FRG: Collaborative Research: Modeling and Computation of Crystalline Nanostructures

该项目旨在推动纳米晶体材料模拟技术的发展。制造这种材料的一种常用技术是在不同组成的单晶衬底上沉积单晶薄膜（异质外延）；在这个过程中，弹性相互作用是非常重要的。该项目将开发高效的计算工具，结合连续介质力学来处理远程弹性相互作用和动力学蒙特卡罗（KMC）模拟，可以准确地描述原子水平上的输运动力学。所开发的方法将广泛适用，但目前的重点是量子点纳米结构。将使用三种不同的方法来完成这项任务。其中之一将使用KMC来推断连续统模型中使用的各种参数。另一种方法将以KMC的新公式为基础，它可以用统计力学来证明与化学势有关。这将允许我们的KMC公式和连续介质力学之间的相当无缝的连接。我们可以利用这种联系在小的、分离良好的区域上使用KMC，然后使用宏观变量，如原子通量和弹性位移场，将这些区域组合在一起。另一种方法是在任何地方执行KMC，但使用在宏观时间尺度上更新的粗粒度连续域。纳米晶材料在固态激光器、存储器件和光伏电池等领域的应用前景广阔。预计本研究中开发的建模和计算方法将为执行器件级模拟铺平道路，并为应变合金系统的实验测量解释提供有价值的指导。我们的小组与半导体行业和学术界的实验小组有着密切的联系，这将使我们能够评估我们的建模进展。

This project is aimed at advancing the state of the art for simulating nanocrystalline materials. A common technique to manufacture such materials is depositing a monocrystalline film on a monocrystalline substrate of a different composition (heteroepitaxy); in the process elastic interactions are very important. The project will develop highly efficient computational tools by combining continuum mechanics to handle long-range elastic interactions with kinetic Monte Carlo (KMC) simulations that can accurately describe transport kinetics at the atomic level. The methods developed will be broadly applicable, but the immediate focus is on quantum dot nano-structures. Three different approaches will be used to accomplish this task. One of these will use KMC to deduce various parameters used in continuum models. Another approach will be based on a new formulation of KMC which can be shown, using statistical mechanics, to be connected with the chemical potential. This will allow a fairly seamless connection between our KMC formulation and continuum mechanics. We can exploit this connection to use KMC on small, well separated regions and then combine these regions together using macroscopic variables, such as atomic flux and elastic displacement fields. Another approach is to perform KMC everywhere but using coarse-grained continuum fields that are updated on a macroscopic time scale.Nanocrystalline materials have shown great promise for many applications such as solid state lasers, memory devices, and photovoltaic cells. It is anticipated that the modeling and computation methods developed in this research will pave the way for performing device level simulations and provide valuable guidance in the interpretation of experimental measurements for strained alloy systems. Our group has close ties with experimental groups based in the semiconductor industry and academia, which will allow us to assess our modeling progress.