Epilayer thickness and strain dependence of Ge(113) surface energies

The stability and growth of three-dimensional (3D) nanostructures in the Ge on Si system is controlled in part by the strain- and overlayer-thickness-dependent surface energies of the crystal facets involved. Here, we use density functional theory (DFT) with local-density approximation calculations to calculate the strain- and thickness-dependent energy of various Ge(113) and Si(113) surface reconstructions. Results of DFT calculations are compared to Tersoff potential calculations to assess the relative importance of stress-strain effects compared to electronic effects not captured by empirical atomistic potentials. We find that the self-interstitial-based 3×2 adatom-dimer-interstitial and 3×2 adatom-interstitial surface reconstructions are stable for Ge overlayer thicknesses from 0 to 4 monolayers and at applied biaxial strains from ∼-4% to 0%. We leverage calculated surface energies to determine net effective surface energies of various experimentally observed 3D Ge on Si nanostructures.