Microstructural Modeling and Probabilistic Prediction of Micro-Electro-Mechanical Systems Response (REU Supplement)

这是一个研究项目，旨在更好地了解在制造微电子机械系统(MEMS)中使用的材料和结构元件(梁、板、膜)的行为，根据材料表现出的微观结构，目的是评估这种系统的性能可靠性。有效的(整体)物理性能，主要是弹性和强度，相关的结构响应将在认识到存在许多微结构效应的情况下进行评估，这些微结构效应在与MEMS相关的长度尺度上是重要的，但在较大长度尺度上是不重要的。这些包括材料内的微晶的典型线性尺寸与膜的厚度相同的数量级，颗粒大小和形状的明显的贯穿厚度的变化，颗粒(织构)的大量排列导致响应的各向异性，以及用于制造MEMS的过程中产生的大量残余应力。这种影响可能会阻碍经典理论在结构构件中的直接应用，因此有必要发展新的理论。此外，微结构固有的可变性强烈依赖于工艺条件，这就要求对材料行为进行概率描述和结构响应评估，目的是评估MEMS的性能可靠性。为此，本研究将致力于：(1)材料强度和有效性能的数学建模；(2)微结构对MEMS结构响应的影响；(3)基于随机有限元方法的MEMS可靠性分析。

This is a research project aimed at developing an improved understanding of the behavior of materials and structural elements (beams, plates, membranes) employed in the manufacture of micro-electro-mechanical systems (MEMS), on the basis of the microstructure exhibited by the materials, with the goal of assessing the performance reliability of such systems. Effective (overall) physical properties, primarily elasticity and strength, and the associated structural response will be evaluated with the recognition that there are a number of microstructural effects that are important at the length scales associated with MEMS but which are unimportant at larger length scales. These include the typical linear dimension of a crystallite within the material being on the same order of magnitude as the thickness of the film, substantial through-thickness variations in grain size and shape, the presence of considerable alignment of the grains (texture) leading to anisotropy of response, and large levels of residual stress arising form the processes used to create may MEMS. Such effects may preclude direct application of classical theories for structural elements, thus necessitating the development of new theories. Furthermore, the variability inherent in the microstructure, which depends strongly on the process conditions, requires a probabilistic description of the material behavior and structural response evaluation aimed at assessing the performance reliability of MEMS. To this end, this research will address: (1) mathematical modeling of material strength and effective properties, (2) influence of microstructure on the structural response of MEMS, and (3) reliability analysis of MEMS using stochastic finite-element methods.