FRG: Collaborative Research: Modeling and Computation of Crystalline Nanostructures

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This project is aimed at advancing the state of the art for simulating nanocrystalline materials. A common technique to manufacture such materials is depositing a monocrystalline film on a monocrystalline substrate of a different composition (heteroepitaxy); in the process elastic interactions are very important. The project will develop highly efficient computational tools by combining continuum mechanics to handle long-range elastic interactions with kinetic Monte Carlo (KMC) simulations that can accurately describe transport kinetics at the atomic level. The methods developed will be broadly applicable, but the immediate focus is on quantum dot nano-structures. Three different approaches will be used to accomplish this task. One of these will use KMC to deduce various parameters used in continuum models. Another approach will be based on a new formulation of KMC which can be shown, using statistical mechanics, to be connected with the chemical potential. This will allow a fairly seamless connection between our KMC formulation and continuum mechanics. We can exploit this connection to use KMC on small, well separated regions and then combine these regions together using macroscopic variables, such as atomic flux and elastic displacement fields. Another approach is to perform KMC everywhere but using coarse-grained continuum fields that are updated on a macroscopic time scale.Nanocrystalline materials have shown great promise for many applications such as solid state lasers, memory devices, and photovoltaic cells. It is anticipated that the modeling and computation methods developed in this research will pave the way for performing device level simulations and provide valuable guidance in the interpretation of experimental measurements for strained alloy systems. Our group has close ties with experimental groups based in the semiconductor industry and academia, which will allow us to assess our modeling progress.