Level-set method for island dynamics in epitaxial growth

A level-set model for the simulation of epitaxial growth is described. In this model, the motion of island boundaries of discrete atomic layers is determined by the time evolution of a continuous level-set function Phi. The adatom concentration is treated in a mean-field manner. We use this model to systematically examine the importance of various fluctuations in the submonolayer and multilayer regimes. We find that, in the submonolayer regime for large values of D/F, the dominant fluctuations are associated with the spatial seeding of islands. We also show how different microscopic mechanisms can be included into this formalism. In the multilayer regime, our model exhibits surface roughening.