A Novel Closed-Form Expression Obtained by Using Differential Evolution Algorithm to Calculate Pull-In Voltage of MEMS Cantilever

In this paper, a novel, computationally efficient, and simple closed-form expression has been derived to accurately calculate the pull-in voltage value of microelectromechanical system (MEMS) cantilever. At first, MEMSs actuators with various physical parameters have been simulated by a software that employs the finite element method, and then, the pull-in voltage expression has been derived by using the differential evolution optimization algorithm together with the simulation data. Since the formula is derived from the simulation data, it implicitly contains the fringing field effect. In order to verify the accuracy and robustness, the predictions of closed-form formula proposed in this paper have been compared with those of the theoretical ones through the simulation and experimental studies previously presented in the literature. The key advantage of the presented model is delivering a satisfying estimation of the pull-in voltage in a simple fashion.