A Multiscale Reliability Model for Brittle MEMS Materials and Structures

微机电系统（MEMS）器件广泛应用于汽车、生物医学、航空航天、能源和通信行业。为了确保系统可靠性，期望针对非常低的故障概率（大约0.0001或更低）来设计MEMS器件。对于如此低的失效概率，目标强度的纯实验测定需要测试数万个试样，这是一项成本高昂的工作。因此，对脆性和准脆性固体在小尺度下的概率破坏有一个基本的了解是至关重要的。该奖项支持基础研究，以开发一种新的基于力学的概率模型，用于理解小尺度下的故障统计。该模型是基于原子尺度的材料失效机制。它将使小规模结构的可靠性的准确测定，而不需要测试大量的样本。这项研究的成果将为小特征尺寸系统的故障概率提供基础知识，并将影响MEMS器件可靠性设计和制造的工程实践。计划与高中生、本科生和研究生的教育活动紧密结合。教育计划包括参加高中暑期方案，招收女研究生和少数民族研究生，在主要会议上组织讲习班和专题讨论会，以及开发新的本科生和研究生课程。经典威布尔分布是基于极值统计的假设。该假设不适用于与MEMS器件相关的尺度，其中与特征结构尺寸相比，晶粒尺寸不可忽略。在本研究中，连续非局部有限最弱环节模型将代表小规模结构的故障统计。该模型将预测试样尺寸和几何形状对强度分布和平均强度的影响。使用准连续方法模拟原子尺度损伤将确定模型统计参数，考虑随机晶粒尺寸、几何形状和取向。 利用准连续介质方法，可以实现原子区域和连续区域之间的无缝耦合。该模型将通过使用松弛链测试配置对多晶硅试样进行广泛的强度直方图测试来验证。基于该模型，平均强度的尺寸效应曲线将与强度分布明确相关。这一关系为脆性和准脆性小尺度结构的可靠性分析提供了一种新的实验方法。这种方法有望比传统的直方图测试更有效和准确。

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.