Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.

Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis.

In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.

INTRODUCTION

MEMS and NEMS

A Capsule History of MEMS and NEMS

Dimensional Analysis and Scaling

Exercises

A REFRESHER ON CONTINUUM MECHANICS

Introduction

The Continuum Hypothesis

Heat Conduction

Elasticity

Linear Thermoelasticity

Fluid Dynamics

Electromagnetism

Numerical Methods for Continuum Mechanics

SMALL IS DIFFERENT

The Backyard

Scaling

Systems

Exercises

THERMALLY DRIVEN SYSTEMS

Introduction

Thermally Driven Devices

From PDE to ODE: Lumped Models

Joule Heating of a Cylinder

Analysis of Thermal Data Storage

Exercises

MODELING ELASTIC STRUCTURES

Introduction

Examples of Elastic Structures in MEMS/NEMS

The Mass on a Spring

Membranes

Beams

Plates

The Capacitive Pressure Sensor

Exercises

MODELING COUPLED THERMAL-ELASTIC SYSTEMS

Introduction

Devices and Phenomena in Thermal-Elastic Systems

Modeling Thermopneumatic Systems

The Thermoelastic Rod Revisited

Modeling Thermoelastic V-Beam Actuators

Modeling Thermal Bimorph Actuators

Modeling Bimetallic Thermal Actuators

Exercises

MODELING ELECTROSTATIC-ELASTIC SYSTEMS

Introduction

Devices Using Electrostatic Actuation

The Mass-Spring Model

Modeling General Electrostatic-Elastic Systems

Electrostatic-Elastic Systems - Membrane Theory

Electrostatic-Elastic Systems - Beam and Plate Theory

Analysis of Capacitive Control Schemes

Exercises

MODELING MAGNETICALLY ACTUATED SYSTEMS

Introduction

Magnetically Driven Devices

Mass-Spring Models

A Simple Membrane Micropump Model

A Small-Aspect Ratio Model

Exercises

MICROFLUIDICS

Introduction

Microfluidic Devices

More Fluidic Scaling

Modeling Squeeze Film Damping

Exercises

BEYOND CONTINUUM THEORY

Introduction

Limits of Contiuum Mechanics

Devices and Systems Beyond Continuum Theory

Exercises

REFERENCES

APPENDICES

Mathematical Results

Physical Constants

INDEX

Each chapter also contains Related Reading and Notes sections.

"Researchers in MEMS and NEMS … are likely to find much of interest [in this book], … and to date there is no other book on MEMS and NEMS that is focused on the modeling process to the same extent. Graduate students of MEMS and NEMS will find the book to be between useful and indispensable. … [This] is a thought-provoking book for those with interests in modeling and is likely to have a longevity well beyond the usual half-life of a textbook."

- SIAM Review, Vol. 46, No. 1

"Although the exposition is primarily intended for the engineering community … applied mathematicians can also get a lot of inspiration [from this book]. … The large number of exercises makes it suitable … also as a textbook for graduate students … ."

- EMS Newsletter

"…whether or not the next small thing turns out to be the next big thing, the topic offers interesting science to be explored, and here is a good book to guide you through it. …very broad scope … Generous references are given … Elasticity and heat transfer are perhaps the domains that are most prominent, although there is plenty of insight and interest in other areas, and the choice of core problems is excellent. …

"Researchers in MEMS and NEMS, where modeling and simulation are increasingly recognized as important first steps in design, are likely to find much of interest … and to date there is no other book on MEMS and NEMS that is focused on the modeling process to the same extent. … Graduate students of MEMS and NEMS will find the book to be between useful and indispensable … well suited to a graduate course …

"The writing style is very clear and lively, producing a readable--even vibrant--text. But above all, it is a thought-provoking book for those with interest in modeling and is likely to have a longevity well beyond the usual half-life of a textbook."

- SIAM Review, March 2004

"Starting from the deep principles of physical scaling and dimensional analysis, Pelesko and Bernstein introduce a wide range of MEMS and NEMS devices to motivate their review of the essential continuum mathematical physics of coupled-domain micro-scaled devices. Their book is bound to become the standard text for modelers of MEMS and NEMS, as well as an essential volume on the bookshelves of all MEMS and NEMS designers. Given the book's sophisticated, yet straightforward, approach to the fundamental physics of several energy domains (thermal, elastic, electrostatic, magnetic, and fluid) the volume can be recommended as the basis for general courses in applied science and engineering."

- Seldon B. Crary, President and CEO, Crary Group, Inc., Palo Alto, California, USA and Copenhagen, Denmark