A Material Selection Criterion for Electrostatic Switches Based on Stability Considerations

Abstract

Recent impressive advances of MEMS technology thanks to integration of emerging materials exhibiting exclusive properties, has led to fabrication of numerous high performance devices. Further development of the field necessitates more accurate analytical models capable of precisely accounting for all existing physical phenomena affected by new materials properties. In this regard, the present paper investigates how finite electrical conductivity of the composing materials may affect the pull-in instability of an electrostatically actuated cantilever MEMS switch. The governing coupled nonlinear equations of an equivalent lumped parameter model are derived by introducing an assumed mode solution to the extended Hamilton’s principle. A Lyapunov-based method is then employed to derive an estimation for the basin of attraction of the stable equilibrium and determine the minimum voltage needed for the cantilever to escape the attractor and touch the contact. Results indicate the substantial effect of electrical resistivity on both instability range and maximum switching frequency of the device. As evidenced by the presented findings the material selection for this type of switches should be made with a broader view bringing into focus the effect of electrical conductivity of the material on stability characteristics of the device.