Development and accuracy assessment of simplified electromechanical coupling solvers for MEMS applications

Electromechanical coupling is one of the most critical issues in microelectromechanical systems (MEMS). The current commercial MEMS CADs use highly meshed three-dimensional (3D) models to perform analysis, and this approach can be computationally expensive and may not be needed for most MEMS structures in which their geometries are inherently two-dimensional (2D) shape. In this paper, we report on two solvers that have been developed for performing coupling analysis in a 2D manner to reduce the computational cost and to improve the efficiency of electromechanical coupling analysis. The electromechanical sequential solver (EMS) method, which combines ABAQUS structural analysis with FastCap electrostatic analysis, provides detailed coupling analysis. On the other hand, the electrostatic distributed load solver (EDS) method, which utilizes an ABAQUS DLOAD user-defined subroutine, concentrates on the net effect in the mechanical field. Both methods are verified by the commercial package CoventorWare. It is found that the accuracy of these solvers is within 5% for MEMS structures with typical physical dimensions. Therefore, both EMS and EDS methods can be used to replace the full 3D coupled analysis for most surface micromachined MEMS structures. However, it is also important to indicate that, for short beams, large air gaps and large rotation, the performance of both methods degrades, especially for the EDS method.