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

Ratsch/Margetis/Gibou1412392/1412769/1412695 外延生长是一种材料沉积在另一种材料上的过程。 它具有基本的技术重要性，因为许多现代光电器件都是通过这种工艺制造的。 重要的例子包括微电子学中的晶体管、光子晶体激光器的量子点、能源领域基于量子点的产品增强以及非易失性存储介质，这些介质正在寻求取代硬盘、闪存和RAM存储器。 其他应用包括，例如，催化剂（加速化学反应），通常依赖于金属外延。 催化剂用于能源部门，食品加工，环境科学和其他地方;一个众所周知的例子是用于车辆排放控制的催化转化器。 这个合作项目的研究人员开发的模型，导致外延生长更好，更根本的理解。 结果的工作是感兴趣的不仅数学家，而且物理学家，材料科学家和工程师，和医学科学家的问题的数学结果适用。 三名研究生被包括在这个跨学科的项目。 该项目的目标是开发分析和计算工具，以无缝和有效地连接外延的几个长度和时间尺度。 这些工具包括渐近方法，用于将原子模型与中尺度现象联系起来，以及在并行计算环境中自适应四叉树/八叉树网格上的有效数值方法，以模拟大型材料系统。 研究人员设计并实现了一个层次的增长模型，结合联合收割机原子主方程的背景下，动力学的固体对固体模型，密度泛函理论（DFT），偏微分方程为基础的岛屿动力学增长模型，和一个有效的计划来解决弹性方程，包括弹性应变。 这种合作努力提供了解决长期存在的关于动力学和热力学效应在形成晶体结构（如土丘和量子点）中所起作用的争议的方法。 三名研究生被包括在这个跨学科的项目。

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.