An efficient relaxation based DIPIE algorithm for computer aided design of electrostatic actuators

Pull-In parameters are important properties of electrostatic actuators. Efficient and accurate analysis tool that can capture these parameters for different design geometries, are therefore essential. Current simulation tools approach the Pull-In state by iteratively adjusting the voltage applied across the actuator electrodes. The convergence rate of this scheme gradually deteriorates as the Pull-In state is approached. Moreover, the convergence is inconsistent and requires many mesh and accuracy refinements to assure reliable predictions. As a result, the design procedure of electrostatically actuated MEMS devices can be time-consuming. In this paper a novel Displacement Iteration Pull-In Extraction (DIPIE) scheme is presented. The DIPIE scheme is shown to converge consistently and far more rapidly than the voltage iterations (VI) scheme (>100 times faster!). A relaxation based DIPIE scheme that requires separate mechanical and electrostatic field solvers is suggested. Therefore, it can be easily implemented into existing MOEMS CAD packages. Moreover, using the DIPIE scheme, the Pull-In parameters extraction can be performed in a fully automated mode, and no user input for search bounds is required.