Accuracy of the Heyd-Scuseria-Ernzerhof hybrid functional to describe many-electron interactions and charge localization in semiconductors

Hybrid functionals, which mix a fraction of Hartree-Fock exchange with local or semilocal exchange, have become increasingly popular in quantum chemistry and computational materials science. Here, we assess the accuracy of the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional to describe many-electron interactions and charge localization in semiconductors. We perform diffusion quantum Monte Carlo calculations to obtain the accurate ground-state spin densities of the negatively charged (${\mathrm{SiV})}^{-}$ and the neutral (${\mathrm{SiV})}^0$ silicon-vacancy center in diamond and of the cubic silicon carbide (3C-SiC) with an extra electron. We compare our diffusion quantum Monte Carlo results with those obtained with the HSE functional and find a good agreement between the two methods for (${\mathrm{SiV})}^{-}$ and (${\mathrm{SiV})}^0$, whereas the correct description of 3C-SiC with an extra electron crucially depends on the amount of Hartree-Fock exchange included in the functional. Also, we examine the case of the neutral Cd vacancy in CdTe, for which we assess the performance of HSE versus the many-body GW approximation for the description of the position of the defect states in the band gap.

Figure 1

Schematic of the electronic structure and the corresponding electron spin density ($\rho =20$% of the maximum) obtained by HSE and DMC calculations of the negatively charged silicon-vacancy center in diamond in ${\mathrm{D}}_{3d}$ (left) and ${\mathrm{C}}_{2h}$ symmetry (right).

Figure 2

Schematic of the electronic structure and the corresponding electron spin density ($\rho =20$% of the maximum) obtained by HSE and DMC calculations of the silicon-vacancy center in diamond in the neutral charge state in ${\mathrm{D}}_{3d}$ symmetry.

Figure 3

Dissociation energy curve of the ${\mathrm{H}}_2$ molecule obtained by DMC, PBE, and HSE calculations.

Figure 4

Electron spin density ($\rho =40$% of the maximum) of 3C-SIC obtained by HSE (left) and DMC (right) calculations. Beige and turquoise spheres represent Si and C atoms, respectively.

Figure 5

Electronic band structures and charge density isosurfaces ($\rho =0.002e/{\mathrm{bohr}}^3$) corresponding to the energy level labeled A of the neutral cation vacancy in CdTe (left) and ZnTe (right), in ${\mathrm{C}}_{2v}$ symmetry. Brown spheres represent Te atoms; beige and azure spheres represent Cd and Zn atoms, respectively. Calculations were performed at the DFT-PBE level in a 128-atom supercell.