Over the last 17 years, we have developed a model for epitaxial growth that employs an island dynamics model with the level-set technique. In the island dynamics model islands are treated as continuous in the x-y-plane, while individual atomic layers are resolved in the z-direction. Adatoms are treated as a mean field quantity by solving a diffusion equation. The relevant (microscopic) input parameters for our model can be obtained from density-functional theory calculations. We will present a number of results we have obtained with this model, including the effects of strain that lead to self-organized patterns, and our most recent work that includes the effect of a step-edge barrier via a mixed Robin-type boundary condition for the diffusion equation, that leads to the formation of three-dimensional mounds.
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