Analytical and FEM Pull-in Study on Rigid and Deformable Electrostatic Micro Actuators

A general theory and method are presented and employed to analyze the static behaviors of rigid and deformable electrostatic actuator systems with various electrode configurations. This method utilizes capacitance-based generalized equations and provides an easy and time-saving platform over complicated coupled finite element method (FEM) simulations for pull-in analysis of a complex system. Analytical results show that the travel range of rigid electrostatic actuators can be extended by manipulating the shape of the electrode. Even a full travel range (100%) can be realized by a general power function shaped electrode. It is found that the partial actuation can avoid pull-in and reach full travel ranges with the sacrifice of the bias voltage. Analytical results of cantilever rectangular and circular actuators with a partial electrode are in good agreement with simulation results. Actuation curves of various actuators are also derived using this method. It is found that partial actuation curves are exactly the same as full actuation curves, and all types of cantilever torsion actuators with various electrode shapes follow the same actuation curve. Analytical and FEM simulations are carried out to study the pull-in behavior of deformable electrostatic actuators of three electrode configurations. The analytical results agree with FEM simulation results. It is found that the normalized deformation curves of these three electrode configurations are independent of geometry and voltage. The fringing field is considered in this analytical method