Electrostatic BEM for MEMS with thin conducting plates and shells

Micro-electro-mechanical systems (MEMS) sometimes use beam or plate shaped conductors that can be very thin-with h/L approximate to O(10(-2) - 10(-1)) (in terms of the thickness It and length L of the side of a square pate). Conventional Boundary Element Method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry Out accurately and efficiently-especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such plates. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with weakly singular kernels, results in a powerful technique for the BEM analysis of such problems. This new approach, in fact, works best for very thin plates. This thin plate BEM is derived and discussed in this work. Numerical results, from several BEM based methods, are presented and compared for the model problem of a parallel plate capacitor. (C) 2004 Elsevier Ltd. All rights reserved.