Compressible squeeze-films in vibrating MEMS structures at high frequencies

A simple model is presented to approximate the damping due to gas in vibrating MEMS squeeze-film structures at high frequencies. The model is based on the observation that at high frequencies, where the compressible force dominates (the squeeze number sigma Gt 1), the gas flows only close to the damper borders. This new compact damping model, valid for high squeeze numbers, is derived from an analytic 1-dimensional solution of the Reynolds equation with non zero-pressure boundary conditions. Since the damping at high frequencies is a border phenomenon, the 1-dimensional model is sufficient for any damper surface geometry, and the non-idealistic border conditions are essential in the accurate model. The border conditions are stronger, and become even more important, if the gas is rarefied, that is the Knudsen number is large. In the presented model, the only surface dimension needed is the length of the periphery of the surface. This makes the model easily applicable to complex geometries, too. The damping in accelerometer structures with two perforations in the seismic mass has been calculated with the model at high frequencies. These results are compared with FEM simulations.