MSM 2000
MSM 2000
Technical Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems

Numerics, Algorithms Chapter 11

Mathematical Analysis of Electrostatically Actuated MEMS Devices

Authors: D. Bernstein, P. Guidotti and J.A. Pelesko

Affilation: California Institute of Technology, United States

Pages: 489 - 492

Keywords: actuator, MEMS, asymptotics, modeling, continuation

We perform a rigorous mathematical analysis of a simple membrane based model of an electrostatiacallyh actuated MEMS device. Using both analytical and numerical techniques, we prove the existence of a fold in the solution space of the displacement, implying the existence f a critical voltage beyond which there are no solutions of the equations. This critical voltage corresponds to the pull-in voltage observed in simpler lumped models, the numerical solution of three dimensional models, and also in experimental devices. We show how pseudo-arclength continuation may be used to efficiently compuet the solutions on both sides of the fold.

Mathematical Analysis of Electrostatically Actuated MEMS Devices

ISBN: 0-9666135-7-0
Pages: 741