

3.2 Free Body Diagram

3.3 Neutral Plane and Curvature

3.4 Pure Bending

3.5 Moment of Inertia and Bending Moment

3.6 Beam Equation

3.7 End-loaded Cantilever

3.8 Equivalent Stiffness

3.9 Beam Equation for Point Load and Distributed Load

3.10 Castigliano’s Second Theorem

3.11 Flexures

3.12 Rectangular Membrane

3.13 Simplified Model for a Rectangular Membrane Under Pressure

3.14 Edge-clamped Circular Membrane

Problems

4 Piezoresistance and Piezoelectricity

4.1 Electrical Resistance

4.2 One-dimensional Piezoresistance Model

4.3 Piezoresistance in Anisotropic Materials

4.4 Orthogonal Transformation of Ohm’s Law

4.5 Piezoresistance Coefficients Transformation

4.6 Two-dimensional Piezoresistors

4.7 Pressure Sensing with Rectangular Membranes

4.8 Piezoelectricity

Problems

Notes

5 Electrostatic Driving and Sensing

5.1 Energy and Co-energy

5.2 Voltage Drive

5.3 Pull-in Voltage

5.4 Electrostatic Pressure

5.5 Contact Resistance in Parallel-plate Switches

5.6 Hold-down Voltage

5.7 Dynamic Response of Pull-in-based Actuators

5.8 Charge Drive

5.9 Extending the Stable Range

5.10 Lateral Electrostatic Force

5.11 Comb Actuators

5.12 Capacitive Accelerometer

5.13 Differential Capacitive Sensing

5.14 Torsional Actuator

Problems

Notes

6 Resonators

6.1 Free Vibration: Lumped-element Model

6.2 Damped Vibration

6.3 Forced Vibration

6.4 Small Signal Equivalent Circuit of Resonators

6.5 Rayleigh–Ritz Method

6.6 Resonant Gyroscope

6.7 Tuning Fork Gyroscope

Problems

Notes

7 Microfluidics and Electrokinetics

7.1 Viscous Flow

7.2 Flow in a Cylindrical Pipe

7.3 Electrical Double Layer

7.4 Electro-osmotic Flow

7.5 Electrowetting

7.6 Electrowetting Dynamics

7.7 Dielectrophoresis

Problems

Notes

8 Thermal Devices

8.1 Steady-state Heat Equation

8.2 Thermal Resistance

8.3 Platinum Resistors

8.4 Flow Measurement Based on Thermal Sensors

8.5 Dynamic Thermal Equivalent Circuit

8.6 Thermally Actuated Bimorph

8.7 Thermocouples and Thermopiles

Problems

Notes

9 Fabrication

9.1 Introduction

9.2 Photolithography

9.3 Patterning

9.4 Lift-off

9.5 Bulk Micromachining

9.6 Silicon Etch Stop When Using Alkaline Solutions

9.7 Surface Micromachining

9.8 Dry Etching

9.9 CMOS-compatible MEMS Processing

9.10 Wafer Bonding

9.11 PolyMUMPs Foundry Process

Problems

Notes

Appendices

A     Chapter 1 Solutions

Problem 1.1

Problem 1.2

Problem 1.3

Problem 1.4

Problem 1.5

Problem 1.6

Problem 1.7

Problem 1.8

Problem 1.9

Problem 1.10

Problem 1.11

B     Chapter 2 Solutions

Problem 2.1

Problem 2.2

Problem 2.3

Problem 2.4

Problem 2.5

Problem 2.6

Problem 2.7

Problem 2.8

Problem 2.9

Problem 2.10

C     Chapter 3 Solutions

Problem 3.1

Problem 3.2

Problem 3.3

Problem 3.4

Problem 3.5

Problem 3.6

Problem 3.7

Problem 3.8

Problem 3.9

Problem 3.10

Problem 3.11

Problem 3.12

Problem 3.13

D     Chapter 4 Solutions

Problem 4.1

Problem 4.2

Problem 4.3

Problem 4.4

Problem 4.5

Problem 4.6

Problem 4.7

Problem 4.8

Problem 4.9

E     Chapter 5 Solutions

Problem 5.1

Problem 5.2

Problem 5.3

Problem 5.4

Problem 5.5

Problem 5.6

Problem 5.7

Problem 5.8

Problem 5.9

Problem 5.10

Problem 5.11

Problem 5.12

Problem 5.13

Problem 5.14

Problem 5.15

F     Chapter 6 Solutions

Problem 6.1

Problem 6.2

Problem 6.3

Problem 6.4

Problem 6.5

Problem 6.6

Problem 6.7

Problem 6.8

Problem 6.9

G     Chapter 7 Solutions

Problem 7.1

Problem 7.2

Problem 7.3

Problem 7.4

Problem 7.5

Problem 7.6

Problem 7.7

Problem 7.8

Problem 7.9

Problem 7.10

Problem 7.11

H     Chapter 8 Solutions

Problem 8.1

Problem 8.2

Problem 8.3

Problem 8.4

Problem 8.5

Problem 8.6

Problem 8.7

Problem 8.8

Problem 8.9

Problem 8.10

Problem 8.11

Notes

I     Chapter 9 Solutions

Problem 9.1

Problem 9.2

Problem 9.3

Problem 9.4

Problem 9.5

Problem 9.6

Problem 9.7

Problem 9.8

Problem 9.9

Problem 9.10

Problem 9.11

References

Index

EULA

List of Tables

Chapter 1

Table 1.1

Chapter 2

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Chapter 3

Table 3.1

Chapter 4

Table 4.1

Table 4.2

Table 4.3

B Chapter 2 Solutions

Table B.1

Table B.2

F Chapter 6 Solutions

Table F.1

G Chapter 7 Solutions

Table G.1

Table G.2

H Chapter 8 Solutions

Table H.1

Table H.2

Guide

Cover

Table of Contents

Preface

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Preface

The field of microelectromechanical systems (MEMS) has greatly expanded in recent years since Richard Feyman's speech – ‘there is plenty of room at the bottom’ – opened the minds of researchers and companies to the possibility of exploring the potential of microstructures of minute dimensions.

The need for skilled professionals has steadily grown as businesses and research labs engage in challenging projects. Students are motivated because they are aware that they have, in their phones, watches or tablets, accelerometers, compasses and sensors and useful applications relying on them. Students see in the MEMS field, job opportunities and exciting career prospects.

Ultimately those devices have to work together with front-end electronics and digital processing to interface with the user. Students in electrical engineering and computer science departments in universities around the world are probably the most exposed to the field. Simultaneously, engineers and professionals working in the electronics and semiconductor industry face the challenge of integrating MEMS devices into chips, systems on chips or, broadly speaking, into electronic systems. The added value of those devices enables the expansion of high tech businesses.

In my experience of teaching MEMS in an electronic engineering department to engineering students from many countries I have faced the difficulty of selecting material for one-semester course and having to decide on the depth and breadth of the subjects covered.

The field is inherently multidisciplinary, and if the basics are not sufficiently covered, students will not achieve the intellectual satisfaction of a full understanding. However, if the coverage is too complex it cannot be extended to the various fundamental domains underlying the field. Solving problems is an important part of the learning process as it allows for concepts to be reviewed.

Those are the reasons why I have chosen to approach the subject using analytical solutions as far as possible, but with the help of two software tools: one very popular among science and engineering students, Matlab; and the other, very popular among electrical engineering students, PSpice. I have used Matlab to solve ordinary differential equations subject to boundary or initial conditions, applied to mechanical, electromechanical, electrokinetic and thermal problems. This allows numerical results to be found quickly which can then be discussed and put into context.

I have used PSpice to solve Laplace transforms of transfer functions and to solve electrical equivalent circuits of lumped thermal problems. Apart from the clarity of analytical solutions, this approach places the subject of MEMS in the same tool environment as other subjects the student will already have taken. Commonality of tools is important at this level of the learning process, because it means that students do not have to spend a significant amount of time learning how to use new software.

The book includes 52 worked examples in the text and 100 solved problems in the appendices, organized by chapters. In my view this allows this textbook to be used not only as support material for a conventional course but also as a self-study resource for distance learning. I am very greatful to faculty colleagues, researchers and students with whom I have interacted all these years that have taken me to complete this book.

Luis Castañer

April 2015

Barcelona, Spain

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/castaner/understandingmems

The website includes:

Matlab

PSpice codes

Chapter viewgraphs