Experiments have shown that the failure loads of Microelectromechanical Systems (MEMS) devices usually exhibit a considerable level of variability, which is believed to be caused by the random material strength and the geometry-induced random stress field. Understanding the strength statistics of MEMS devices is of paramount importance for the device design guarding against a tolerable failure risk. In this study, we develop a continuum-based probabilistic model for polycrystalline silicon (poly-Si) MEMS structures within the framework of first passage analysis. The failure of poly-Si MEMS structures is considered to be triggered by fracture initiation from the sidewalls governed by a nonlocal failure criterion. The model takes into account an autocorrelated random field of material tensile strength. The nonlocal random stress field is obtained by stochastic finite element simulations based on the information of the uncertainties of the sidewall geometry. The model is formulated within the contexts of both stationary and non-stationary stochastic processes for MEMS structures of various geometries and under different loading configurations. It is shown that the model agrees well with the experimentally measured strength distributions of uniaxial tensile poly-Si MEMS specimens of different gauge lengths. The model is further used to predict the strength distribution of poly-Si MEMS beams under three-point bending, and the result is compared with the Monte Carlo simulation. The present model predicts strong size effects on both the strength distribution and the mean structural strength. It is shown that the mean size effect curve consists of three power-law asymptotes in the small, intermediate, and large-size regimes. By matching these three asymptotes, an approximate size effect equation is proposed. 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 used in the weakest-link model.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support under Grant NSF/CMMI-1361868 to the University of Minnesota from the U.S. National Science Foundation .
- Asymptotic analysis
- Size effect
- Stochastic process
- Structural reliability
- Weakest-link model