Charge-neutral disorder and polytypes in heterovalent wurtzite-based ternary semiconductors: The importance of the octet rule

We investigate lattice ordering phenomena for the heterovalent ternaries that are based on the wurtzite lattice, under the constraint that the octet rule be preserved. We show that, with the single exception of a highly symmetric twinned structure, all allowed lattice orderings can be described by a pseudospin model corresponding to the two different stackings ABAB of rows of atoms in the basal plane that occur in the Pna2[sub 1] and Pmc2[sub 1] crystal structures. The Raman and photo-luminescence spectra of ZnSnN[sub 2] are interpreted in light of the ordering model developed here. The observation that ZnSnN[sub 2] orders in the Pna2[sub 1] structure under appropriate growth conditions is consistent with the larger difference in the energies of formation of Pna2[sub 1] the and Pmc2[sub 1] structures for this material. The ordering model presented here has important implications for the optical, electronic, and lattice properties of all wurtzite-based heterovalent ternaries.