Capacitance and Force Computation Due to Direct and Fringing Effects in MEMS/NEMS Arrays

Abstract

An accurate computation of electrical force is significant in analyzing the performance of microelectromechanical systems and nanoelectromechanical systems. Many analytical and empirical models are available for computing the forces, especially, for a single set of parallel plates. In general, these forces are computed based on the direct electric field between the overlapping areas of the plates and the fringing field effects. Most of the models, which are based on direct electric field effect, consider only the trivial cases of the fringing field effects. In this paper, we propose different models which are obtained from the numerical simulations. It is found to be useful in computing capacitance as well force in simple and complex configurations consisting of an array of beams and electrodes. For the given configurations, the analytical models are compared with the available models and numerical results. While the percentage error of the proposed model is found to be under 6% with respect to the numerical results, the error associated with the analytical model without the fringing field effects is $\sim 50$ %. The proposed model can be applied to the devices in which the fringing field effects are dominant.