A Coupled Model Between Torsion and Bending in Nano/Micromirrors Under the Combined Effect of Van Der Waals Force and Capillary Force

Abstract

The coupling effect between torsion and bending in nano/micromirrors under the combined effect of capillary force and van der Waals (vdW) force is presented in this paper. At the first, the dimensionless equations governing the statical behavior of the nano/micromirror are obtained using the minimum total potential energy principle. Then the equations governing the pull-in state of the mirror are obtained using the implicit function theorem. The related results show that neglecting bending effect can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirror under combined vdW and capillary forces. It is observed that vdW force reduces the pull-in angle and pull-in deflection of the supporting torsion beams of the mirror. The static behavior of the nano/micromirror under capillary and vdW loading is also studied and the results reveal that the static behavior of the nano/micromirror under capillary and vdW forces highly depends on the bending of the torsion beams. The results of this paper can be used for a safe and stable design and fabrication of mirrors using the wet etching process, where the gap between the mirror and the underneath substrate is sufficiently small and as a results both capillary and vdW forces have significant role in the stability of the system.