Convergence of supercell calculations for point defects in semiconductors: Vacancy in silicon

Puska, Martti J.; Pöykkö, S.; Pesola, M.; Nieminen, Risto M.

doi:10.1103/physrevb.58.1318

Cited by 249 publications

(203 citation statements)

References 44 publications

(38 reference statements)

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“…The original choice of the FCC supercell [8] for the calculations in 3C-polytype is somewhat unfortunate in the case of defects inducing large ionic replacements, as the elastically rigid [110] zigzag-chains directly connect the defects to their periodic images [25]. This, in together with the defect band dispersion, the Γ-point sampling of the first Brillouin zone, and the small energy gap of 3C structure compared to 4H and 6H structures, may result in an incorrect description of the ionic and electronic structures even when using moderately sized supercells [26]. Intuitively, and based on the ab inito calculations in the 4H-polytype [27], one would expect that the stable structure of the silicon interstitial in 3C-SiC would be a split configuration as well.…”

Section: Discussionmentioning

confidence: 99%

Self-interstitials in 3C-SiC

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Torpo

Staab

et al. 2004

J. Phys.: Condens. Matter

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Abstract. We report results from density-functional plane-wave pseudopotential calculations for carbon and silicon self-interstitials in cubic silicon carbide (3C-SiC). Several initial ionic configurations are used in the search for the global totalenergy minimum including tetragonal, split [100] and split [110] geometries. Neutral carbon interstitials are found to have several nearly degenerate total-energy minima configurations in split-interstitial geometries, with formation energies rangingbesides higher metastable ones -from 6.3 to 6.7 eV in stoichiometric SiC. In contrast, the neutral silicon interstitials have a clear single minimum total-energy configuration at the tetrahedral configuration with carbon nearest neighbours, exhibiting a formation energy of 6.0 eV. The split interstitial in the [110] direction at silicon site and the tetrahedral configuration with silicon nearest neighbours are metastable and have significantly higher formation energies. The present calculations indicate that the carbon interstitial introduces deep levels in the band gap while the silicon interstitial at the tetrahedral site behaves like a shallow donor.

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Section: Discussionmentioning

confidence: 99%

Self-interstitials in 3C-SiC

Lento

Torpo

Staab

et al. 2004

J. Phys.: Condens. Matter

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“…42,43 One can get even qualitatively different results with two different approximations, e.g., for the exchange-correlation potential. 43 We study now the monovacancy in Si including the forces caused by the localized positron.…”

Section: Neutral Monovacancy In Simentioning

confidence: 99%

Modeling the momentum distributions of annihilating electron-positron pairs in solids

2006

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Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material. Vacancy-type defects in solids localize positrons and the measured spectra are sensitive to the detailed chemical and geometric environments of the defects. However, the measured information is indirect and when using it in defect identification comparisons with theoretically predicted spectra is indispensable. In this article we present a computational scheme for calculating momentum distributions of electron-positron pairs annihilating in solids. Valence electron states and their interaction with ion cores are described using the all-electron projector augmented-wave method, and atomic orbitals are used to describe the core states. We apply our numerical scheme to selected systems and compare three different enhancement ͑electron-positron correlation͒ schemes previously used in the calculation of momentum distributions of annihilating electron-positron pairs within the density-functional theory. We show that the use of a state-dependent enhancement scheme leads to better results than a position-dependent enhancement factor in the case of ratios of Doppler spectra between different systems. Further, we demonstrate the applicability of our scheme for studying vacancy-type defects in metals and semiconductors. Especially we study the effect of forces due to a positron localized at a vacancytype defect on the ionic relaxations.

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“…In the present calculations, we ensure k-point sampling convergence of the formation energies, as the importance of this issue has been highlighted several times in the study of defect corrections. 2,34,35 The formation energies are plotted with respect L −1 , where L is the side of the supercell. In all figures, lines of the form aL −1 + bL −3 + c are fitted to the calculated values to obtain extrapolated values corresponding to the limit L → ∞.…”

Section: A Computational Detailsmentioning

confidence: 99%

Finite-size supercell correction schemes for charged defect calculations

2012

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Various schemes for correcting the finite-size supercell errors in the case of charged defect calculations are analyzed and their performance for a series of defect systems is compared. We focus on the schemes proposed by Makov and Payne (MP), Freysoldt, Neugebauer, and Van de Walle (FNV), and Lany and Zunger (LZ). The role of the potential alignment is also assessed. We demonstrate a connection between the defect charge distribution and the potential alignment, which establishes a relation between the MP and FNV schemes. Calculations are performed using supercells of various sizes and the corrected formation energies are compared to the values obtained by extrapolation to infinitely large supercells. For defects with localized charge distributions, we generally find that the FNV scheme improves upon the LZ one, while the MP scheme tends to overcorrect except for pointcharge-like defects. We also encountered a class of defects, for which all the correction schemes fail to produce results consistent with the extrapolated values. These are found to be caused by partial delocalization of the defect charge. We associate this effect to hybridization between the defect state and the band-edge states of the host. The occurrence of defect charge delocalization also reflects in the evolution of the defect Kohn-Sham levels with increasing supercell size. We discuss the physical relevance of the latter class of defects.

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Convergence of supercell calculations for point defects in semiconductors: Vacancy in silicon

Cited by 249 publications

References 44 publications

Self-interstitials in 3C-SiC

Self-interstitials in 3C-SiC

Modeling the momentum distributions of annihilating electron-positron pairs in solids

Finite-size supercell correction schemes for charged defect calculations

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