Calculation of the diameter-dependent polytypism in GaAs nanowires from an atomic motif expansion of the formation energy

The formation energies of GaAs nanowires have been calculated from a structural motif approach supported by first-principles data for small-diameter nanowires. GaAs bulk material has zincblende (ZB) structure, but the ground state of nanowires may be either ZB or wurtzite (WZ), possibly depending on energetic contributions from their surfaces and edges. The calculated nanowires are cut from the bulk material in the [111] direction and the [0001] direction for ZB and WZ structure, respectively. We consider nanowires with hexagonal cross sections and 112̄0 and 101̄0 facets in the case of WZ, and 101̄ and 112̄ for ZB nanowires. It is found that the WZ formation energy of small nanowires is lower than the ZB one due to the lower WZ surface energy. This holds if edge energies are neglected. The role of additional dangling bonds at the edges and its effect on the WZ-ZB transition is discussed.