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): $\gamma_{\{111\}}^{\rm B1}=410\uu{meV/\AA}^2$, $\gamma_{\{100\}}^{\rm B3}=346\uu{meV/\AA}^2$, $\gamma_{\{111\}}^{\rm B3}=360\uu{meV/\AA}^2$, and $\gamma_{\{0001\}}^{\rm B4}=365\uu{meV/\AA}^2$. The difference between Al- and N-terminated surfaces in these cases is less then $20\uu{meV/\AA}^2$. The stoichiometric facets have energies lower by $100\uu{meV/\AA}^2$ or more. The obtained trends could be rationalised by a simple nearest-neighbour broken-bond model.