Model for gas film damping in a silicon accelerometer

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.