We study numerically the equilibrium shape, shape transition and dislocation nucleation in strained epitaxial islands with a two-dimensional atomistic model, using interatomic potentials of Lennard-Jones type. The phase diagram for the equilibrium island shapes as a function of island size and lattice misfit with the substrate is obtained by an energy minimization procedure which does not require predefined faceted shapes. We determine the energy barrier and transition path for transition between different shapes of the islands and for dislocation nucleation in initially coherent islands using a method introduced recently, based on a systematic search of the transition paths for activated events.

We have studied numerically the stability and defect nucleation in epitaxial layers on a substrate with lattice mismatch. Stress relaxation and energy barriers for misfit dislocation nucleation are estimated using modern methods for saddle point search based on a combination of activation with local repulsive potential and the Nudged Elastic Band method. Stress relaxation processes correspond to different transition paths from coherent to incoherent states of the epitaxial layer.Using a two-dimensional atomistic model with Lennard-Jones interacting potential, we and different equilibrium critical thickness and activation energy behavior for dislocation nucleation of epitaxial films under tensile and compressive strain. For tensile strain, the energy barrier decreases with thickness while it reaches a constant value for compressive strain.