First-principles finite-size correction schemes for point defects of Cu$_3$N
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arXiv
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| Format: | Preprint |
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2026
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| author | Reyes, Abdul M. Reyes-Lillo, Sebastian E. Menéndez-Proupin, Eduardo |
| author_facet | Reyes, Abdul M. Reyes-Lillo, Sebastian E. Menéndez-Proupin, Eduardo |
| contents | Point defects play a key role in determining semiconductor properties, such as electrical conductivity and photoluminescence, and often enable functional behavior. Accurate first-principles supercell simulations of point defects require reliable finite-size corrections. In this study, we combine PBE+U structural relaxations with HSE hybrid-functional calculations to determine defect formation energies and thermodynamic transition levels of Cu$_3$N. Finite-size trends are quantified using $Γ$-point calculations in supercells containing 256, 864, and 2048 atoms. We assess and extend the Makov-Payne and Lany-Zunger correction schemes by introducing additional $1/L^n$ terms, together with core-level potential alignment and defect-specific scaling models. Using Cu$_3$N as a case study, we show that charged vacancies with strongly localized defect states are accurately described by the Makov-Payne-type scaling ($1/L + 1/L^{3}$), whereas interstitial defects with shallow or weakly localized electronic character are better captured by a hydrogenic impurity model that accounts for defect-band dispersion. Residual trends for neutral or weakly localized defects are described by higher-order polynomial fits in $1/L^{3}$ and $1/L^{4}$. Hybrid-functional energetics corrected using PBE+U-based finite-size trends confirm the intrinsic $p$-type character of Cu$_3$N under the conditions considered and demonstrate that no single finite-size correction can be transferred across all defect types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | First-principles finite-size correction schemes for point defects of Cu$_3$N Reyes, Abdul M. Reyes-Lillo, Sebastian E. Menéndez-Proupin, Eduardo Materials Science Point defects play a key role in determining semiconductor properties, such as electrical conductivity and photoluminescence, and often enable functional behavior. Accurate first-principles supercell simulations of point defects require reliable finite-size corrections. In this study, we combine PBE+U structural relaxations with HSE hybrid-functional calculations to determine defect formation energies and thermodynamic transition levels of Cu$_3$N. Finite-size trends are quantified using $Γ$-point calculations in supercells containing 256, 864, and 2048 atoms. We assess and extend the Makov-Payne and Lany-Zunger correction schemes by introducing additional $1/L^n$ terms, together with core-level potential alignment and defect-specific scaling models. Using Cu$_3$N as a case study, we show that charged vacancies with strongly localized defect states are accurately described by the Makov-Payne-type scaling ($1/L + 1/L^{3}$), whereas interstitial defects with shallow or weakly localized electronic character are better captured by a hydrogenic impurity model that accounts for defect-band dispersion. Residual trends for neutral or weakly localized defects are described by higher-order polynomial fits in $1/L^{3}$ and $1/L^{4}$. Hybrid-functional energetics corrected using PBE+U-based finite-size trends confirm the intrinsic $p$-type character of Cu$_3$N under the conditions considered and demonstrate that no single finite-size correction can be transferred across all defect types. |
| title | First-principles finite-size correction schemes for point defects of Cu$_3$N |
| topic | Materials Science |
| url | https://arxiv.org/abs/2605.25153 |