Principles of Microelectromechanical Systems E-Book

Ki Bang Lee

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

Seitenzahl: 786

Veröffentlichungsjahr: 2011

Beschreibung

The building blocks of MEMS design through closed-form solutions

Microelectromechanical Systems, or MEMS, is the technology of very small systems; it is found in everything from inkjet printers and cars to cell phones, digital cameras, and medical equipment. This book describes the principles of MEMS via a unified approach and closed-form solutions to micromechanical problems, which have been recently developed by the author and go beyond what is available in other texts. The closed-form solutions allow the reader to easily understand the linear and nonlinear behaviors of MEMS and their design applications.

Beginning with an overview of MEMS, the opening chapter also presents dimensional analysis that provides basic dimensionless parameters existing in large- and small-scale worlds. The book then explains microfabrication, which presents knowledge on the common fabrication process to design realistic MEMS. From there, coverage includes:

• Statics/force and moment acting on mechanical structures in static equilibrium

• Static behaviors of structures consisting of mechanical elements

• Dynamic responses of the mechanical structures by the solving of linear as well as nonlinear governing equations

• Fluid flow in MEMS and the evaluation of damping force acting on the moving structures

• Basic equations of electromagnetics that govern the electrical behavior of MEMS

• Combining the MEMS building blocks to form actuators and sensors for a specific purpose

All chapters from first to last use a unified approach in which equations in previous chapters are used in the derivations of closed-form solutions in later chapters. This helps readers to easily understand the problems to be solved and the derived solutions. In addition, theoretical models for the elements and systems in the later chapters are provided, and solutions for the static and dynamic responses are obtained in closed-forms.

This book is designed for senior or graduate students in electrical and mechanical engineering, researchers in MEMS, and engineers from industry. It is ideal for radio frequency/electronics/sensor specialists who, for design purposes, would like to forego numerical nonlinear mechanical simulations. The closed-form solution approach will also appeal to device designers interested in performing large-scale parametric analysis.

Leseprobe

Table of Contents

Cover

Table of Contents

Title page

Copyright page

Dedication

PREFACE

CHAPTER 1 INTRODUCTION

1.1 MICROELECTROMECHANICAL SYSTEMS

1.2 COUPLED SYSTEMS

1.3 KNOWLEDGE REQUIRED

1.4 DIMENSIONAL ANALYSIS

CHAPTER 2 MICROFABRICATION

2.1 BULK AND SURFACE MICROMACHINING

2.2 LITHOGRAPHY

2.3 LAYER DEPOSITION

2.4 LAYER ETCHING

2.5 FABRICATION PROCESS DESIGN

CHAPTER 3 STATICS

3.1 STATIC EQUILIBRIUM

3.2 STRESS–STRAIN RELATIONSHIP

3.3 THERMAL STRESS

3.4 BEAM BEHAVIOR SUBJECTED TO A TORSIONAL MOMENT

3.5 MOMENT–CURVATURE RELATIONSHIP

3.6 BEAM EQUATION

3.7 GALERKIN’S METHOD

3.8 ENERGY METHOD

3.9 ENERGY METHOD FOR BEAM PROBLEMS

CHAPTER 4 STATIC BEHAVIOR OF MICROSTRUCTURES

4.1 ELEMENTS OF MICROSTRUCTURES

4.2 STIFFNESS OF COMMONLY USED BEAMS

4.3 TRUSSES

4.4 STIFFNESS TRANSFORMATION

4.5 STATIC BEHAVIOR OF PLANAR STRUCTURES

4.6 RESIDUAL STRESS

4.7 CUBIC FORCE OF STRUCTURES

4.8 POTENTIAL ENERGY

4.9 ANALOGY BETWEEN POTENTIAL ENERGIES

CHAPTER 5 DYNAMICS

5.1 CUBIC EQUATION

5.2 DESCRIPTION OF MOTION

5.3 GOVERNING EQUATIONS OF DYNAMICS

5.4 ENERGY CONVERSION BETWEEN POTENTIAL AND KINETIC ENERGY

5.5 FREE VIBRATION OF UNDAMPED SYSTEMS

5.6 VIBRATION OF DAMPED SYSTEMS

5.7 MULTIDEGREE-OF-FREEDOM SYSTEMS

5.8 CONTINUOUS SYSTEMS

5.9 EFFECTIVE MASS, DAMPING, AND STIFFNESS

5.10 SYSTEMS WITH REPEATED STRUCTURES

5.11 DUFFING’S EQUATION

CHAPTER 6 FLUID DYNAMICS

6.1 VISCOUS FLOW

6.2 CONTINUITY EQUATION

6.3 NAVIER–STOKES EQUATION

6.4 REYNOLDS EQUATION

6.5 COUETTE FLOW

6.6 OSCILLATING PLATE IN A FLUID

6.7 CREEPING FLOW

6.8 SQUEEZE FILM

CHAPTER 7 ELECTROMAGNETICS

7.1 BASIC ELEMENTS OF ELECTRIC CIRCUITS

7.2 KIRCHHOFF’S CIRCUIT LAWS

7.3 ELECTROSTATICS

7.4 FORCE AND MOMENT DUE TO AN ELECTRIC FIELD

7.5 ELECTROSTATIC FORCES AND MOMENTS ACTING ON VARIOUS OBJECTS

7.6 ELECTROMAGNETIC FORCE

7.7 FORCE ACTING ON A MOVING CHARGE IN ELECTRIC AND MAGNETIC FIELDS

7.8 PIEZORESISTANCE

7.9 PIEZOELECTRICITY

CHAPTER 8 PIEZOELECTRIC AND THERMAL ACTUATORS

8.1 COMPOSITE BEAMS

8.2 PIEZOELECTRIC ACTUATORS

8.3 THERMAL ACTUATORS

CHAPTER 9 ELECTROSTATIC AND ELECTROMAGNETIC ACTUATORS

9.1 ELECTROSTATIC ACTUATORS

9.2 COMB DRIVE ACTUATOR

9.3 PARALLEL-PLATE ACTUATOR

9.4 TORSIONAL ACTUATOR

9.5 FIXED–FIXED BEAM ACTUATOR

9.6 CANTILEVER BEAM ACTUATOR

9.7 DYNAMIC RESPONSE OF GAP-CLOSING ACTUATORS

9.8 APPROXIMATION OF GAP-CLOSING ACTUATORS

9.9 ELECTROMAGNETIC ACTUATORS

CHAPTER 10 SENSORS

10.1 FORCE AND PRESSURE SENSORS

10.2 ACCELEROMETERS

10.3 ELECTROSTATIC ACCELEROMETERS

10.4 VIBRATORY GYROSCOPES

10.5 OTHER ISSUES

APPENDIX

REFERENCES

Index

Copyright © 2011 by Ki Bang Lee. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Principles of microelectromechanical systems / Ki Bang Lee.

p. cm.

ISBN 978-0-470-46634-6 (cloth)

ISBN 978-1-118-10224-4 (ebk)

 1. Microelectromechanical systems. I. Lee, Ki Bang. II. Title: Principles of Microelectromechanical systems.

TK7875.P75 2010

621.381–dc22

2010007955

To

my parents, Won Eui Lee and Cha Won Cho

parents-in-law, Jong Hoon Suh and Soon Ja Chung

wife, Jeong Soo Seo

and children, Jong Eun Lee, Jong Min Lee, and Jong Hyeon Lee

PREFACE

This book aims to describe the principles of microelectromechanical systems (MEMS) via a unified approach and closed-form solutions that I have newly developed. The book is designed for senior (or graduate) students in universities and engineers from industry who want to design MEMS without numerical simulation. Since readers will have diverse backgrounds (e.g., electrical engineering, mechanical engineering, physics, chemistry), the book is organized so that it will be easy to understand the theory and closed-form solutions presented, which are used to design micro- and even nanosystems.

Through eighteen years of professional experience on MEMS, I have come to realize that most systems are so complicated that their static and dynamic behavior is too difficult to be expressed in closed forms. MEMS are systems whose mechanical behavior is coupled with electrical or other behavior, such as optical behavior. As a result, the governing equations for many MEMS become complicated or nonlinear, and their solutions have generally been obtained using numerical methods. For example, parallel plates connected to a voltage source show highly nonlinear behavior, including the pull-in phenomenon (jumping at a critical voltage), and it was too difficult to obtain simple and exact solutions for the interplate gap, resonant frequency, and capacitance, and their sensitivity at arbitrary voltages. In order to develop theory on linear and nonlinear MEMS, I spent four years, and then another year, in writing this book, which is a compilation of my research notebooks. Some of these theories and solutions have been published in journals and others are published in this book for the first time. I believe that the theory and closed-form solutions will help readers to understand coupled or nonlinear behavior of micro- and nanosystems and to easily design systems using micro- and nanoelements.

The book consists of ten chapters and presents building blocks for MEMS design in each chapter. MEMS behavior can be understood by combining the building blocks so that the reader can design a MEMS device for a specific purpose. Chapter 1 is an introduction, in which MEMS are defined and the knowledge required to understand them is examined briefly. Also presented is dimensional analysis, which provides basic dimensionless parameters existing in large- and small-scale worlds which we can use to understand the forces and other parameters in the small-scale world. Chapter 2 covers basic microfabrication, which presents knowledge on common fabrication processes employed in designing realistic MEMS. Chapter 3 is focused on statics, which is concerned with forces and moments acting on mechanical structures in static equilibrium. The static response of such mechanical elements as a prismatic beam is described using the governing equations obtained from force and moment equilibria. Chapter 4 treats the static behavior of structures consisting of mechanical elements. Chapter 5 deals with dynamic responses of mechanical structures by solving linear as well as nonlinear governing equations. Chapter 6 presents fluid flow in MEMS and evaluates the damping force acting on moving structures. Chapter 7 covers basic equations of electromagnetics, which govern the electrical behavior of MEMS and by which movable elements are actuated or sensing elements work.

Subsequent chapters are devoted to combing MEMS building blocks to form actuators and sensors for specific purposes. In Chapter 8 I set up models for actuators using piezoelectric material and thermal expansion and find closed-form solutions from the models. Chapter 9 deals with electrostatic and electromagnetic actuators whose mechanical and electrical behavior is coupled. Chapter 10 provides sensors that employ mechanical and electrical elements and the actuators covered in Chapters 8 and 9. In each chapter, theoretical models are presented for the elements and systems, and solutions for the static and dynamic responses are obtained in closed form. For easy understanding of complex MEMS, I use analogies and illustrations.

I would like to acknowledge my parents, Won Eui Lee and Cha Won Cho, and parents-in-law, Jong Hoon Suh and Soon Ja Chung, who live in South Korea and have supported me through thick and thin. My lovely wife, Jeong Soo Seo, gave me the confidence to write. Finally, I would like to thank George J. Telecki, Lucy Hitz, Angioline Loredo, and many other staff members of John Wiley & Sons, Inc. for their support. The book would not exist had it not been for their continuous encouragement and patience. If I become a professor at a university, I will use this book as a textbook.

KI BANG LEE

[email protected]

CHAPTER 1

INTRODUCTION

1.1 MICROELECTROMECHANICAL SYSTEMS

MEMS, microelectromechanical systems, are systems that consist of small-scale electrical and mechanical components for specific purposes. MEMS were translated into systems with electrical and mechanical components but have extended their boundaries to include optical, radio-frequency, and nano devices. As a result, depending on the components included and applications desired, MEMS have different names: for example, MOEMS (micro-optoelectromechanical systems) for optical applications, RF MEMS (radio-frequency MEMS) to refer to radio-frequency components and applications, and NEMS (nanoelectromechanical systems) if the systems include at least one component whose dimension is less than 1 µm. When MEMS use bio-related material (e.g., strands of DNA) to detect desired targets or to manipulate cells, the corresponding MEM system is currently called bioMEMS. Different names may refer to MEMS: microsystems technology (MST) in Europe and micromachines in Japan. Throughout this book, MEMS will be referred to as systems that include at least one set of electrical and mechanical components for a specific purpose. Depending on the specific purpose, more components, such as a reflective surface for a micromirror, can be added to a MEMS device. A typical dimension of a component of MEMS varies from 1 µm to a few hundred micrometers, and the overall size is approximately less than 1 mm. In this book we describe MEMS principles via a unified approach and newly developed closed-form solutions. Readers are assumed to be familiar with mathematical background at the third-year college and university level.

1.2 COUPLED SYSTEMS

MEMS are coupled systems since they consist of electrical and mechanical components; the mechanical behavior of MEMS are in general coupled with the electrical behavior. For example, let us consider the first electrostatic MEMS device (Fig. 1.1), presented by Nathanson et al. in the 1960s to filter or amplify electrical signals using the resonance of an electroplated cantilever. When an input signal (electrical signal) is applied across the end of the cantilever and the actuation electrode on a substrate, the electrical attractive force, given by Coulomb’s law, actuates the cantilever, and a detection circuit formed under the cantilever detects the filtered or amplified electrical signal that is generated by the mechanical vibration of the cantilever.

Figure 1.1 Resonant gate transistor.

Since the development of the first MEMS device, many other MEMS have been developed. For example, as one of the important components of MEMS, the parallel plate shown in Fig. 1.2 (similar to the cantilever of Fig. 1.1) is widely used in many microdevices that employ electrostatic forces for actuation of a microstructure or detection of a physical quantity. The typical parallel plate shown in Fig. 1.2 illustrates the basic knowledge that is required to understand MEMS behavior. The parallel plate consists of a movable plate suspended by flexures, a stationary plate, and a voltage source to supply voltage or electrical charge to the movable and stationary plates. The flexures are used to support the movable plate and act as a spring. The gap between plates can be adjusted when a force (e.g., electrostatic force or inertial force) acts on the plate.

Figure 1.2 Parallel plate.

Let us suppose that we apply a voltage across the movable and stationary plates. Upon applying the voltage, positive charges (or negative charges, depending on the electrical connection) are accumulated on the movable plate while opposite charges are accumulated on the stationary plate. As a result, the positive and negative charges on the plates generate an attractive force, the electrostatic force, which can push down the movable plate. The movable plate is displaced until the spring force (restoring force) due to the flexures balances the electrostatic force; that is, the displaced movable plate is in equilibrium while the voltage is applied. However, when the voltage is greater than a critical voltage called the pull-in voltage, the movable plate collapses into the lower plate.

A thermal actuator (Fig. 1.3) utilizes the thermal expansion due to Joule heating. As a voltage source supplies electrical current through the flexible beam that acts as a heater, heat is generated in the heater. The thermal expansion of the beam provides the displacement shown in the figure. The displacement depends on the voltage applied, the resistance of the beam, and the stiffness. Therefore, the mechanical behavior (e.g., displacement) of thermal actuators is coupled with the electrical and thermal behavior.

Figure 1.3 Electrothermal actuator.

A piezoelectric actuator (Fig. 1.4) utilizes a piezoelectric material whose shape is deformed when exposed to an electric field. In Fig. 1.4 a piezoelectric layer is glued or deposited on a substrate. A thin conductive electrode is placed or deposited on the piezoelectric layer so that the layer is exposed to an electric field when a voltage source applies a voltage across the layer. In this situation, the layer expands or contracts, depending on the polarity of the voltage. For example, if the piezoelectric layer expands in the longitudinal direction, the right end of the actuator moves downward. The end of the actuator moves upward when the polarity of the voltage is reversed. The mechanical behavior of the piezoelectric actuator is then coupled with the piezoelectric constants that relate the voltage to the deformation of the piezoelectric layer, the mechanical properties (e.g., Young’s modulus), and the layer geometry.

Figure 1.4 Piezoelectric actuator.

Electromagnetic force is also used to actuate microstructures. Figure 1.5 shows a model of an electromagnetic relay, one type of electromagnetic actuator. The relay consists of a movable bar (called an armature), a stationary core connected to the movable bar, a coil to generate magnetic field in the movable bar and stationary core, and a spring to provide the movable bar with a restoring force. When an electric current is applied to the coil, the relay is magnetized to generate an attractive force between the movable bar and the stationary core, and the movable bar is then attached to the stationary core. If the current is removed, the movable bar returns to its initial position under the restoring force of the spring. Thus, the mechanical behavior of electromagnetic actuators depends on the applied current, the magnetic and mechanical properties of the material used, the geometry of the actuator, and the stiffness of the spring.

Figure 1.5 Electromagnetic relay.

As briefly discussed above, actuators use electricity to generate mechanical motion such as displacement, and the resulting mechanical behaviors are then coupled with electrical behavior, material properties, geometry, and so on. As a result of the coupling, the mechanical behavior is, in general, related nonlinearly to electric input (e.g., applied voltage) except in a few cases, or are expressed as complicated functions of electric input. To understand these nonlinear actuators and sensors, numerical analyses have been widely used. For example, to obtain the sensitivity to voltage of the capacitance of a parallel plate (Fig. ), numerical analyses have been used to solve the equilibrium equation that governs the equilibrium position of the movable plate. Therefore, researchers, designers, and students have required commercial software to solve a problem or the skill to develop codes or programs that obtain the solution numerically. This book is designed to provide analytical closed-form solutions of both linear and nonlinear actuators in which mechanical behavior and electrical behavior are coupled. Since most MEMS-based sensors use actuators to measure physical quantities, this book can be used to design and analyze sensors.