Kinetic Monte Carlo Methods for Epitaxial Growth

本建议适用于材料科学的计算方法，特别是薄膜外延生长的原子模型的蒙特卡罗模拟。该项目是多学科的，涉及数学和材料科学，多机构，涉及学术界和工业界。动力学蒙特卡罗（KMC）模拟简单原子模型，如简单立方固体对固体（SOS）模型，已经成功地描述了外延生长的许多基本性质，准确地预测了岛大小分布和阶跃边缘密度等数量。然而，其他数量，包括详细的表面形态和表面重建，没有被考虑在内，并且对器件质量半导体材料的生长有重要影响。此外，由于模型中对晶体结构的描述只是示意图，其相互作用速率为有效速率，不易与原子量相关联。我们建议开发高保真的KMC方法，将包括外延生长的主要特征，包括非立方晶格结构，多物种和表面重建。这项工作将由一名博士后学者完成，他将在HRL实验室的计算物理小组和加州大学洛杉矶分校的计算与应用数学（CAM）小组工作。加州大学洛杉矶分校的Russel Caflisch将负责研究的数学方面，包括数学建模、算法开发和蒙特卡罗加速；HRL的Mark Gyure将监督材料方面的工作，包括物理建模、实施和与实验数据的对比验证。该博士后学者将与Gyure和Caflisch以及他们研究小组的其他成员进行广泛的互动，从中可以学到很多新的和令人兴奋的东西。大力鼓励发展博士后的个人研究视角。例如，博士后研究的一部分将是基于博士后研究兴趣的个人项目，博士后主要负责该项目。该项目由MPS多学科活动办公室（OMA）和数学科学司共同支持。

This proposal is for computational methods in material science, in particular for Monte Carlo simulation of atomistic models for epitaxial growth of thin films. The project is multi-disciplinary, involving both mathematics and materials science, and multi-institutional, involving both academia and industry. Kinetic Monte Carlo (KMC) simulation of simple atomistic models such as simple cubic Solid-On-Solid (SOS) models, has been successful in describing many basic properties of epitaxial growth, accurately predicting quantities such as island size distribution and step edge density. Other quantities, however, including detailed surface morphology and surface reconstructions, are not accounted for and have important effects on growth of device-quality semiconductor materials. Moreover, since the description of the crystal structure is only schematic in the model, its interaction rates are effective rates and cannot be easily related to atomistic quantities. We propose to develop high-fidelity KMC methods that will realistically include the mainfeatures of epitaxial growth, including non-cubic lattice structure, multiple species, and surface reconstructions.This work will be performed by a postdoctoral scholar who will work in the Computational Physics Group at HRL Laboratories and the Computational and Applied Mathematics (CAM) group at UCLA. Russel Caflisch at UCLA will supervise the mathematical aspects of the research including mathematical modeling, algorithm development and Monte Carlo acceleration; Mark Gyure at HRL will supervise the materials aspects including physical modeling, implementation and validation by comparison to experimental data.This postdoctoral scholar will have extensive interactions with Gyure and Caflisch, as well as with other members of their research group, from which the postdoc should learn a lot that is new and exciting. Development of the postdoc's individual research perspective will be strongly encouraged. For example, part of the postdoc's research will be an individual project based on the postdoc's research interests and for which the postdoc is primarily responsible. This project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences.