Surface energies of AlN allotropes from first principles

In this letter we present first-principles calculations of the surface energies of rock-salt (B1), zinc-blende (B3) and wurtzite (B4) AlN allotropes. Of several low-index facets, the highest energies are obtained for monoatomic surfaces (i.e. of only either Al or N atoms): γ{111}B1=410meV/Å2,γ{100}B3=346meV/Å2,γ{111}B3=360meV/Å2 and γ{0001}B4=365meV/Å2. The difference between Al- and N-terminated surfaces in these cases is less then 20 meV/Å2. The stoichiometric facets have energies lower by 100 meV/Å2 or more. The obtained trends could be rationalized by a simple nearest-neighbour broken-bond model.