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Electrostatic gap models for hierarchical MEMS circuit design are studied and parameterized through a series of finite element simulations and mathematical modeling. The models take into account the fringing fields which contribute large capacitances in low-aspect-ratio surface-micromachined devices. Angular orientation of electrode sidewall is taken into account to accommodate simulation of manufacturing variations. Results show that capacitances reconstructed from these models deviate from the original data by less than 5% on the average. Simulations on cantilever beam actuators show comparable results between the MEMS hierarchical circuit analysis and the electromechanical finite element analysis. Experimentally, less than 7% error in the pull-in voltages is obtained by considering the sidewall angle.
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