Modeling gas damping and spring phenomena in MEMS with frequency dependent macro-models

In this paper, we present an efficient macromodel extraction technique for gas damping and spring effects for arbitrarily shaped MEMS devices. The technique applies an Arnoldi-based model-order-reduction algorithm to generate low-order models from an FEM approximation of the linearized Reynolds equation. We demonstrate that this approach for generating the frequency-dependent gas-damping model is more than 100 times faster than previous approaches, which solve the linearized Reynolds equation using a transient FEM solver. The low-order gas-damping model can be easily inserted into a system-level modeling package for transient and frequency analysis. The simulated results are in good agreement with experimental results for four different devices.