Achieving accurate energetics beyond (semi-)local density functional theory: Illustrated with transition metal disulfides, Cu2ZnSnS4 , and Na3PS4 related semiconductors

Abstract

Understanding, designing, and processing functional metal sulfides are significant challenges in part because of the high temperatures and pressures and the number of secondary phases encountered in these complex systems. In particular, the underlying thermochemical properties are not well understood that would allow prediction of equilibrium conditions and driving forces. In addition, obtaining accurate values for the energetics of metal sulfide systems is far from complete, suggesting application of density functional theory (DFT) calculations. Here, the results of an examination of 69 phases by DFT using 12 exchange-correlation (X-C) functionals indicate that (i) the key source of error in predicting the Gibbs energy of a phase is the enthalpy calculated at 0 K rather than entropy at finite temperatures from phonon calculations and (ii) an improved prediction of the thermodynamic properties at 0 K relies on the selected nonlocal X-C functional such as the hybrid potential. Regarding metal sulfides, we conclude from the present DFT results that (1) the secondary phase ${\mathrm{Cu}}_{2}{\mathrm{ZnSn}}_{3}{\mathrm{S}}_{8}$, associated with the desired photovoltaic material ${\mathrm{Cu}}_{2}{\mathrm{ZnSnS}}_{4}$, is not stable at 0 K, but it becomes slightly stable with increasing temperature (i.e., g800 K), primarily due to the vibrational entropy, which makes it difficult to be detected in a typical thin-film growth process; (2) the hybrid X-C functional improves the predicted energetics for most of the layered transition-metal disulfides such as ${\mathrm{TiS}}_{2}$, ${\mathrm{MoS}}_{2}$, and ${\mathrm{WS}}_{2}$, but not for the nonlayered ${\mathrm{RuS}}_{2}$, ${\mathrm{OsS}}_{2}$, and ${\mathrm{IrS}}_{2}$ as well as the layered ${\mathrm{PdS}}_{2}$; and (3) the formation of the solid-state electrolyte ${\mathrm{Na}}_{3}{\mathrm{PS}}_{4}$ is thermodynamically favored. We further conclude that accurate energetics as a function of temperature for the materials of interest is feasible to be achieved beyond the semilocal DFT calculations with the key being enthalpy predicted at 0 K.