Computation of Electrostatic Properties of 3D MEMS Structures

Abstract

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($μm$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of thin beams which, owing to their smallness, can be moved or deflected easily through the application of low voltages. Since electrostatic forces play a very major role in maneuvering these devices, a thorough understanding of the electrostatic properties of these structures is of critical importance, especially in the design phase of MEMS. In many cases, the electrostatic analysis of MEMS is carried out using boundary element method (BEM), while the structural analysis is carried out using finite element method (FEM). In this paper, we focus on accurate electrostatic analysis of MEMS using BEM. In particular, we consider the problem of computing the charge distribution and capacitance of thin conducting plates relevant to the numerical simulation of MEMS. The reason behind the accuracy of the solver is the fact that it uses closed-form analytic expressions that are valid seamlessly throughout the physical domain for computing the influence coefficients. Thus, it is possible to avoid one of the most serious approximations of the BEM, namely, the assumption that the effect of a charge distributed over a boundary element can be approximated by charge located at the centroid of the element. Comparison with other results available in the literature seems to indicate that the present results are more accurate than the existing ones.