Intrinsic deep hole trap levels in $Cu_{2}O$ with self-consistent repulsive Coulomb energy

Abstract

The large error of the DFT+U method on full-filled shell metal oxides is due to the residue of self-energy from the localized d orbitals of cations and p orbitals of the anions. U parameters are self-consistently found to achieve the analytical self-energy cancellation. The improved band structures based on relaxed lattices of ${Cu_{2}O}$ are shown based on minimization of self-energy error. The experimentally reported intrinsic p-type trap levels are contributed by both Cu-vacancy and the O-interstitial defects in ${{Cu}_{2}O}$. The latter defect has the lowest formation energy but contributes a deep hole trap level while the Cu-vacancy has higher energy cost but acting as a shallow acceptor. Both present single-particle levels spread over nearby the valence band edge, consistent to the trend of defects transition levels. By this calculation approach, we also elucidated the entanglement of strong p-d orbital coupling to unravel the screened Coulomb potential of fully filled shells.