Calculation of equilibrium island morphologies for strained epitaxial systems

Strained islands grown coherently on a relatively thick substrate with similar elastic properties are considered within the framework of continuum mechanics. The condition of uniform surface chemical potential is imposed to calculate two-dimensional equilibrium island shapes. The stress distribution in the equilibrium islands is shown to be highly non-homogeneous. The effects of introducing a single misfit dislocation at the island-substrate interface are considered. It is found that there is critical island volume above which a dislocation decreases the total free energy of the system. The dislocation alters the stress distribution in the island, causing the island to relax via mass transport to an equilibrium shape with a lower height-to-width aspect ratio and a smaller surface chemical potential than the island prior to the introduction of the dislocation.