On the bandgap underestimation of delafossite transparent conductive oxides CuMO₂ (M = Al, Ga and In): Role of pseudopotentials

We report a first-principles study on the electronic and optical properties of delafossite CuMO₂ (M = Al, Ga and In) using the recently developed hybrid functional pseudopotentials. We obtain trends of the fundamental and optical gaps with increasing M-atomic number, in agreement with experiment. In particular, we reproduce the experimental fundamental gap, optical gap, and Cu 3d energy of CuAlO₂ almost perfectly, in contrast to the various calculations that have traditionally focused on valence electrons, which are unable to reproduce these key properties simultaneously. Since all that distinguishes our calculations is simply the use of a different Cu pseudopotential with a partially exact exchange interaction, this suggests that an inappropriate description of the electron-ion interaction may play a role in the density functional theory bandgap problem for CuAlO₂. Applying Cu hybrid pseudopotentials to CuGaO₂ and CuInO₂ is also effective, yielding optical gaps that are very close to experiment. However, due to the limited experimental data for these two oxides, a comprehensive comparison as that for CuAlO₂ is not possible. Furthermore, our calculations yield large exciton binding energies for delafossite CuMO₂, all around 1 eV.