Closed form Models for Pull-In Voltage of Electrostatically Actuated Cantilever Beams and Comparative Analysis of Cantilevers and Microgripper

Pull-in voltage Evaluation is significant for the design of electrostatically actuated MEMS devices. In this work simple closed form models are derived for computation of pull-in voltage of cantilever beams. These models are obtained based on five different capacitance models suitable for wide range of dimensions. Using these models pull-in voltages are computed for a range of dimensions and the results are compared with the experimentally verified 3D finite element analysis results. The results show that, for every given range of dimension, choice of the model changes for the evaluation of the pull-in voltage with a maximum deviation of 2%. Therefore for a given range of dimension appropriate closed form model is to be chosen for accurate computation of pull-in voltage. Computation of pull-in voltage of microgripper further validates the closed form models. The results again show that for a given range of dimension only a particular model evaluates the pull-in voltage with less error.