Ordering in the mixed ZnGeN2-GaN alloy system: Crystal structures and band structures of ZnGeGa2N4 from first principles

While ZnGeN2 and GaN are closely lattice matched and have almost equal band gaps around 3.5 eV, their band offset is of order 1 eV. This situation suggests that there could be an opportunity for tuning the band gap in the alloy system. In particular, we examine here the 50 at. % composition, ZnGeGa2N4. It is shown that there are two 16-atom unit cell ordered structures, with space groups Pmn2(1) and P1n1, that obey the octet rule, with each N bound to two Ga, one Zn, and one Ge. The Pmn2(1) structure is a superlattice along the orthorhombic b direction of the ZnGeN2 Pbn2(1) structure, in which half the cell is replaced by GaN; consequently, octet-rule-preserving polytypes spanning the entire range of composition can be formed based upon this structure. Two other structures that do not obey the octet rule are also considered for comparison. These are superlattices consisting of 1/2 cell GaN and 1/2 cell ZnGeN2 along the orthorhombic a or c direction. By means of fully relaxed density functional calculations, we find that the structures that obey the octet rule have significantly lower total energy than the ones that do not. Detailed crystallographic data on these four structures: space group, lattice constants, relaxed Wyckoff positions, and predicted x-ray diffraction spectra, are provided. The lowest energy structure is found to have a negative energy of formation, comparable to those of ZnGeN2 and GaN. However, the mixing energy is slightly positive, indicating a tendency toward phase separation into ZnGeN2 and GaN even when only considering low energy octet-rule-preserving structures. The band gaps of the octet-rule-preserving structures, calculated using the quasiparticle self-consistent GW method, are found to be slightly higher than those of ZnGeN2 and GaN. This result can be explained in terms of size quantization effects compensating the reduced interface band gap.