Fast and Precise 3D Computation of Capacitance of Parallel Narrow Beam MEMS Structures

Efficient design and performance of electrically actuated MEMS devices necessitate accurate estimation of electrostatic forces on the MEMS structures. This in turn requires thorough study of the capacitance of the structures and finally the charge density distribution on the various surfaces of a device. In this work, nearly exact BEM solutions have been provided in order to estimate these properties of a parallel narrow beam structure found in MEMS devices. The effect of three-dimensionality, which is an important aspect for these structures, and associated fringe fields have been studied in detail. A reasonably large parameter space has been covered in order to follow the variation of capacitance with various geometric factors. The present results have been compared with those obtained using empirical parametrized expressions keeping in view the requirement of the speed of computation. The limitations of the empirical expressions have been pointed out and possible approaches of their improvement have been discussed.