Abstract
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.
Highlights
In recent years, it became possible to accurately calculate the formation energy of defects in crystalline solids using ab-initio methodologies
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
We present the results of calculations of formation energy of charged defects and their optical transition levels in zinc oxide (ZnO) crystals
Summary
It became possible to accurately calculate the formation energy of defects in crystalline solids using ab-initio methodologies. The calculation of neutral defects is relatively straight-forward, the calculation of charged defects is more complicated [1]. We present the results of calculations of formation energy of charged defects and their optical transition levels in zinc oxide (ZnO) crystals. A complete description of the proposed method for energy corrections can be found in [2]. Our calculations are performed for ZnO doped with single charged nitrogen (N) and phosphorus (P) atoms.
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