A new analytical model for the pull-in voltage of clamped diaphragms subject to electrostatic force

A simple, easy-to-use, new closed-form model to evaluate the pull-in voltage associated with a rigidly clamped square or circular diaphragm subject to electrostatic force has been developed. The approach is based on a linearized uniform approximation model of the nonlinear electrostatic pressure due to a bias voltage and a 2-D load-deflection model of a square or circular diaphragm under uniform pressure. The spring softening effect associated with the nonlinear characteristics of the electrostatic force developed by the bias voltage and the spring hardening effect associated with nonlinear stretching of the central region of a uniformly loaded fully clamped diaphragm with residual stress are both considered. The method allows for a more accurate determination of the developed electrostatic pressure, maximum diaphragm deflection and the pull-in voltage. The model has been verified by three-dimensional electromechanical finite element analysis and also by comparing the results with published experimental results of similar structures. The models lead to an integrated design strategy to optimize the electrical and mechanical design variables for MEMS-based capacitive-type sensors having square or circular diaphragms.