Energetics of {105}-faceted Ge nanowires on Si(001) : An atomistic calculation of edge contributions

Heteroepitaxial growth in the $\mathrm{Ge}∕\mathrm{Si}$ (001) system is known to lead to the formation of pyramid-like ``hut'' islands with {105}-oriented facets. Recent calculations of island formation energies in this system have suggested that edge energies lead to an important contribution to the barrier to island formation at small sizes. Here we provide an independent calculation of the magnitude of the average edge energy for $\mathrm{Ge}∕\mathrm{Si}(001)$ by matching the results of atomistic simulations to continuum theory for the energy of faceted surfaces. We consider an infinitely long Ge island, or wire, bounded by {105} facets with the recently proposed rebonded-step-model reconstruction, on a (001) wetting-layer terrace with the $2\ifmmode\times\else\texttimes\fi{}8$ dimer-vacancy-line reconstruction. To perform these calculations we derive models for edge structures between {105} facets and between {105} and (001) facets, leading in both cases to atomic coordinations with no more than one dangling bond per atom. For these model edge structures we obtain an average value for the edge energy on the order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{\AA{}}$.

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