Uncertainty Quantification of Pull-In Phenomenon in Capacitive Rf-Mems

The goal of this paper is to elucidate the effects of device geometry and fabrication process variations on the statistical pull-in performance of an electrostatically-actuated capacitive radio frequency micro electro-mechanical system (RF-MEMS) switch through the use of uncertainty quantification. The prediction of switch dynamics and pull-in voltage involves the coupled interaction of elastodynamics, fluid dynamics, and electrostatics. A comprehensive computational framework based on the finite volume method (FVM) is developed to account for these effects. The immersed boundary method (IBM) is employed to couple the fluid, structure and electrostatics. A population of switches is fabricated, and geometry and material properties measured; these measurements provide the probabilistic input information needed for uncertainty quantification. Deterministic simulations are first made for a specific device, and the gap-versus-voltage and pull-in voltage predicted compare favorably with measurements and theoretical estimation. Uncertainty quantification of dynamic pull-in is performed next, using the stochastic collocation method for uncertainty propagation. Probability density functions (PDFs) of pull-in voltage and gap-versus-time are computed. The primary determinants of uncertainty in pull-in voltage are found to be the membrane thickness and gap size, with uncertainty in residual stress having a relatively small effect.