This paper studies short-range order (SRO) in the semiconductor alloy ${\left(\mathrm{GaN}\right)}_{1-x}{\left(\mathrm{ZnO}\right)}_x$. Monte Carlo simulations performed on a density functional theory (DFT)-based cluster expansion model show that the heterovalent alloys exhibit strong SRO because of the energetic preference for the valence-matched nearest-neighbor Ga-N and Zn-O pairs. To represent the SRO-related structural correlations, we introduce the concept of special quasiordered structure (SQoS). Subsequent DFT calculations reveal the dramatic influence of SRO on the atomic, electronic, and vibrational properties of the ${\left(\mathrm{GaN}\right)}_{1-x}{\left(\mathrm{ZnO}\right)}_x$ alloy. Due to the enhanced statistical presence of the energetically unfavored Zn-N bonds with the strong $\mathrm{Zn}3d-\mathrm{N}2p$ repulsion, the disordered alloys exhibit much larger lattice bowing and band-gap reduction than those of the short-range ordered alloys. Lattice vibrational entropy tilts the alloy toward less SRO.

• Received 9 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.054207