The Effect of Squeeze-Film Damping on the Step Response of Electrostatic Micro-Actuators

In this paper we study the response to a step-function actuation of variously shaped parallel plates electrostatic MEMS actuators subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. We conclude that mass inertial effects are negligible and that switching times are governed by pressure equilibration through ambient gas diffusion into the squeeze film gap. We then introduce a new lumped model which is derived by applying an effective viscosity correction in the Reynolds equation solution and coupling the corresponding squeeze-film force to the electro-mechanics of the device. The model's simple formula enables to obtain rapid and sufficiently precise switching time estimates for various actuation conditions including ambient pressure level and initial gap size. Utilizing the dimensionless gas diffusion rate of the model, we introduce a new and unique method for calibrating the effective viscosity correction function for various gases and surfaces by directly measuring the dynamic response of parallel plates electrostatic MEMS actuators to a step-function actuation. Lastly, the model predictions are compared to numerical simulations and experiments in the transition and free molecular flow regimes, with Knudsen numbers in the 1 - 50 range.