Nonlinear cc-beam microresonator model for system level electrical simulations: Application to bistable behavior analysis

Microelectromechanical resonators nonlinearities can be exploited in many ways to obtain a set of diverse new applications. In particular, some applications of bistable behavior includes threshold mechanical switches, memory cells, energy harvesting and chaotic signal generators. A key step for practical and efficient design for bistability behavior involves accounting for accurate and efficient models. In this paper we present a nonlinear electromechanical model for capacitive clamped-clamped beam resonators implemented in an analog hardware description language (AHDL) enabling system level electrical simulations. The model accounts for nonlinearities from variable resonator-electrode gap, residual fabrication stress, fringing field contributions as well as an accurate resonator deflection profile in contrast to parallel plate approximations. The model has been applied to derive for first time accurate analytical expressions for bistability design conditions. The work includes FEM analysis and experimental data that corroborates the correctness of the model in describing the required bias voltage conditions for bistability.