Modeling and Input Optimization Under Uncertainty for a Collection of RF MEMS Devices

Abstract

The dynamic response of an RF MEMS device 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 design life of these switches. The switch is modeled as a classical vibro-impact system: a single degree-of-freedom oscillator subject to mechanical impact with a single rigid barrier. Certain model parameters are described as random variables to represent the significant unit-to-unit variability observed during fabrication and testing of the 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 velocity at switch closure for the collection of nominally-identical switches is minimized subject to design constraints. The methodology is also applied to search for design changes that reduce the impact velocity and to predict the effect of fabrication process improvements.