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Importance of the correct Fermi energy on the calculation of defect formation energies in semiconductors
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10.1063/1.4745779
/content/aip/journal/apl/101/8/10.1063/1.4745779
http://aip.metastore.ingenta.com/content/aip/journal/apl/101/8/10.1063/1.4745779

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of the ambiguity introduced into when the transition level is corrected to reflect its position in the actual band gap. (a) The formation energy, as a function of Fermi energy, of a prototypical donor calculated with DFT (note the underestimated band gap). (b) The formation energy of the same donor within the actual gap if we make the assumption that is correctly calculated within DFT. (c) The formation energy of the same donor within the actual gap if we make the different assumption that is correctly calculated within DFT.

Image of FIG. 2.
FIG. 2.

A schematic diagram showing the parameters used in the theory. In drawing the diagram, we made the assumption that vacuum levels in DFT and exact method calculations are the same.

Image of FIG. 3.
FIG. 3.

A schematic illustration of the (a) ideal relationship between calculated by DFT and by exact method. When is nonzero, one should not use a single to define the position of the Fermi level . Rather, they are offset by . For example, for the (2+) charge state is too high than by 2. In practice, Eq. (7) is only approximate, yielding the difference exaggerated and indicated in (b).

Image of FIG. 4.
FIG. 4.

(a) (xy-plane) averaged electrostatic potential as a function of z for half of the 〈1120〉 ZnO slab and bulk-region average of this average potential. Atomic positions are shown at the bottom. (b) Comparison of the VBM and CBM calculated by different methods and measured by experiments for Si, GaAs, and ZnO.

Image of FIG. 5.
FIG. 5.

Formation energies calculated from PBE and HSE, shown as dashed (red) and solid (black) lines, respectively. The shaded area indicates the PBE band gap which is offset from the VBM of HSE by the calculated .

Tables

Generic image for table
Table I.

Calculated formation energies of charged defects in eV using the PBE and HSE functionals, with at their respective VBMs. is the difference between the formation energies and (defined in the text) is the difference after the ionization energy is corrected.

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/content/aip/journal/apl/101/8/10.1063/1.4745779
2012-08-22
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Importance of the correct Fermi energy on the calculation of defect formation energies in semiconductors
http://aip.metastore.ingenta.com/content/aip/journal/apl/101/8/10.1063/1.4745779
10.1063/1.4745779
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