Bond-length distribution in tetrahedral versus octahedral semiconductor alloys: The case ofGa1−xInxN

Large $\left(\approx 1000\mathrm{atoms}\right)$ supercell valence force-field simulations are used to investigate the nearest-neighbor bond-length distribution in relaxed tetrahedral (zinc blende and wurtzite) and octahedral (rocksalt) ${\mathrm{Ga}}_{1-x}{\mathrm{In}}_x\mathrm{N}$ alloys. We find that, due to the rigidity of the octahedron, the distribution of each anion-cation bond length in rocksalt alloys has two contributions: unrelaxed bonds and relaxed bonds. These two peaks have a large width and overlap slightly, leading to a broad nearest-neighbor distance distribution. On the other hand, the anion-cation nearest-neighbor distribution in zinc-blende alloys can be decomposed into a sum over four closely spaced and sharp peaks associated with different clusters, leading to a narrow, single-peaked nearest-neighbor distribution. Finally the wurtzite alloys exhibit bond-length distributions that are very similar to the corresponding ones in the zinc-blende alloys, leading to a nearly identical strain energy in random zinc-blende and wurtzite alloys.