Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using a multistate lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These local deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We apply the model to study a kinetic limited growth regime. Transitions from stepped mounds into faceted islands under deposition conditions are demonstrated. It is shown that a significantly reduced growth rate after faceting leads to a continuous nucleation of new islands until overcrowding occurs. The island size distribution is now dominated by fluctuations in the initial island size during faceting and the increased diversity in the ages of the islands. This multistate model may find applications in kinetic simulations of other nanostructures or nanoclusters involving arbitrary high-index surfaces.