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

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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.