Study of the pull-in voltage for MEMS parallel plate capacitor actuators

Abstract

This paper provides new investigation for the static and dynamic behavior of a MEMS parallel plate capacitor derived by analytical and numerical design modeling programs developed in Matlab. One significant finding is about the role, which has so far overlooked in many analyses, of a dielectric layer normally placed on top of the ground electrode to avoid short circuiting risks. It is demonstrated in this paper that this layer produces an increased force between electrodes that in turns decreases the well-known pull-in voltage, V pi, as compared to the one calculated when this dielectric layer is not considered on the system's static analysis. Expressions for the static V pi and its corresponding maximum stable electrode swing x pi are derived to take the above effect into account. The system dynamic analysis is done with a user-friendly Simulink interface constructed to allow easy introduction of capacitor design dimensions, material parameter values and voltage signal stimuli. The impact of any combination of these parameters on the electro-mechanical system behavior, that is, the voltage-electrode position dependence data can be easily extracted and become of help for design decision making on the early design stages of this type of structures. This modeling tool interface is based on solving the full differential equation that describes the free electrode displacement without relying on linearizing the inverse quadratic electrode separation dependence of the electro-static force term. This approach intrinsically takes into account the voltage dependant k-spring softening effect derived precisely from a linearizing simplification. Finally, by applying a saw-tooth voltage waveform, the dynamic pull-in voltage and the maximum stable electrode travel range are observed to go well beyond the predicted static pull-in voltage and travel range values.