Anisotropic charge screening and supercell size convergence of defect formation energies

Murphy, Samuel T.; Hine, Nicholas D. M.

doi:10.1103/physrevb.87.094111

Cited by 108 publications

(114 citation statements)

References 43 publications

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“…Such excellent linear behavior also indicates that the dielectric properties of the benzene crystal are isotropic. If this was not the case, then the data obtained for supercells of different shapes would have shown a large spread, and only data for supercells constructed by repeating the same units along a specific crystallographic direction would have been on a straight line [60]. We remark here that our CDFT energies have an uncertainty of about 10-20 meV with our calculation parameters.…”

Section: Resultsmentioning

confidence: 81%

Fundamental gap of molecular crystals via constrained density functional theory

et al. 2016

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The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.

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Section: Resultsmentioning

confidence: 81%

Fundamental gap of molecular crystals via constrained density functional theory

et al. 2016

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“…The isotropic FNV correction with a dielectric constant, which is a typical approximation, does not avail to correct E f [V Ti ] as also reported in Ref. 54. The potential alignmentlike term in the anisotropic FNV scheme corrects the remaining cell size/shape dependence, and it almost vanishes in large supercells.…”

Section: Without Corrections E F [V −4mentioning

confidence: 93%

Electrostatics-based finite-size corrections for first-principles point defect calculations

2014

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Finite-size corrections for charged defect supercell calculations typically consist of image-charge and potential alignment corrections. A wide variety of schemes for both corrections have been proposed for decades. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a novel method that enables us to accurately estimate the correction energy a posteriori through alignment of the defect-induced potential to the model charge potential [C. Freysoldt, J. Neugebauer, and C. G. Van de Walle, Phys. Rev. Lett. 102, 016402 (2009).] This method, however, still has two issues in practice. Firstly, it uses planar-averaged electrostatic potential for determining the potential offset, which cannot be readily applied to relaxed atomic structure. Secondly, the long-range Coulomb interaction is assumed to be screened by a macroscopic dielectric constant. This is valid only for cubic systems and can bring forth huge errors for defects in anisotropic materials, particularly with layered and low-dimensional structures. In the present study, we use the atomic site electrostatic potential as a potential marker instead of the planar-averaged potential, and extend the FNV scheme by adopting the point charge model in an anisotropic medium for estimating long-range interactions. We also revisit the conventional potential alignment correction and show that it is fully included in the image-charge correction and therefore unnecessary. In addition, we show that the potential alignment corresponds to a part of first-order and full of third-order image-charge correction; thus the third-order imagecharge contribution is absent after the potential alignment. Finally, a systematic assessment of the accuracy of the extended FNV correction scheme is performed for a wide range of material classes: β-Li 2 TiO 3 , ZnO, MgO, corundum Al 2 O 3 , monoclinic HfO 2 , cubic and hexagonal BN, Si, GaAs, and diamond. The defect formation energies with -6 to +3 charges calculated using around 100-atom supercells are successfully corrected even after atomic relaxation within a few tenths of eV compared to those in the dilute limit.

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“…Finally, E corr [q] allows for corrections due to 'finite size effects', this is usually split into three corrections; (i) the potential alignment which aligns the VBM of the host supercell and the VBM of the defective supercell, (ii) an image charge correction which accounts for the interaction with the charged defect and its periodic images due to the long ranged nature of the Coulomb interaction. 51,52 The correction scheme used for this takes into account the dielectric tensor in a method laid out by Murphy et al 53 Lastly (iii) a band filling correction is applied to account for the high defect concentrations present in supercells in a formalism defined by Lany and Zunger.…”

Section: 45mentioning

confidence: 99%