A conformal mapping-based approach for fast two-dimensional FEM electrostatic analysis of MEMS devices

In this paper, a methodology is proposed for expediting the coupled electro-mechanical two-dimensional finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by mapping the deformed electrostatic domain to the reference undeformed domain 'conformally'. A 'conformal' map preserves the form of the Laplace equation and the boundary conditions; thus the electrostatic problem is solved only once in the undeformed electrostatic domain. The conformal map itself is generated through the solution of the same Laplace equation on the undeformed geometry and with displacement boundary conditions dictated by the movement of the mechanical domain. The proposed methodology is demonstrated through its application to the modeling of three MEMS devices with varying length-to-gap ratios, multiple dielectrics and complicated geometries. The accuracy of the proposed methodology is confirmed through comparisons of its results with results obtained using the conventional finite element solution.