1st Edition

# Modeling MEMS and NEMS

By John A. Pelesko, David H. Bernstein Copyright 2002
384 Pages 106 B/W Illustrations
by CRC Press

384 Pages
by CRC Press

Also available as eBook on:

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.

### Biography

John A. Pelesko, David H. Bernstein

"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 … ."