An Efficient Macromodeling Methodology for Lateral Air Damping Effects

In this paper, a macromodeling methodology for lateral air damping effect is presented. This methodology employs a simplified governing equation, the Quasi-3D (Q3D) Stokes equation , and an Arnoldi-based model-order-reduction algorithm. A finite-difference (FDM) solver based on the Q3D-Stokes equation is implemented, and then the Arnoldi-based algorithm is used to create macromodels from the system matrices generated by the solver. This methodology can also be realized by using commercial MEMS packages for solid-model generation, and by using commercial finite-element (FEM) thermal packages for system-matrix generation. The generated macromodels are compatible with system-level modeling simulators, such as SPICE, Saber, or Simulink for fast transient and frequency analyses. It is demonstrated that the macromodels are at least 600 times more efficient than the FDM Q3D Stokes solver, while are still capable of capturing the three-dimensional (3-D) effect that usually requires very expensive 3-D FEM Stokes-flow calculations. Experimental results of comb-drive devices show that the error of the macromodel is less than 10%, which is a significant improvement when compared with the results by widely used 1-D analytical approaches. Finally, the guidelines of using this macromodeling methodology for typical MEMS devices are also provided.