Electronic structure of nanostructured ZnO from x-ray absorption and emission spectroscopy and the local density approximation

Abstract

$\mathrm{O}\phantom{\rule{0.3em}{0ex}}1s$ absorption spectroscopy (XAS) and $\mathrm{O}\phantom{\rule{0.3em}{0ex}}K\ensuremath{\alpha}$ emission spectroscopy (XES) were performed to study the electronic structure of nanostructured ZnO. The band gap is determined by the combined absorption-emission spectrum. Resonantly excited XES spectra showing an energy dependence in the spectral shape reveal the selected excitations to the different $\mathrm{Zn}\phantom{\rule{0.3em}{0ex}}3d$, $4s$, and $4p$ states in hybridization with $\mathrm{O}\phantom{\rule{0.3em}{0ex}}2p$ states. The partial density of state obtained from local density approximation (LDA) and $\mathrm{LDA}+U$ calculations are compared with the experimental results. The $\mathrm{LDA}+U$ approach is suitable to correct LDA self-interaction error of the cation $d$ states. The atomic eigenstates of $3d$ in zinc and $2p$ in oxygen are energetically close, which induces the strong interaction between $\mathrm{Zn}\phantom{\rule{0.3em}{0ex}}3d$ and $\mathrm{O}\phantom{\rule{0.3em}{0ex}}2p$ states. This anomalous valence band cation-$d$--anion-$p$ hybridization is verified by taking into account the strong localization of the $\mathrm{Zn}\phantom{\rule{0.3em}{0ex}}3d$ states.