Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS

Dynamic analysis of microelectromechanical systems (MEMS) is characterized by the nonlinear coupling of electrical and mechanical domains. The nonlinear coupling between the two domains gives rise to several interesting dynamic phenomena besides the well established pull-in phenomenon in electrostatic MEMS. For proper understanding and detailed exploration of MEMS dynamics, it is important to have a reliable and efficient physical level simulation method. In this paper, we develop relaxation and Newton schemes based on a Lagrangian description of both the mechanical and the electrical domains for the analysis of MEMS dynamics. The application of a Lagrangian description for both mechanical and electrostatic analysis makes this method far more efficient than standard semi-Lagrangian scheme-based analysis of MEMS dynamics. A major advantage of the full-Lagrangian scheme is in the accurate computation of the interdomain coupling term (mechanical to electrical) in the Jacobian matrix of the Newton scheme which is not possible with a semi-Lagrangian scheme. The full-Lagrangian based relaxation and Newton schemes have been validated by comparing simulation results with published data for cantilever and fixed-fixed MEM beams. The Newton scheme has been used for the dynamic analysis of two classes of comb-drives widely used in MEMS, namely, transverse and lateral comb-drives. Several interesting MEM dynamic phenomena and their possible applications have been presented. Spring-hardening and softening of MEM devices has been shown. The existence of multiple resonant peaks in MEM devices has been analyzed under different electrical signals and their possible applications in multiband/passband MEM filters/oscillators is discussed. Switching speed is a serious constraint for capacitive based RF-MEM switches. We have shown that a DC bias along with an ac bias at the resonant frequency can give very fast switching at a considerably less peak power requirement.