Morphologies of epitaxial islands on a lattice-misfitted substrate

Under certain growth conditions for systems with a film/substratelattice misfit, the deposited material is known to aggregate intoisland-like shapes. We have obtained an analytical expression of thetotal free energy, which consists of strain energy, surface energyand interfacial energy of a coherent island/substrate system, andthe change of equilibrium aspect ratio versus the volume of theisland and the misfit of lattices in the system, which provides abroad perspective on island behaviour. These then were used to studythe equilibrium shapes of the system. The results show that in orderto minimize the total free energy, a coherent island will have aparticular height-to-width aspect ratio, called equilibrium aspectratio, that is a function of the island volume and misfit. Theaspect ratio is increased with increasing island volume at a fixedmisfit, and with increasing misfit strain between the island andsubstrate at a fixed island volume. Moreover, the effect of misfitdislocation on the equilibrium shape of the island is also examined.The results obtained are in good agreement with experiment ofobservations and thus can serve as a basis for interpreting theexperiments.