Analysis of squeeze-film air damping of thick perforated plate in MEMS device

Moving plates in silicon microstructures are sometimes perforated to reduce the air damping for many applications. Most of the perforated plates are manufactured by anisotropic wet etching and DRIE. In fact, the cross-sections of these holes are not uniform, and the areas are variational. When the plates move against the substrate, squeeze-film air damping will badly affect the dynamic characteristics of the vibratory structure. Generally, the damping of air flow is determined by the Reynolds equation. However, the Reynolds equation is not used for the thick perforate plate, especially for the holes with variational cross-section. In this paper, the lava pipe model for air flow in the variational cross-section holes is used to obtain the velocity of air flow. Use the velocity of air flow to modify the conventional Reynolds equation, to obtain the pressure of the holes with variational cross-section. The pressure between the two ends of the hole can be obtained by the use of the modified Reynolds equation. It is valuable for design of MEMS device with thick perforated plate.