Heteroepitaxial growth modes with dislocations in a two-dimensional elastic lattice model

We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.