  The formation of dislocation-free three-dimensional islands during the
heteroepitaxial growth of lattice-mismatched materials has been observed
experimentally for several material systems. The equilibrium shape of the
islands is governed by the competition between the surface energy and the
elastic relaxation energy of the islands as compared to the uniform strained
film. As an exemplification we consider the experimentally intensively
investigated growth of InAs quantum dots on a GaAs(001) substrate, deriving the
equilibrium shape as a function of island volume. For this purpose InAs surface
energies have been calculated within density-functional theory, and a continuum
approach has been applied to compute the elastic relaxation energies.
