Numerical modeling and validation of squeezed-film damping in vacuum-packaged industrial MEMS

Several high-performance, industrial micro-electromechanical (MEM) devices, such as gyroscopes, magnetometers, high-Q resonators and piezoelectric energy harvesters, require wafer bonding and packaging under near-vacuum conditions. One very challenging aspect of the design, verification and characterisation of these devices is to predict their performance characteristics in the presence of any residual gases post-packaging. Such gases contribute to the energy losses resulting from device surfaces squeezing or sliding against the gas films within the device cavities. In this paper, we fully expose the modelling assumptions used in commercial FEM tools to estimate the squeezed-film damping (SFD) experienced by MEM devices that are packaged under near-vacuum conditions. We also explain the various meshing options to enable the extraction of the most accurate Q factors under existing SFD assumptions. In addition, we compare the computational results across a variety of commercial FEM codes against measurements obtained under realistic vacuum conditions for an industrial high-Q magnetometer. These measurements suggest that existing computational models may deviate by as much as 25% on Q factor values for gas flow regimes under operating cavity pressures of less than 1 Torr.