ZnO is a prototypical semiconductor with occupied $d^{10}$ bands that interact with the anion $p$ states and is thus challenging for electronic structure theories. Within the context of these theories, incomplete cancellation of the self-interaction energy results in a Zn $d$ band that is too high in energy, resulting in upwards repulsion of the valence band maximum (VBM) states, and an unphysical reduction of the band gap. Methods such as GW should significantly reduce the self-interaction error, and in order to evaluate such calculations, we measured high-resolution and resonant angle-resolved photoemission spectroscopy (ARPES) and compared these to several electronic structure calculations. We find that, in a standard GW calculation, the $d$ bands remain too high in energy by more than 1 eV irrespective of the Hamiltonian used for generating the input wave functions, causing a slight underestimation of the band gap due to the $p-d$ repulsion. We show that a good agreement with the ARPES data over the full valence band spectrum is obtained, when the Zn-$d$ band energy is shifted down by applying an on-site potential $V_d$ for Zn-$d$ states during the GW calculations to match the measured $d$ band position. The magnitude of the GW quasiparticle energy shift relative to the initial density functional calculation is of importance for the prediction of charged defect formation energies, band-offsets, and ionization potentials.

• Received 19 September 2012

DOI:https://doi.org/10.1103/PhysRevB.86.235113