Uncertainty in microscale gas damping: Implications on dynamics of capacitive MEMS switches

Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150 V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness.