A New Analytical Model to Estimate the Voltage Value and Position of the Pull-In Limit of a MEMS Cantilever

In this study, a new analytical model is developed for an electrostatic Microelectromechanical System (MEMS) cantilever actuator to establish a relation between the displacement of its tip and the applied voltage. The proposed model defines the micro-cantilever as a rigid beam supported by a hinge at the fixed-end with a spring point force balancing the structure. The approach of the model is based on calculation of the electrostatic pressure centroid on the cantilever beam to localize the equivalent electrostatic point load. Principle outcome of the model is just one formula valid for all displacements ranging from the initial to the pull-in limit position. Our model also shows that the pull-in limit position of a cantilever is approximately 44% of the initial gap. This result agrees well with both simulation results and experimental measurements reported previously. The formula has been validated by comparing the results with former empirical studies. For displacements close to the pull-in limit, the percentage errors of the formula are within 1% when compared with real measurements carried out by previous studies. The formula also gives close results (less than 4%) when compared to simulation outcomes obtained by finite element analysis. In addition, the proposed formula measures up to numerical solutions obtained from several distributed models which demand recursive solutions in structural and electrostatic domains.