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Surface energies of AlN allotropes from first principles

In this Letter we present first principle calculation of surface energies of rock-salt (B1), zinc-blende (B3), and wurtzite (B4) AlN allotropes. Out of several low-index facets, the highest energies are obtained for mono-atomic surfaces (i.e. only by either Al or N atoms): $γ_{\{111\}}^{\rm B1}=410\uu{meV/Å}^2$, $γ_{\{100\}}^{\rm B3}=346\uu{meV/Å}^2$, $γ_{\{111\}}^{\rm B3}=360\uu{meV/Å}^2$, and $γ_{\{0001\}}^{\rm B4}=365\uu{meV/Å}^2$. The difference between Al- and N-terminated surfaces in these cases is less then $20\uu{meV/Å}^2$. The stoichiometric facets have energies lower by $100\uu{meV/Å}^2$ or more. The obtained trends could be rationalised by a simple nearest-neighbour broken-bond model.