Transition levels of acceptor impurities in ZnO crystals by DFT-LCAO calculations

Large scale ab-initio calculations are carried out to study the charge state transition levels of nitrogen and phosphorus impurity defects in zinc oxide crystals using the DFT-LCAO approximation as implemented into the CRYSTAL computer code. It is shown that at a high concentration of defects (close location of defects) their formation energy is underestimated due to a significant delocalization of the charge within the supercell. After inclusion the energy offset correction and defect-defective interaction, the formation energy is improved, in a comparison with that calculated in a large supercell. The optical transition levels obtained by a direct calculation confirm the experimental observation: nitrogen and phosphorus impurities are deep acceptor centers with large formation energy in a charged state and, therefore, cannot serve as the effective source of hole charge. The obtained results are in good agreement with the previous theoretical work, in which other calculation methods were used, and are capable of qualitatively describing the energy characteristics of the charged defects.