Use of the neBEM solver to Compute the 3D Electrostatic Properties of Comb Drives

Abstract

Micro-Electro-Mechanical Systems (MEMS) comb drives are used for both as sensors and actuators. As a result, they have been considered to be very important in MEMS technology and has been under intense study for last few years. The actuation and the sensitivity are both dependent in a major way on the electrostatic configuration of the comb structure. As a result, accurate estimation of the electrostatic configuration of comb drives is crucial in both design and interpretation phases. The nearly exact Boundary Element Method (neBEM) solver has been developed recently and used successfully to solve difficult problems related to electrostatics. This solver uses exact analytic expression for computing the influence of singularity distributions instead of adopting the conventional and convenient approximation of nodal concentration of charges. Due to the exact foundation expressions, the solver has been found to be exceptionally accurate in the complete physical domain, including the near field. In this work, we explore the possibility of using the neBEM solver to solve 3D electrostatic problems related to comb drives. In particular, we investigate the relationship between the accuracy achieved and the computational expenses incurred for a realistic comb drive geometry. In the process, we estimate the charge density distribution, potential distribution and the capacitance of the comb structure. The study has led us to the conclusion that the neBEM solver can yield very accurate estimates of all the properties of interest at a reasonable computational expenditure.