Modelling of the Squeeze Film Air Damping in Mems

Abstract

We propose a formulation for modeling the squeeze film air damping in micro-plates typical of micro-electromechanical devices for micro switch applications. A special finite element is developed, in which the nonlinear Reynolds equation for compressible film is used to analyze the air pressure field, whereas a standard linear elastic model is used for the displacement field. The formulation is based on a finite element discretization of both the pressure and displacement fields. The coupled equations of motion are established and, for harmonic oscillations, we show that the resulting damping matrix depends on the frequency. The typical dimensions and properties of the MEMS device are in the order of hundred micrometers length and some micrometers (3-8 um) thick, with a separation from the substrate of also some micrometers (e.g. 3-5 um). For these dimensions, the influence of damping owing to the surrounding air cannot be neglected, having an important contribution to the quality factor of the device. The influence of plate holes, which are necessary because of the fabrication process, determines also the dynamic behavior of the plate. Examples are presented, with comparisons to results of the bibliography.