The Equilibrium Shape of Quantum Dots

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.