Stochastic Analysis of Electrostatic MEMS Subjected to Parameter Variations

This paper presents an efficient stochastic framework for quantifying the effect of stochastic variations in various design parameters such as material properties, geometrical features, and/or operating conditions on the performance of electrostatic microelectromechanical systems (MEMS) devices. The stochastic framework treats uncertainty as a separate dimension, in addition to space and time, and seeks to approximate the stochastic dependent variables using sparse grid interpolation in the multidimensional random space. This approach can be effectively used to compute important information, such as moments (mean and variance), failure probabilities, and sensitivities with respect to design variables, regarding relevant quantities of interest. The approach is straightforward to implement and, depending on the accuracy required, can be orders of magnitude faster than the traditional Monte Carlo method. We consider two examples-MEMS switch and resonator-and employ the proposed approach to study the effect of uncertain Young's modulus and various geometrical parameters, such as dimensions of electrodes and gap between microstructures, on relevant quantities of interest such as actuation behavior, resonant frequency, and quality factor. It is demonstrated that, in addition to computing the required statistics and probability density function, the proposed approach effectively identifies critical design parameters, which can then be controlled during fabrication, in order to improve device performance and reliability.