Structural stability of clean GaAs nanowires grown along the [111] direction

Using a first-principles approach we have calculated the formation energies of small diameter GaAs nanowires (NWs) with both zinc-blende and wurtzite structure grown along the [111] direction. The section of the wires is hexagonal and the side facets are oriented either {11-20} and {10-10} in the case of the wurtzite structure, and {110} and {112} for the zinc-blende structure. The formation energy of the nanowires as a function of their radius is then interpreted in terms of a model in which the energy contributions from the bulks, the flat surfaces and the ridges are taken explicitly into account. We find that the nanowire stability is mainly explained by the competition between the bulk energy, favoring the zincblende structure and the surface energies favoring the wurtzite structure. We find also that the directly calculated formation energies of some small diameter wurtzite NWs can be reproduced by our model taking into account only the bulk and flat surface contributions. That is, the ridges do not contribute substantially to the nanowire formation energy. Inspection of the ridge structure and band structure reveals that this good agreement occurs when the NWs are semiconducting and the ridges do not add more dangling bonds to the surface with respect to those provided by the sidewalls. Within our model we find the critical diameter for the wurtzite-zinc-blende transition at 6.3 nm