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Volumn 78, Issue 23, 2008, Pages

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs

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EID: 57749196971     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.235104     Document Type: Article
Times cited : (1175)

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    • Since ideally delocalized, i.e., bandlike, free electrons and holes do not break translational symmetry, EH (+1) and EH (-1) are calculated using a four-atom ZnO unit cell with the corresponding carrier density. A 18×18×12 k mesh and the linear tetrahedron method are used for Brillouin-zone integrations. The interaction of the electronic charge with the jellium background is included (see Sec. 2).
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    • Due to finite-size effects in the supercell used in Refs., the energy of the a1 state of VO appears at somewhat too low energy at the Brillouin-zone center (cf. Fig. 5 and discussion in Sec. 4 2). Therefore, we take here the Brillouin-zone average of the a1 state as shown in Figs. 2 and 4 of Ref. and in Fig. 3 of Ref..
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    • In order to avoid the large (positive and negative) local charge differences caused by a shift of atoms, we determine the second-order moment Qr in Eq. 11 with the same atomic relaxation pattern in the defect and host-reference calculations.
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    • This slow convergence is likely related to the fact that in the fcc supercell symmetry, the defect images are connected along the cation-anion "zigzag" chains in the [110] direction of the zinc-blende lattice, which apparently causes larger residual defect-defect interactions than in case of the sc or bcc symmetries, where the defect images are oriented along the [001] and [111] lattice directions, respectively.
    • This slow convergence is likely related to the fact that in the fcc supercell symmetry, the defect images are connected along the cation-anion "zigzag" chains in the [110] direction of the zinc-blende lattice, which apparently causes larger residual defect-defect interactions than in case of the sc or bcc symmetries, where the defect images are oriented along the [001] and [111] lattice directions, respectively.
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