Intrinsic deep hole trap levels in Cu2O with self-consistent repulsive Coulomb energy

• We elucidated 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.
• We attempted a self-consistent manner to determine the U parameters for localized orbitals of both cations and anions of fully occupied shell semiconductor like Cu2O.
• We showed the improved band structures based on relaxed lattices of Cu2O on minimization of self-energy error.
• We discussed the experimentally reported intrinsic p-type trap levels are contributed by both Cu-vacancy and the O-interstitial defects in Cu2O.
• We pointed out 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.

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 selfconsistently found to achieve the analytical self-energy cancellation. The improved band structures based on relaxed lattices of Cu2O 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 Cu2O. The latter defect has the lowest formation energy but contributes a deep hole trap level while the Cuvacancy 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.