Modeling Effects of Three Nano-scale Physical Phenomena on Instability Voltage of Multi-layer MEMS/NEMS: Material Size Dependency, van der Waals Force and Non-classic Support Conditions

摘要

Although many microano-electromechanical systems (MEMS/NEMS) are implemented by multi-layer components, only few researchers have modeled the instability of these multi-layer structures. Herein, the electrostatic instability of multi-layer MEMS/NEMS is modeled using a non-classic continuum mechanics theory. Three nano-scale physical phenomena which highly affect the pull-in performance of MEMS/NEMS including size dependency, van der Waals force and non-classic support conditions have been considered in the model for the first time. The modified couple stress theory is applied to examine the size effect on the instability of the MEMS/NEMS at submicron separations. The proposed model takes non-classic boundary conditions into account using translational and rotational springs at supported end of the MEMS/NEMS. In order to solve the constitutive equation of the MEMS/NEMS, modified Adomian decomposition method is employed as well as lumped parameter model and numerical method. The obtained analytical solution is more accurate than lumped model and agrees well with numerical one. The results reveal significant influence of the size dependency, elastic boundary condition and van der Waals attraction on the pull-in characteristics of MEMS/NEMS.