Origin of apparent critical thickness for island formation in heteroepitaxy

We find that a continuum model of heteroepitaxy exhibits a sharp crossover with increasing coverage, from planar growth to island formation. The "critical thickness" at which this Stranski-Krastanov transition occurs depends sensitively on misfit strain, with a dependence strikingly similar to that seen experimentally. The initial planar growth occurs because of intermixing of deposited material with the substrate. While the transition is strictly kinetic in nature, it depends only weakly on growth rate. The role of surface segregation is also discussed.