Macromodels of 3D lateral viscous damping effects for MEMS devices

In this work, a fast algorithm of generating accurate time-domain macromodels of viscous lateral damping for three-dimensional MEMS geometries is described. A three-dimensional finite-difference (FDM) Stokes flow solver for simulating lateral damping effects was developed. The system matrices generated by the solver was then reduced to low-order macromodels that can be easily inserted into a system-level modeling simulators, such as Saber, Simulink or SPICE for transient and frequency analysis. The macromodels have proved to be about three-order-of-magnitude as efficient as the FDM solver, while preserve the 3-D edge effects that usually require expensive 3-D BEM or FEM calculations. Experimental results of quality factors for comb-drive devices demonstrated that the error of the results estimated by the macromodels is within 15%.