Equilibrium shapes of coherent islands in heteroepitaxial systems

An analytical expression of the free energy consisting of the strain energy, surface energy and interfacial energy for the coherent island/substrate system, as well as the evolving relations of aspect ratio against volume of the island and misfit of the system, which provides a broad perspective on island behavior, is obtained, and used to study the equilibrium shapes of the systems. Under certain growth conditions in systems with a film/substrate lattice misfit, deposed material is known to aggregate into islandlike shapes with geometries having triangular shaped cross-sections. A two-dimensional model assuming liner elastic behavior is used to analyze an isolated triangular shaped island with elastic properties similar to those of the substrate assumed to be semi-infinite. The results show that in order to minimize the total free energy, a coherent island will adopt a particular height-to-width aspect ratio that is a function of only the island volume. The effect of a misfit dislocation on the equilibrium shape of an island is in passing examined. These can serve as a basis for interpretation of experiments