First principles simulations of Cu$_2$ZnSnS$_x$O$_{4-x}$ alloys*

Crystalline Cu$_2$ZnSnS$_4$ (CZTS) has been well studied for its photo-voltaic properties. This paper reports a systematic computational study of CZTS alloys with oxygen substituting for S in the form Cu$_2$ZnSnS$_x$O$_{4-x}$ in order to understand their stability and structural forms. The calculations find the heat formation of Cu$_2$ZnSnO$_{4}$ (CZTO) to be 4.7 eV lower than that of CZTS, a result which is consistent with the general observation that CZTS is very reactive when exposed to air. Interestingly, the results find that CZTS is stable with respect to its decomposition products; the calculated enthalpy for CZTS $\rightarrow$ Cu$_2$S + ZnS + SnS$_2$ is $\Delta H_{cal}$= +0.6 eV. However, for CZTO the corresponding decomposition is predicted to be exothermic; the calculated enthalpy for CZTO $\rightarrow$ Cu$_2$O + ZnO + SnO$_2$ is $\Delta H_{cal}$= -1.7 eV. The simulations of S/O alloys show that there are preferred structures for the O configurations. For example, for alloys with $x=2$, the energy difference between the lowest and highest energy O arrangements is 0.25 eV/formula unit.