SGER: Green's Function-Based Multiscale Modeling of the Micro- and Nanomechanics of Defects in Multilayer Heterostructures

该SGER项目旨在开发精细的多尺度模型以及缺陷的连续模型技术，并研究多层异质结构中的缺陷行为。多层异质结构是许多先进电子/光电器件的基础结构，也被用于防护涂层、热障和防弹衣。在这种材料非均匀、高深宽比和缺陷奇异性的结构中，应力和缺陷核的三维分析给计算科学界和工程界带来了巨大的挑战。该项目采用格林函数(Green‘s Function，简称GF)方法来解决多层异质结构建模的困难，将平面层特征分层地包含在可在连续介质水平上半解析求解的参考GF中。在此多层矩阵的基础上，引入缺陷。这样，多层异质结中的缺陷问题就简化为只对局域缺陷进行数值处理。在连续介质GF(CGF)的基础上，实现了多层异质结在长波极限下对CGF的渐近逼近，得到了多层异质结构的晶格GF(LGF)。LGF和CGF的结合为有效和准确地解决多层异质结中的缺陷问题提供了一个强大的数学工具。在迭代格式中考虑了缺陷中心的非线性效应。这个项目将建立一个强大的计算工具，可以导致对连续和晶格尺度上以及两者之间的缺陷力学和动力学的深刻理解。这将建立一个用于预测缺陷行为的框架，该框架可用于预测器件的使用寿命，定制具有所需纳米结构的新型材料，并用于防止可以改善器件性能的缺陷问题。这项研究的结果将被纳入并将影响到PI一直在教授的计算力学课程以及他一直在开发的微/纳米力学课程。它将特别向学生介绍新颖的计算工具(即多尺度建模)，并总体上吸引他们对新兴纳米技术的兴趣。该研究项目将涉及一名研究生，他将接受应用力学、材料科学和固体物理这一多学科领域的培训。因此，该项目有助于实现国家科学基金会在培养新一代有能力的工人方面的目标，这些工人拥有在新兴纳米技术方面快速发展所需的知识和技能。此外，PI将通过这个项目与NIST的科学家密切合作。他将把开发的具有用户友好界面的计算机代码张贴在美国国家科学基金会/美国国家科学技术研究院绿色功能数字图书馆的网站上：http://www.ctcms.nist.gov/gf/，供公众访问。这将扩大该项目的更广泛影响，以增强美国行业的实力，并促进研究学会使用基于GF的计算工具。

This SGER project aims to develop elegant multiscale modeling as well as continuum modeling techniques of defects and to investigate defect behaviors in multilayer heterostructures. Multilayer heterostructures are used as the base structure in many advanced electronic/optoelectronic devices as well as used for protective coating, thermal barrier and body armor. A three-dimensional analysis of stress and defect cores in such a structure of material heterogeneity, high aspect ratio and defect singularities poses a great challenge to the community of computational sciences and engineering. This project takes a Green's function (GF) approach to attack the difficulty of modeling multilayer heterostructures by hierarchically including the planar-layer feature in the reference GF that can be solved semi-analytically on the continuum level. Based on this multilayer matrix, defects are introduced. In this way, the problem of defects in multilayer heterostructures is reduced to numerically treating only the localized defects. Furthermore, the lattice GF (LGF) of multilayer heterostructures is derived based on the continuum GF (CGF) by realizing the asymptotic approach of the former to the latter at the long-wavelength limit. The LGF and CGF in combination facilitate a powerful mathematical tool for efficient and accurate solution of defect problems in multilayer heterostructures. Nonlinear effect in the core of a defect is taken into consideration in an iterative scheme. This project will establish a powerful computational tool that can lead to a profound understanding of the defect mechanics and dynamics on both continuum and lattice scales and in between. This will establish a framework for prediction of defect behaviors that can be used to predict service lives of devices and to tailor-make novel materials with desired nanostructures, and for prevention of defect problems that can improve device performances. The results of the research will be incorporated in and will impact the Computational Mechanics courses that the PI has been teaching and the micro/nanomechanics courses that he has been developing. It will introduce the students to the novel computational tools (i.e., multiscale modeling) in particular and draw their interest in the emerging nanotechnology in general. The research project will involve a graduate student, who will be trained in this multidisciplinary field of Applied Mechanics, Materials Science, and Solid State Physics. Thus, the project contributes to the NSF goal in development of a new generation of capable workers who have knowledge and skills necessary for rapid progress in the emerging nanotechnology. Furthermore, the PI will closely collaborate with scientists at NIST through this project. He will post developed computer codes with user-friendly interface on the NSF/NIST Digital Library of Green's Functions website: http://www.ctcms.nist.gov/gf/ for public access. This will expand the broader impact of this project to enhance the strength of the US industry and to promote the use of GF-based computational tools in the research society.