Micro-electro-mechanical systems (MEMS) devices find wide used in the automotive, biomedical, aerospace, energy and communication industries. To ensure system reliability, it is desirable to design MEMS devices against a very low failure probability, on the order of 0.0001 or lower. The pure experimental determination of the target strength for such a low failure probability requires the testing of tens of thousands of specimens, a cost-prohibitive effort. Therefore, a fundamental understanding of the probabilistic failure of brittle and quasi-brittle solids at small length-scales is of paramount importance. This award supports fundamental research to develop a new mechanics-based probabilistic model for understanding the failure statistics at small scales. The model is based on material failure mechanisms at the atomistic scale. It will enable the accurate determination of the reliability of small-scale structures without the need to test a large number of specimens. The output of this research will create fundamental knowledge on the probability of failure for systems with small characteristic dimensions and will impact engineering practice in reliability-based design and manufacturing of MEMS devices. A tight integration with educational activities for high-school students, undergraduate students and graduate students is planned. The educational plan includes participation in the high-school summer program, recruitment of female and minority research students, organizing workshops and symposiums at major conferences and development of new undergraduate and graduate courses.
Classical Weibull distributions are based on the assumption of extreme-value statistics. This assumption is not applicable at the scales relevant to MEMS devices where the grain size is not negligible compared to the characteristic structural dimensions. In this research, a continuum nonlocal finite weakest link model will represent the failure statistics of small-scale structures. This model will predict the effects of specimen size and geometry on the strength distribution and mean strength. Simulations of atomic-scale damage using a quasi-continuum method will determine the model statistical parameters, accounting for random grain size, geometry and orientation. With the quasi-continuum method a seamless coupling between atomistic and continuum regions is enabled. The model will be validated by extensive strength histogram testing on polycrystalline silicon specimens using a slack-chain test configuration. Based on this model, the size effect curve of mean strength will be explicitly related to the strength distribution. This relationship will represent a new experimental method for the reliability analysis of brittle and quasi-brittle structures at small length scales. This approach is expected to be far more efficient and accurate than conventional histogram testing.
