An improved two-dimensional coupled electrostatic-mechanical model for RF MEMS switches

Abstract

An improved two-dimensional (2D) coupled electrostatic-mechanical model for RF-MEMS shunt-capacitive switches is presented, where both axial and residual stresses in the bridge of the switch are considered. The electrostatic model is based on solving Laplace's equation in the different homogenous regions using the finite difference method (FDM), while Gauss's law is employed at the interface nodes between the different media. The mechanical model is based on solving the beam equation using the FDM, where the quadratic interpolation is used to approximate the derivatives. The interaction between the mechanical and electrostatic models is considered iteratively. The coupled model results in an accurate determination of the capacitance of the switch, the induced charges and forces on the membrane, and the beam deformation in terms of the biasing voltage. The pull-down voltage is also calculated for different structures and agrees well with the published data. The presented model gives accurate results in a quite short CPU time.