First passage based modeling of probabilistic failure of polycrystalline silicon MEMS structures

This study presents a first passage based analysis of probabilistic failure of polycrystalline silicon (poly-Si) MEMS structures. The model takes into account both the autocorrelated random strength field and the random stress field. The model is formulated based on the concepts of stationary and non-stationary stochastic processes. It is shown that the model agrees well with the measured strength distributions of uniaxial tensile poly-Si MEMS specimens of different sizes. The present model predicts strong size effects on both the strength distribution and the mean structural strength. An approximate mean size effect equation is developed based on asymptotic matching. The present model is shown to be a generalization of the classical weakest-link statistical model, and it provides a physical interpretation of the material length scale of the weakest-link model.