Modeling, Simulation and Analysis of Epitaxial Film Growth

奖项编号：0103825PI: Schulze， TimothyInstitution: University of Tennessee， knoxville项目：应用数学项目经理：Catherine mavriplis标题：外延膜生长的建模，仿真和分析本提案涉及外延膜的生长。本文讨论的模拟技术和粗粒度模型是基于动力学蒙特卡罗（KMC）模拟的，这是一种基于原子的模拟晶体生长的成熟方法。虽然被认为是忠实于微观尺度物理，但KMC模拟非常缓慢，并且公认需要适合更大长度和时间尺度的模型。本文讨论的两种方法中的第一种是一种新的模拟技术，称为原子差分格式。在这种方法中，人们假设薄膜表面的原子分布处于接近平衡状态，并且可以通过直接由KMC跃迁概率导出的时步差分方程来计算。另一方面，晶体的形貌被认为是在一个较慢的时间尺度上进化的，并且是在一个守恒质量的离散基础上计算的。第二种方法寻求微观尺度模型的均质化、连续化版本。连续体模型采用偏微分方程的形式，描述系统在宏观长度和时间尺度上的演化。本研究的最后一个组成部分考虑了这两种方法在连续处理配置中的应用，其中衬底（磁带）连续通过沉积带。不断移动的接触线及其稳定性特别令人感兴趣。外延薄膜在半导体工业中具有重要的技术意义。随着高温超导体（HTSC）应用的发展，外延薄膜仍有进一步的前景，人们正在努力生产具有巨大载流能力的高温超导体导线和带。与此同时，薄膜生长过程是应用数学家的灵感源泉，需要广泛的数学技术和模拟工具来探索这些系统在巨大长度尺度范围内的行为。特别地，在本提案中进行的研究旨在提高我们理解和控制材料纳米尺度结构的能力，特别强调将原子尺度模型与传统建模方法联系起来。日期：2001年6月22日

DMS Award AbstractAward #: 0103825PI: Schulze, TimothyInstitution: University of Tennessee, KnoxvilleProgram: Applied MathProgram Manager: Catherine MavriplisTitle: Modeling, Simulation and Analysis of Epitaxial Film GrowthThis proposal concerns the growth of epitaxial films. The simulation technique and coarse-grained model discussed in this proposal are based on kinetic Monte-Carlo (KMC) simulations, which are an established method of simulating crystal growth on an atom-by-atom basis. While believed to be faithful to the micro-scale physics, KMC simulations are extremely slow and there is a recognized need for models appropriate for larger length and time scales. The first of the two approaches discussed in this proposal is a new simulation technique referred to as an Atomistic Difference Scheme. In this method, one assumes that the distribution of atoms on the surface of the film is in near equilibrium and can be computed by time-stepping difference equations derived directly from the KMC transition probabilities. The topography of the crystal, on the other hand, is assumed to evolve on a slower time-scale and is computed on a discrete basis that conserves mass. The second approach seeks a homogenized, continuum version of this micro-scale model. The continuum model takes the form of partial differential equations that describe the system's evolution on macroscopic length and time scales. A final component of this investigation considers the application of these two methods to a continuous processing configuration where substrate (a tape) is continuously passed through a deposition zone. The continuously moving contact-line and its stability are of particular interest.Epitaxial films are of vital technological importance in the semi-conductor industry. As applications for high-temperature super-conductors (HTSC) develop, epitaxial films hold still further promise, with extensive efforts under way to produce HTSC wires and tapes that have enormous current-carrying capacities. At the same time, the film growth process is a burgeoning source of inspiration for applied mathematicians, requiring a wide range of mathematical techniques and simulation tools to explore the behavior of these systems over an enormous range of length scales. In particular, the research undertaken in this proposal seeks to enhance our ability understand and control the nano-scale structure of materials, placing a special emphasis on linking atomic-scale models with traditional modeling approaches.Date: June 22, 2001