Lateral pull-in instability of electrostatic MEMS transducers employing repulsive force

We report on the lateral pull-in in capacitive MEMS transducers that employ a repulsive electrostatic force. The moving element in this system undergoes motion in two dimensions. A two degree-of-freedom mathematical model is developed to investigate the pull-in quantitatively. The nonlinear electrostatic force, which is a vector function of two spatial coordinates, is determined by calculating the potential energy of the system using a boundary element approach. The equilibrium points are found by numerically solving the nonlinear coupled static equations. A stability analysis reveals that depending on the values of the lateral and transverse stiffness, the system undergoes different bifurcations when the voltage on the side electrodes is considered as the control parameter. Three-dimensional bifurcation diagrams are presented and discussed to elucidate the nonlinear nature of the system. The results establish important criteria for designing MEMS transducers with reliable and robust performance.