Uncertainty quantification of MEMS devices with correlated random parameters

Abstract

The concern about process deviations rises because that the performance uncertainty they cause are strengthened with the miniaturization and complication of Microelectromechanical System (MEMS) devices. To predict the statistic behavior of devices, Monte Carlo method is widely used, but it is limited by the low efficiency. The recently emerged generalized polynomial chaos expansion method, though highly efficient, cannot solve uncertainty quantification problems with correlated deviations, which is common in MEMS applications. In this paper, a Gaussian mixture model (GMM) and Nataf transformation based polynomial chaos method is proposed. The distribution of correlated process deviations is estimated using GMM, and modified Nataf transformation is applied to convert the correlated random vectors of GMM into mutually independent ones. Then polynomial chaos expansion and stochastic collection can be implemented. The effectiveness of our proposed method is demonstrated by the simulation results of V-beam thermal actuator, and its computation speed is faster compared with the Monte Carlo technique without loss of accuracy. This method can be served as an efficient analysis technique for MEMS devices which are sensitive to correlated process deviations.