The effect of shape and distribution of perforations on squeeze-film damping in parallel plate capacitors

The effect of the shape and distribution of perforations in parallel plate capacitive MEMS devices on squeeze-film damping is presented. The squeeze film effect is the most important damping effect on the dynamic behavior of most MEMS devices that employ capacitive sensing and actuation, which typically employ narrow air gaps between planar moving surfaces [1, 2]. The stationary plate of a capacitive device is often perforated to reduce the damping and sensor noise and improve the frequency response. The formula for determining the total viscous damping in the gap contains a coefficient Cp that is associated with the geometry and distribution of the holes on the stationary plate. In this study, the coefficient Cp is determined using the finite element method using ANSYS by analogy with heat conduction in a solid with internal heat generation. Round, elliptical, rectangular, and oval holes that are distributed either aligned or offset are analyzed and compared. It is shown that the surface fraction occupied by the perforations is not the only factor that determines Cp. Both the shape and distribution strongly affect the damping coefficient [3, 4]. By using elongated perforations that are properly distributed, the squeeze film damping could be minimized with the minimum amount of perforation. The analysis performed in this work is quite general being applicable to a very large spectrum of frequencies and to various fluids in capacitive sensors. These results can facilitate the design of mechanical structures that utilize capacitive sensing and actuation, such as accelerometers, optical switches, micro-torsion mirrors, resonators, microphones, etc.