Observations on the mechanics of strained epitaxial island growth

An epitaxial material island which has a lattice parameter differing by a small amount for that of its substrate is considered within the framework of continuum mechanics. The strain distribution in the island is determined for a range of aspect ratio, taking into account the compliance of the substrate. It is demonstrated that the total free energy of a strained island is minimum for some value of aspect ratio, and that this value depends on the volume of the island. To consider strain relaxation, the nucleation of a dislocation at the edge of a strained island is examined and the equilibrium aspect ratio of a dislocated island is computed. In particular, it is shown that an island can reduce its free energy by reducing its aspect ratio and, simultaneously, forming an interface misfit dislocation. The simulations are based on the numerical finite element method.