Collaborative Research: Modeling and simulation of out-of-equilibrium processes in Epitaxy

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Ratsch/Margetis/Gibou1412392/1412769/1412695 Epitaxial growth is a process in which one material is deposited on top of another. It is of fundamental technological importance, as many modern opto-electronic devices are fabricated by this process. Important examples include transistors in microelectronics, quantum dots for photonic crystal lasers, quantum dot-based product enhancements in the energy sector, and nonvolatile storage media, which are sought to replace hard drives, flash memories, and RAM memories. Other applications include, for example, catalysts (speeding up chemical reactions), which often rely on metal epitaxy. Catalysis is used in the energy sector, in food processing, in environmental science, and elsewhere; a well-known example is the catalytic converter for vehicle emissions control. The investigators of this collaborative project develop models that lead to a better and more fundamental understanding of epitaxial growth. Results of the work are of interest not only to mathematicians but also to physicists, material scientists and engineers, and medical scientists to whose problems the mathematical results apply. Three graduate students are included in this interdisciplinary project. The goal of the project is to develop analytical and computational tools to seamlessly and efficiently connect several length and time scales in epitaxy. These tools encompass asymptotic methods for linking atomistic models to mesoscale phenomena as well as efficient numerical methods on adaptive quadtree/octree grids in a parallel computing environment to enable the simulation of large material systems. The investigators design and implement a hierarchy of growth models that combine atomistic master equations in the context of kinetic solid-on-solid models, density-functional theory (DFT), a partial differential equation-based island dynamics growth model, and an efficient scheme to solve the elastic equations to include elastic strain. This collaborative effort provides the means to address a long-standing controversy about the role played by kinetic and thermodynamics effects in the formation of crystal structures such as mounds and quantum dots (QDs). Three graduate students are included in this interdisciplinary project.