Growth modes in two-dimensional heteroepitaxy on an elastic substrate

With the use of a two-dimensional harmonic elastic lattice model, in which spontaneous stress caused by the lack of neighboring atoms is incorporated, we determine ground state configuration of adsorbed atoms on a flat elastic substrate. Energy of the system is calculated by direct relaxation dynamics in the epitaxial layer and by using an elastic Green's function method in the substrate. Based on the ground state configurations determined for various coverages, we infer growth mode. As the lattice misfit and the strength of the spontaneous stress increase, the growth mode changes from Frank-van der Merwe (FM) to Stranski-Krastanov (SK) and finally to Volmer-Weber (VW) mode. In a parameter range between the SK and the VW with a large spontaneous stress, the equilibrium configuration changes from a layer to islands in unusual ways as the coverage increases.