Equilibrium morphologies of epitaxially strained islands

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. A two-dimensional model assuming linear elastic behavior is used to analyze an isolated island with elastic properties similar to those of the substrate. The results show that in order to minimize the total free energy, a coherent island will adopt a particular shape and height-to-width aspect ratio that are 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008