Band gap anomalies of the (ZnM2O4)-O-III (M-III = Co, Rh, Ir) spinels

Development of high figure-of-merit p-type transparent conducting oxides has become a global research goal. (ZnM2O4)-O-III (M-III = Co, Rh, Ir) spinels have been identified as potential p-type materials, with ZnIr2O4 reported to be a transparent conducting oxide. In this article the geometry and electronic structure of (ZnM2O4)-O-III are studied using the Perdew-Purke-Ernzerhof generalized gradient approximation (PBE-GGA) to density functional theory and a hybrid density functional, HSE06. The valence band features of all the spinels indicate that they are not conducive to high p-type ability, as there is insufficient dispersion at the valence band maxima. The trend of increasing band-gap as the atomic number of the M-III cation increases, as postulated from ligand field theory, is not reproduced by either level of theory, and indeed is not seen experimentally in the literature. GGA underestimates the band-gaps of these materials, while HSE06 severely overestimates the band-gaps. The underestimation (overestimation) of the band-gaps by GGA (HSE06) and the reported transparency of ZnIr2O4 is discussed.