Using both density functional theory–local density approximation and Tersoff potentials, we calculate (1 1 10), (105), and (001) surface energies relevant to the self-assembly of Ge $\{$105$\}$ ripples on Si (1 1 10) substrates. Surface energies are calculated as a function of Ge overlayer thickness and applied strain. Comparison of density functional theory (DFT) and Tersoff potential results reveals qualitative differences in the predicted dependence of surface energies on Ge overlayer thickness and the stability of the Ge on Si (1 1 10) surface relative to the Ge on Si (001) surface. DFT calculations show that ${\gamma }_{\text{Ge}/\text{Si}}^{\left(1110\right)}$ is strongly influenced by the presence of tilted dimers, and provide an explanation for the differing stability predictions. Finally, a multiscale model including strain- and thickness-dependent ${\gamma }_{\text{Ge}/\text{Si}}$ is used to show that surface energy is a driving force for formation of Ge {105} ripples on Si (1 1 10), supporting recent experimental results of Ge-deposition-induced $\{$105$\}$ faceting on Si (1 1 10).

• Received 5 September 2011

DOI:https://doi.org/10.1103/PhysRevB.85.085312