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.

Modeling MEMS and NEMS

Gas flow rates in microchannels have been rigorously evaluated by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the Bhatnagar, Gross, and Krook model. The Maxwell scattering kernel has been used to describe the gas-wall interactions in the most general case of two surfaces with different accommodation coefficients.

Variational approach to gas flows in microchannels

Mechanics of Rarefied Gases

A mathematical model for the effective viscosity of a gas film in small air gaps between silicon-metal surfaces is presented. The model is based on the solution of the linearized Boltzmann equation and it is valid in viscous, transitional and molecular damping regions. The equation is solved with two different methods and a simple approximate equation for the effective viscosity is given to be used in practical design. With the model, a surface accommodation coefficient for the silicon surface is extracted by comparing accelerometer measurements and the mathematical model.

Model for gas film damping in a silicon accelerometer

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.

Molecular dynamics simulations of shear-driven gas flows in nano-channels

A generalize Reynolds-type lubrication equation valid for both arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, and arbitrary accommodation coefficients at boundaries, is derived form a linearized Boltzmann equation. Numerical analyses of lubrication characteristics through the equation for high Knudsen numbers reveal that, if the accommodation coefficient is less than 1, that is, if not all the molecules reflect diffusely as is the case with real gases, load carrying capacities are smaller than those for diffuse reflection.

Analysis of Ultra-thin Gas Film Lubrication Based on the Linearized Boltzmann Equation : Influence of Accommodation Coefficient

This paper investigates the dynamic characteristics of flying head sliders with ultra-thin spacing through a generalized lubrication equation based on the Boltzmann equation, and compares them with two limiting cases: approximations for bearing number ∧ → 0 and ∧ → ∞. These approximations agree well with numerical results in the limiting conditions. In particular, the approximation for ∧ → ∞ is found to quantitatively explain the characteristics of damping coefficients and correponding unstable phenomena.

Dynamic Analysis of Flying Head Sliders with Ultra-Thin Spacing Based on the Boltzmann Equation : Comparison with Two Limiting Approximations

Magnetic recording is potentially superior to optical recording with respect to recording density. However, to realize the full potential of magnetic disk storage devices, it is necessary to lower the head flying height from the submicrometer range to the sub-submicrometer range. In order to maintain the head at a safe sub-submicrometer flying height, it is necessary to solve the problem of head and medium wear. Consequently, the study of micro-tribology is essential for the development of magnetic recording capability. Compared with magnetic disk drives, optical disk drives have longer seek times and lower data rates. To enhance the seek time and data rate, electromechanics and servo-control technologies are the main concern. Advances in magnetic disk storage devices can be expected in the area of fixed-media on-line files. In contrast, the strong point of optical disk storage devices is their media-interchangeability. New optical disk applications which exploit this special feature can be expected.

Reizo Kaneko

Papers

Analysis of Ultra-thin Gas Film Lubrication Based on the Linearized Boltzmann Equation : Influence of Accommodation Coefficient

Dynamic Analysis of Flying Head Sliders with Ultra-Thin Spacing Based on the Boltzmann Equation : Comparison with Two Limiting Approximations

Magnetic and Optical Disk Storage Technology