Efficient Computation of Epitaxial Growth

外延生长是一种物理过程，其中原子缓慢沉积到衬底上，使得晶体生长，粗略地说，一次一个原子层。 这是一个基本的科学问题，其中纳米尺度和宏观尺度效应都很重要。 由此产生的膜形态是由热力学和动力学效应之间的复杂相互作用决定的。此外，外延生长技术已被用于创建包含量子点（嵌入不同种类原子的矩阵中的纳米尺寸的原子集合）的新型材料。 由此产生的材料具有独特的电子特性。 例如，固态激光器已经由这种材料制成。此外，这种材料有望在量子计算应用中发挥作用。 模拟这种材料的生长仍处于起步阶段。本建议的目的是开发使用计算机模拟外延生长的有效算法。该提案将侧重于原子模型，而不是连续的，因为它们自然包括纳米级的物理效应，如成核和波动。 特别是，将使用动力学蒙特卡罗模型，其中原子运动的简单规则以随机方式演变。该提案旨在设计有效的计算方法来模拟这些模型。我们的计算策略是基于时间和空间的粗粒度，特别注意保持物理保真度。 初步结果表明，我们的算法是5至10倍的速度比目前的最先进的。它认为，这里提出的数值方法将允许模型开发进行更快的速度，从而促进新材料的设计。提议者计划与密歇根大学材料科学和工程系的两个实验研究小组密切合作。

Epitaxial growth is a physical process where atoms are slowly deposited onto a substrate so that a crystal is grown, loosely speaking, one atomistic layer at a time. This is a fundamental scientific problem in which both nanoscale and macroscale effects are important. The resulting film morphology is determined by a complex interaction between thermodynamic and kinetic effects. In addition, epitaxial growth techniques have been used to create novel materials which contain quantum dots (nanometer sized collections of atoms embedded in a matrix of different species of atoms). The resulting material has unique electronic properties. For example, solid-state lasers have been made out of such materials. In addition, there is hope that such materials may be useful in quantum computing applications. Modeling the growth of such a material is still in its infancy.The purpose of this proposal is to develop efficient algorithms for the simulation of epitaxial growth using a computer. The proposal will focus on atomistic models rather than continuous ones since they naturally include nanoscale physical effects such as nucleation and fluctuations. In particular, kinetic Monte Carlo models will be used, in which simple rules for atom motion are evolved in stochastic fashion. The proposal aims at devising efficient computational methods to simulate such models. Our computational strategy is based on coarse-graining both in time and space, taking special care to preserve physical fidelity. Preliminary results indicate that our algorithms are 5 to 10 times faster than the current state-of-the-art. It is felt that the numerical methods proposed here will allow model development to proceed at a much faster pace, thereby facilitating the design of new materials. The proposer plans to work closely with two experimental research groups in the Material Science and Engineering Departments at the University of Michigan.