Phase diagram, structure, and electronic properties of (Ga1−xZnx)(N

We construct an accurate cluster expansion for the (Ga${}_{1\ensuremath{-}x}$Zn${}_{x}$)(N${}_{1\ensuremath{-}x}$O${}_{x}$) solid solution, based on density functional theory (DFT). The subsequent Monte Carlo simulation reveals a phase diagram which has a wide miscibility gap and an $x=0.5$ ordered compound. The disordered phase displays strong short-range order (SRO) at synthesis temperatures. To study the influences of SRO on the lattice and electronic properties, we conduct DFT calculations on snapshots from the Monte Carlo simulation. Consistent with previous theoretical and experimental findings, lattice parameters were found to deviate from Vegard's law with small upward bowing. Bond lengths depend strongly on local environment, with a variation much larger than the difference of bond length between ZnO and GaN. The downward band gap bowing deviates from parabolic by having a more rapid onset of bowing at low and high concentrations. An overall bowing parameter of 3.3 eV is predicted from a quadratic fit to the compositional dependence of the calculated band gap. Our results indicate that SRO has significant influence over both structural and electronic properties.