Probing configurational disorder in ZnGeN2 using cluster-based Monte Carlo

Abstract

${\mathrm{ZnGeN}}_{2}$ is sought as a semiconductor with comparable lattice constant to GaN and tunable band gap for integration in optoelectronic devices. Configurational disorder on the cation sublattice of ${\mathrm{ZnGeN}}_{2}$ can strongly modify the electronic structure compared to the ordered material, and both ordered and disordered forms of ${\mathrm{ZnGeN}}_{2}$ are candidates for light-emitting diodes and other emitters. The nonisovalent character of the disordered species (${\mathrm{Zn}}^{2+}$ and ${\mathrm{Ge}}^{4+}$) subjects the cation ordering to strong short-range order effects. To model these effects, we use Monte Carlo (MC) simulations utilizing a cluster expansion to approximate formation enthalpy. Representative disordered configurations in 1024-atom supercells are relaxed in density functional theory calculations. From the MC structures, we extract a short-range order parameter (the N-cation coordination motif), and two long-range order parameters (Bragg-Williams and stretching parameters), and examine their correlations. We perform a thermodynamic integration to determine the mixing entropy and free energy. ${\mathrm{ZnGeN}}_{2}$ exhibits a first-order phase transition with pronounced discontinuities in enthalpy and entropy, as well as in the structural order parameters. We discuss the relationship between the effective temperature used in the MC simulation and the growth temperatures in experiment in relation to the crossover from the nonequilibrium to the equilibrium growth regime. This work expands on current models of site disorder in ${\mathrm{ZnGeN}}_{2}$ and provides atomic structure models with a systematic variation of the degree of cation disorder.