Factors Affecting the Precision of Electrostatic Computation of 3D MEMS Structures

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play a very major role in maneuvering these devices, and hence, a thorough understanding of the electrostatic properties of these structures is of critical importance. Recently, a nearly exact boundary element method (neBEM) solver has been developed and used to solve difficult problems related to electrostatics of various devices. Because of the exact foundation expressions, this solver has been found to be very accurate while solving critical problems which normally necessitate special formulations involving elegant, but difficult mathematics. In this work, we investigate the effects of various possible approximations on the 3D electrostatic solutions obtained for MEMS structures. In particular, we investigate the effects of discretization, omission of surfaces with small amount of charge accumulation on the final results such as the charge distribution on various surfaces or capacitance of a given MEMS structure.