A model for squeeze-film damping of perforated MEMS devices in the free molecular regime

Abstract

Predicting squeeze-film damping in rare air is crucial for the design of high-Q MEMS devices. In the past, for MEMS structures with no perforations, there have been two approaches to treating the squeeze-film damping in rare air: using effective viscosity coefficient and using the molecular dynamics method. The amount of squeeze-film damping can be controlled by providing perforations in MEMS structures. To model perforation effects on squeeze-film damping, many methods have been proposed. However, the previous methods are all based on the approach using effective viscosity coefficient. The approaches treat the gas in the gap as a continuum. This paper presents an analytical molecular dynamics model for the squeeze-film damping of a perforated microplate in the free molecular regime. The quality factor is found by calculating the energy transfer from the vibrating plate to the surrounding air due to the collisions between the microplate and the molecules. This paper is an extension of the work done by Bao et al (2002 J. Micromech. Microeng. 12 341–6). Bao's work is valid only for non-perforated microplate. The accuracy of the present molecular dynamics model is verified by comparing its results with the experimental results available in the literature. The limitations of the present molecular dynamics model have been reported in this paper.