Tuning the optical bandgap in multi-cation compound transparent conducting-oxides: The examples of In₂ZnO₄ and In₄Sn₃O₁₂

Transparent conducting oxides such as the bixbyite In₂O₃ and rutile SnO₂ systems have large disparities between the optical and fundamental bandgaps, $ΔEgOF$⁠, because selection rules forbid dipolar transitions from the top of the valence band to the conduction-band minimum; however, the optical gaps of multi-cation compounds with the same chemical species often coincide with their fundamental gaps. To explain this conundrum, we have employed density-functional theory to compute the optical properties of multi-cation compounds, In₂ZnO₄ and In₄Sn₃O₁₂, in several crystal structures. We show that a recently proposed mechanism to explain the disparity between the optical and fundamental gaps of M₂O₃ (M = Al, Ga, and In) applies also to other binary systems and to multi-compounds. Namely, a gap disparity will arise if the following three conditions are satisfied: (i) the crystal structure has inversion symmetry; (ii) the conduction-band minimum is formed by the cation and O s-orbitals; and (iii) there is strong p-d coupling and weak p-p in the vicinity of the valence-band maximum. The third property depends critically on the cationic chemical species. In the structures with inversion symmetry, Zn (Sn) strengthens (weakens) the p-d coupling in In₂ZnO₄ (In₄Sn₃O₁₂), enhancing (reducing) the gap disparity. Furthermore, we have also identified a In₄Sn₃O₁₂ structure that is 31.80 meV per formula unit more stable than a recently proposed alternative model.