Input and Design Optimization Under Uncertainty to Minimize the Impact Velocity of an Electrostatically Actuated MEMS Switch

Abstract

The dynamic response of a radio-frequency (RF) microelectromechanical system to a time-varying electrostatic force is optimized to enhance robustness to variations in material properties and geometry. The device functions as an electrical switch, where an applied voltage is used to close a circuit. The objective is to minimize the severity of the mechanical impact that occurs each time the switch closes because severe impacts have been found to significantly decrease the life of these switches. Previous works have demonstrated that a classical vibro-impact model, a single-degree-of-freedom oscillator subject to mechanical impact with a single rigid barrier, captures the relevant physics adequately. Certain model parameters are described as random variables to represent the significant unit-to-unit variability observed during fabrication and testing of a collection of nominally identical switches; these models for unit-to-unit variability are calibrated to available experimental data. Our objective is to design the shape and duration of the voltage waveform so that impact kinetic energy at switch closure is minimized for the collection of nominally identical switches, subject to design constraints. A voltage waveform designed using a deterministic model for the RF switch is found to perform poorly on the ensemble. An alternative waveform is generated using the proposed optimization procedure with a probabilistic model and is found to decrease the maximum impact velocity by a factor of 2 relative to the waveform designed deterministically. The methodology is also applied to evaluate a design change that reduces the impact velocity further and to predict the effect of fabrication process improvements.