Crystal and electronic structure of quaternary chalcogenide semiconductors I$_{2}$-II-IV-VI$_{4}$ (I=Cu, Ag, II=Zn, Cd, IV=Ge, Sn and VI=S, Se, Te)

Sequential cation mutation in zinc-blende chalcogenide semiconductors, from binary to ternary to quaternary compounds, is systematically studied using first-principles calculations. Several universal trends are found for the crystal and electronic structure of the ternary and two classes of quaternary chalcogenides. We find that (i) most I$_{2}$-II-IV-VI$_{4}$ compounds are more stable in the kesterite structure, rather than the widely-recognized stannite structure; (ii) Cu and Zn layers are easy to be randomized in kesterite Cu$_{2}$ZnSnS$_{4}$ and Cu$_{2}$ZnSnSe$_{4}$; (iii) the band gap decreases during the mutation; (iv) the band gap of Cu$_{2}$ZnSnSe$_{4}$ should be around 1.0 eV, not 1.5 eV as reported in previous absorption measurements.