Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional

The Heyd-Scuseria-Ernzerhof (HSE) screened hybrid density functional has been proven to yield lattice constants and energy gaps of semiconductors in better agreement with experiment than standard local and semilocal exchange correlation functionals. The latter underestimate the band gaps of many semiconductors severely, i.e., in the case of ZnO the underestimation amounts to 75% of the experimental value. In this work, we report on the structure optimization and the study of the electronic band gap of ZnO in the wurtzite phase performed within density-functional theory using the semilocal Perdew-Burke-Ernzerhof as well as the HSE functional. Furthermore, the phonon-dispersion relations of ZnO and the dielectric and piezoelectric properties are calculated with both functionals and are compared to experimental findings.

Figure 1

(Color online) Total energy versus unit-cell volume of ZnO calculated with the PBE (circles) and the HSE (squares) functional. The experimental equilibrium volume at ambient conditions is indicated by the vertical dotted line.

Figure 2

(Color online) (left) Density of states and (right) band structure of ZnO obtained using the PBE functional. The character of the bands is indicated by the color [Zn($d$) circles, O($p$) squares], whereas the size of the symbols corresponds to the partial occupancies. The Fermi level is indicated by the horizontal line.

Figure 3

(Color online) Band structure of ZnO obtained using the HSE functional. The $d$ bands (circles) are indicated by the red color, whereas the green color indicates the $p$ bands (squares). The size of the symbols corresponds to the partial occupancies. The Fermi level is indicated by the horizontal line.

Figure 4

(Color online) PBE phonon-dispersion curves of ZnO calculated at the PBE optimized volume (dotted line) as well as at the experimental equilibrium volume (full line). The black dots correspond to the experimental values given in Ref. 37.

Figure 5

(Color online) HSE phonon-dispersion curves of ZnO calculated at the HSE optimized volume (dotted line) as well as at the experimental equilibrium volume (full line). The black dots correspond to the experimental values given in Ref. 37.

Figure 6

(Color online) Phonon-dispersion curves of ZnO calculated using PBE (blue lines) and the HSE functional (red lines). The crystal volume has been fixed to the experimental value. The black dots correspond to the experimental values given in Ref. 37.