Principles of Microelectromechanical Systems (IEEE Press) - Hardcover

Lee, Ki Bang

9780470466346: Principles of Microelectromechanical Systems (IEEE Press)

Hardcover

ISBN 10: 0470466340 ISBN 13: 9780470466346

Publisher: Wiley-IEEE Press, 2011

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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.

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About the Author

ki bang lee, PhD, is Director of KB Lab in Singapore. He has made numerous contributions in micro- and nano-electromechanical systems. From 2000 to 2004, Dr. Lee was a researcher at University of California, Berkeley. He worked for Samsung during 1987-2000, most recently holding the position of principal research scientist. He earned his PhD in mechanical engineering at Korea Advanced Institute of Science and Technology (KAIST).

From the Back Cover

The building blocks of MEMS design through closed-form solutions

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

From the Inside Flap

The building blocks of MEMS design through closed-form solutions

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

Excerpt. � Reprinted by permission. All rights reserved.

Principles of Microelectromechanical Systems

By Ki Bang Lee

John Wiley & Sons

Copyright � 2011 John Wiley & Sons, Ltd
All right reserved.
ISBN: 978-0-470-46634-6

Chapter One

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 (microoptoelectromechanical systems) for optical applications, RF MEMS (radiofrequency 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 1μm. When MEMS use biorelated 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 1μm to a few hundred micrometers, and the overall size is approximately less than 1mm. 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.

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.

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.

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.

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.

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. 1.2), 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.

1.3 KNOWLEDGE REQUIRED

As discussed in the foregoing section, MEMS are systems that consist of mechanical and electrical components and that may also involve other components, such as a reflective layer for a micromirror, depending on the purpose. Since the mechanical behavior of MEMS are coupled with other behavior, we should study interdisciplinary subjects in the fields of science and engineering to understand the coupled behaviors. Figure 1.6 shows an overview of the knowledge required for the research and development of MEMS and their derivatives. Because the most convenient and controllable energy is the electrical energy, electrical and electronic engineering covering electromagnetics, circuit theory, or signal processing is required to control phenomena associated with electric charge (i.e., electron, current). For example, from the point of view of electrical engineering, the parallel plate of Fig. 1.2 may be considered to be a capacitor consisting of movable and stationary plates, so knowledge of electrical engineering is necessary to calculate the capacitance of the parallel plate and to obtain the electrostatic force acting on the movable plate as a function of the interplate gap and the applied voltage. Similarly, since the magnetic relay of Fig. 1.5 is an electromagnet with a variable air gap, we use the magnetic energy that is stored in the electromagnet and calculate the magnetic force pulling the movable bar into the stationary core.

Physically, MEMS are mechanical structures that are designed for specific purposes. For desired functions, components of MEMS must be mechanically stable, vibrate if the mechanical resonance is utilized, and be deformed if deformation or displacement is needed. For the design and analysis of mechanical components, we need statics for the mechanical structure design, dynamics and vibration for resonance and mechanical vibration, heat transfer for thermal actuation, and fluid dynamics for the evaluation of damping due to the movement of microstructures. Let us consider the parallel plate in Fig. 1.2 as an example of a mechanical structure. Since the four flexures support the movable plate under the electrostatic force, we need statics to determine the flexure dimensions: the length, width, and thickness of the flexures. If the movable plate operates at resonance for a mechanical filter, we should use our knowledge of dynamics or mechanical vibration to design the resonant frequency desired. If we wish to set up a mechanical quality factor that affects the bandwidth of a mechanical filter, we should evaluate the damping force or damping coefficient that can be provided by fluid dynamics. If we wish to design an accelerometer or acceleration switch using the parallel plate shown in Fig. 1.2, we need to know the dynamics and mechanical vibration.

All the above-mentioned knowledge is coupled, so the design of a parallel plate for a specific application is very complicated even though the parallel plate in Fig. 1.2 looks simple. In addition to these complexities, we may need physics, chemistry, mathematics, and other subject areas, and MEMS may have different names, as described in Fig. 1.6: MOEMS if a MEMS device involves at least one optical component; RF MEMS if a MEMS device is designed for a radio-frequency application such as an RF filter; bioMEMS if a MEMS device is used for biological applications such as the detection of DNA strands; NEMS if at least one dimension of the mechanical structure is less than 1m; and perhaps other names in future applications if mechanical structures with electrical components are used for a specific purpose.

1.4 DIMENSIONAL ANALYSIS

Dimensional analysis and dimensionless numbers allow us to investigate complicated or coupled systems such as the MEMS described in Section 1.3. Using dimensional analysis and experimental results (or numerical simulation), we can find relationships between variables that are involved in a problem or system. If we apply dimensional analysis to a governing equation that describes a physical phenomenon and cannot be solved due to its nonlinearity, we can obtain useful dimensionless numbers that play crucial roles in describing the phenomenon. We begin with easy dimensionless numbers with which we are familiar.

Let us begin by considering the ratio of the circumference of a circle to its diameter, the well-known constant. Figure 1.7a,b, and c show a circular column, a rectangular column, and an arbitrarily shaped body, respectively. As the radius and height of the circular column (Fig. 1.7a) are represented by r and t, respectively, the perimeter l of the top view, the top-view area A, and the volume V are given by