Computationally efficient model for viscous damping in perforated MEMS structures

Abstract

In this work an analytical model for the flow resistance for viscous air damping in a MEMS structure comprising a perforated plate in close proximity to a solid plate is developed. Such a configuration is widely used for oscillating MEMS sensors and actuators. It was shown that in addition to the resistance caused by the perforation hole and by squeeze film damping between the two plates, an additional resistance in the intermediate region caused by the redirection of the flow between the perforation hole region and the squeeze film region also has to be considered. The overall flow resistance is the sum of the flow resistance of several regions. The models for the individual regions have been derived analytically for the squeeze film damping and using numerical solutions of the Navier-Stokes equation for the perforation hole and the intermediate region. The validity of the derived damping model is limited to cases where the Knudsen number is smaller than 0.1, the porosity is smaller than 0.9 and the ratio between gap height of the two plates and the perforation hole radius is larger than 0.1 and squeeze number σ<<1 – which is typical dimensions MEMS structures. The presented model covers an extended geometry range compared to previously reported damping models.