Thermal decay of nanostructures and Ostwald ripening of homoepitaxial monolayers

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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. ...