Band structure of indium oxide: Indirect versus direct band gap

The nature of the band gap of indium oxide is still a matter of debate. Based on optical measurements the presence of an indirect band gap has been suggested, which is 0.9 to $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ smaller than the direct band gap at the $\ensuremath{\Gamma}$ point. This could be caused by strong mixing of $\mathrm{O}\phantom{\rule{0.3em}{0ex}}2p$ and $\mathrm{In}\phantom{\rule{0.3em}{0ex}}4d$ orbitals off $\ensuremath{\Gamma}$. We have performed extensive density functional theory calculations using the LDA+U and the GGA+U methods to elucidate the contribution of the $\mathrm{In}\phantom{\rule{0.3em}{0ex}}4d$ states and the effect of spin-orbit coupling on the valence band structure. Although an indirect band gap is obtained, the energy difference between the overall valence band maximum and the highest occupied level at the $\ensuremath{\Gamma}$ point is less than $50\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. It is concluded that the experimental observation cannot be related to the electronic structure of the defect free bulk material.