A Probabilistic Model for Failure of Polycrystaline Silicon MEMS Structures

Abstract

Reliable MEMS devices are expected to have a very low failure probability, and thus it is cost-prohibitive to determine design strength values merely based on extensive histogram testings. A theoretical understanding of probabilistic failure in the structure is critical for reliability analysis of MEMS devices. Prediction of failure statistics for MEMS structures are commonly based on the classical Weibull's model for material strength, which has been experimentally proven to be incapable of optimally fitting the failure probability distribution of MEMS structures. A generalized finite weakest-link model is developed to describe the strength statistics of polycrystalline silicon (poly-Si) MEMS structures. Different from the classical Weibull statistics based on extreme value statistics, the present model is applicable for poly-Si structures of all sizes. 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. For each material element, the failure statistics is determined by both the random material strength and stress field induced by random sidewall geometry. The model is shown to agree well with measured strength histograms of poly-Si MEMS specimens of different sizes, and the calibrated mean strength of the material element is in accordance with theoretical strength of silicon. The strength statistics is further related to the effects of structure size on the mean structural strength, and an efficient method to determine the failure statistics of MEMS structures is proposed based on the present model.