Modeling of Pull-In Instability of Nano/Micromirrors Under the Combined Effect of Capillary and Casimir Forces

Abstract

In the current article the effect of the Casimir force on the static behavior and pull-in characteristics of nano/micromirrors under capillary force is investigated. At the first, the dimensionless equation governing the static behavior of nano/micromirrors is obtained. The dependency of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that the Casimir effect can considerably reduce the pull-in instability limits of the nano/micromirror. It is also found that rotation angle of the mirror under capillary force highly depends on the Casimir force applied to the mirror. Finally the analytical tool Homotopy Perturbation Method (HPM) is utilized for prediction of the mirror's behavior under combined capillary and Casimir forces. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this article can be used for successful fabrication of nano/micromirrors using the wet etching process where capillary force plays a major role in the system.