Assessing the accuracy of hybrid functionals in the determination of defect levels: Application to the As antisite in GaAs

The accuracy of nonscreened and screened hybrid functionals for the calculation of defect levels within the band gap is assessed for the As antisite in GaAs, the nature of which is well characterized experimentally. A set of functionals differing by the fraction of nonlocal Fock exchange or by the screening length are examined. The $+2/+1$ and the $+1/0$ charge transition levels as determined with any of the considered functionals line up when referred to the average electrostatic potential, with a defect-level separation in fair agreement with the experimental value. When the band gap is well reproduced, the calculated defect levels are found within 0.2 eV of the experimental levels. The use of the theoretical rather than the experimental lattice constant for the bulk host is found to affect the defect levels by less than 0.1 eV.

Figure 1

Formation energy (left-hand side) and charge transition levels (right-hand side) calculated at the PBE level as a function of the inverse side ($1/L$) of the supercell. The extrapolated values are obtained from a regression to $a+b/L+c/L^3$ of the results without (dashed lines) and with (solid lines) finite-size corrections. In the formation energy, the chemical potential of As corresponds to the As${}_4$ molecule and that of Ga then results from the equilibrium condition for GaAs.

Figure 2

Charge transition levels $+2/+1$ and $+1/0$ of the As antisite in GaAs calculated with various functionals, aligned with respect to (a) the average electrostatic potential and to (b),(c) the valence-band maximum. In (a) and (b), the defect structure is relaxed at the HSE level and the experimental lattice constant is adopted. In (c), the lattice constant and the defect structure are consistently determined with the adopted functional. Experimental levels (dashed) are from Ref. 11. The numerical values used in (b) and (c) are given in Table .

Figure 3

Band edges of GaAs aligned with respect to the average electrostatic potential as a function of lattice constant for various functionals. The defect levels of the unrelaxed As antisite are calculated with PBE, but their energies are also representative of the other functionals [cf. Fig. 2a]. The experimental and various theoretical lattice constants are indicated. The required fraction $\alpha$ of Fock exchange for tHSE increases from 0.34 to 0.53 as the lattice constant varies from 5.65 to 5.75 Å.

Figure 4

(a) Electron density of the defect state of the neutral As antisite in GaAs as calculated within the PBE. Two isosurfaces are superimposed, corresponding to high (opaque, red) and low (transparent, blue) values of charge density. (b) Comparison between the spherically integrated radial densities of the defect wave function as calculated in PBE (solid, blue) and in tHSE (dashed, red).