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

外延生长是一种材料沉积在另一种材料上的过程。它具有重要的基础技术意义，因为许多现代光电器件都是用这种工艺制造的。重要的例子包括微电子领域的晶体管、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，以及旨在取代硬盘驱动器、闪存和RAM存储器的非易失性存储介质。其他应用包括，例如催化剂（加速化学反应），这通常依赖于金属外延。催化用于能源部门、食品加工、环境科学和其他领域；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，导致一个更好的和更基本的理解外延生长。这项工作的结果不仅引起数学家的兴趣，而且引起物理学家、材料科学家、工程师和医学科学家的兴趣，因为数学结果适用于他们的问题。这个跨学科项目包括三名研究生。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中的几个长度和时间尺度。这些工具包括将原子模型与中尺度现象联系起来的渐近方法，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，以实现对大型材料系统的模拟。研究人员设计并实现了一个层次增长模型，该模型结合了动力学实体模型中的原子主方程、密度泛函理论（DFT）、基于偏微分方程的岛屿动力学增长模型，以及求解弹性方程（包括弹性应变）的有效方案。这一合作努力提供了解决长期以来关于动力学和热力学效应在丘和量子点（QDs）等晶体结构形成中所起作用的争议的手段。这个跨学科项目包括三名研究生。

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.