The core effect of misfit dislocations in heteroepitaxy

We study energetics of the misfit dislocations at the interface between a semi-infinite substrate and an epitaxial layer, using a two-dimensional elastic lattice model. The model includes not only the elastic deformation but also the effect of a spontaneous force. Elastic energy of a system with a regular array of misfit dislocations at the interface is calculated by using an elastic lattice Green's function. For a small positive misfit, the optimum dislocation period of the lattice model agrees with that of the continuum elasticity theory, and is insensitive to the core structure. For a large misfit, an additional force distribution at the core brings about a strong effect. With a positive misfit, the system has a compressive force distribution at the core, and the optimum dislocation period of the lattice model is larger than that of the continuum elasticity theory. The result is in agreement with experiments.