On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

The evaluation of gas dissipation occurring in inertial polysilicon MEMS is addressed focusing the attention on the free-molecule flow. In this regime, which is very often of interest for industrial applications, collisions between molecules can be neglected and the momentum transfer to the moving shuttle can be easily computed. Since the surfaces of silicon MEMS are generally very rough, a complete diffusion model is adopted to describe the wall–molecule interaction. A Boundary Integral Equation approach is proposed and compared to a classical Test Particle Monte Carlo method, pointing out the clear advantages of the former for the applications at hand. It is shown that the introduction of the key assumptions of small perturbations and quasi-static response is crucial in the development of a robust and fast numerical tool. Several examples are presented validating the formulation with analytical and experimental results.