Time-Efficient Quasi-Static Algorithm for Simulation of Complex Single-Sided Clamped Electrostatic Actuators

This paper reports on a very time- and resource-efficient numerical algorithm for quasi-static modeling of the static behavior and the "quasi-static movement" of highly nonlinear electrostatic actuators with single-side clamped moving elements. The algorithm is capable of simulating prestressed materials and multicontact touching surfaces with complex geometries, including distance-keeping stoppers and thickness and material inhomogeneities of the moving parts. Thus, it is very suitable for predicting the behavior of actuators such as laterally moving curved-electrode actuators or vertically moving touch-mode or zipper actuators. In contrast to conventional, very time- and memory-consuming simulation methods such as finite-element analysis, the proposed algorithm-even if implemented in the slow script-language of MATLAB-takes only a fraction of a second to solve a complex problem, which makes it a very powerful design tool for parameter optimization of the actuator geometry. The reason for the efficiency of this algorithm is that its core is based on the one-dimensional mathematical description of a two-dimensional model geometry and that the differential equation is solved by a simple triple-integration for each iteration step, which is a method very suitable for thin-film single-side clamped moving elements. This paper describes the algorithm, analyzes its accuracy and its limitations, and reports on its performance as compared to other methods such as simplified analytical models for very basic structures, finite-element method (FEM) simulations of complex structures, and measurements of fabricated devices, including laterally moving microelectromechanical systems (MEMS) switches and vertically closing prestressed thin-film zipper actuators. Furthermore, the efficiency of the algorithm as a design tool was evaluated for the parameter optimization of electrostatic curved-electrode actuators. The algorithm\´s main application is seen in the fast determination of su- - itable parameter sets for MEMS electrostatic actuators, but it cannot substitute for a more accurate FEM analysis to investigate a final design in great detail