Design of I$_{2}$-II-IV-VI$_{4}$ Semiconductors through Element-substitution: the Thermodynamic Stability Limit and Chemical Trend

Through element substitution in kesterite Cu$_{2}$ZnSnS$_{4}$ or Cu$_{2}$ZnSnSe$_{4}$, a class of I$_{2}$-II-IV-VI$_{4}$ semiconductors can be designed as novel functional materials. Using the first-principles calculations, we show that this element-substitution design is thermodynamically limited, i.e., although I$_{2}$-II-IV-VI$_{4}$ with I$=$Cu, Ag, II$=$Zn, Cd, Hg, IV$=$Si, Ge, Sn and VI$=$S, Se, Te are stable quaternary compounds, those with II$=$Mg, Ca, Sr, Ba, IV $=$Ti, Zr, Hf, and VI$=$O are unstable against the phase-separation into the competing binary and ternary compounds. Three main phase-separation pathways are revealed. In general, we show that if the secondary II-VI or I$_{2}$-IV-VI$_{3}$ phases prefer to have non-tetrahedral structures, then the I$_{2}$-II-IV-VI$_{4}$ semiconductors tend to phase separate. This finding can be used as a guideline for future design of new quaternary semiconductors.