A Weakest Link Failure Model of Polycrystalline MEMS Structures

Abstract

MEMS devices typically need to be designed against a very low failure probability, which is beyond the capacity of histogram testing. Therefore, the understanding of the probabilistic failure of MEMS devices is crucial for the design process. Currently available probabilistic models for predicting the strength statistics of MEMS structures are based on classical Weibull statistics. Significant advances in experimental techniques for measuring the strength of MEMS devices have produced data that have unambiguously demonstrated the inadequacy of the Weibull distribution. This paper presents a robust probabilistic model for the strength distribution of polycrystalline silicon (poly-Si) MEMS structures. The overall failure probability of the structure is related to the failure probability of each material element along its sidewalls through a weakest-link statistical model. The failure statistics of the material element is determined by both the intrinsic random material strength and the random stress field induced by the sidewall geometry. Different from the classical Weibull statistics, the present model accounts for structures consisting of a finite number of material elements, and it predicts an intricate scale effect on their failure statistics. It is shown that the model agrees well with the measured strength distributions of poly-Si MEMS specimens of different sizes. The present model also explicitly relates the strength distribution to the size effect on the mean structural strength, and therefore provides an efficient means of determining the failure statistics of MEMS structures.