The ternary semiconductors ${\text{Cu}}_2\text{Sn}{X}_3$ ($X=\text{S}$, Se) are found frequently as secondary phases in synthesized ${\text{Cu}}_2{\text{ZnSnS}}_4$ and ${\text{Cu}}_2{\text{ZnSnSe}}_4$ samples, but previous reports on their crystal structures and electronic band gaps are conflicting. Here we report their structural and electronic properties as calculated using a first-principles approach. We find that (i) the diverse range of crystal structures such as the monoclinic, cubic, and tetragonal phases can all be derived from the zinc-blende structure with tetrahedral coordination. (ii) The energy stability of different structures is determined primarily by the local cation coordination around anions, which can be explained by a generalized valence octet rule. Structures with only Cu${}_3$Sn and Cu${}_2$Sn${}_2$ clusters around the anions have low and nearly degenerate energies, which makes Cu and Sn partially disordered in the cation sublattice. (iii) The direct band gaps of the low-energy compounds ${\text{Cu}}_2{\text{SnS}}_3$ and ${\text{Cu}}_2{\text{SnSe}}_3$ should be in the range of 0.8–0.9 and 0.4 eV, respectively, and are weakly dependent on the long-range structural order. A direct analogy is drawn with the ordered vacancy compounds found in the $\text{Cu}(\text{In},\text{Ga}){\text{Se}}_2$ solar-cell absorbers.

• Received 23 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.075213