Thermal decay of nanostructures and Ostwald ripening of homoepitaxial monolayers

了解通过外延生长在表面上形成的纳米结构的衰变过程对于使用纳米结构材料作为器件和基本原因都是重要的。在这个项目中，我们开发并实现了在大时间尺度上模拟这些衰变过程的数值方案。我们将考虑所谓的阶梯流模型，它在高度上是离散的，但在横向上是连续的。由于底层晶体结构的各向异性和各步骤附着/脱离过程的动力学，它们非常适合纳入微观效应。原则上，阶跃流模型是阶跃的2+1维自由边界问题，在我们考虑的应用中，它将由多达一千个自由边界组成。挑战在于开发足够有效和准确的数值方案，以允许长时间的模拟，这是预测/确认标度定律所必需的，并研究微观参数对宏观尺度上系统行为的影响。数值方案将基于前跟踪方法，水平集方法和相场近似，并将在精度和效率方面进行比较. ...

An understanding of the decay process of nanostructures formed on a surface by epitaxial growth is important both for using nanostructured materials as devices and for fundamental reasons. In this project we develop and implement numerical schemes for simulating these decay processes over large time scales. We will consider so-called step flow models, which are discrete in the heigth but continuous in the lateral direction. They are well suited to incorporate microscopic effects due to anisotropy of the underlying crystal structure and kinetics due to attachment/detachment processes at steps. In principle, a step flow model is a 2+1 dimensional free boundary problem for the steps, which in the applications we have in mind will consist of up to a thousand free boundaries. The challenge is to develop numerical schemes being efficient and accurate enough to allow for long time simulations, which are necessary to predict/confirm scaling laws, and to investigate the influence of microscopic parameters on the behaviour of the system on a macroscopic scale. The numerical schemes will be based on front tacking methods, level set methods and phase field approximations and will be compared regarding accuracy and efficiency. ...