Correlation Effects on Lattice Relaxation and Electronic Structure of ZnO within the GGA plus U Formalism

The electronic structures of ZnO were calculated using density functional theory, in which the electronic interactions are described within the GGA+U (GGA = generalized gradient approximation) formalism, where on-site Coulomb corrections are applied on the Zn 3d orbitals (U-d) and O 2p orbitals (U-p). The relaxed GGA+U calculation can correct completely the band gap, the position of Zn 3d states, the transition levels of O vacancy in band gap, and so on, which is different from other GGA+U (equivalent LDA+U) calculations partially correcting the energy band structure for fixed lattice constants. By comparing with experimental data, the pair of U-d = 10 and U-p = 7 eV was identified as an optimum choice for the energy band structure of W-ZnO. Then, the proper pair of U-d and U-p parameters was taken to predict the energy band structure of ZB- and RS- ZnO, of which the former is in good agreement with experimental values, and the latter is in dispute, relating to the decrease of the octahedral symmetry. Subsequently, we pay special attention to the possible causes of the decrease of lattice constants deriving from the +U correction. Further, the formation energies and transition levels of O vacancy in W-ZnO were calculated using three different schemes to address possible routes to presenting the defect states in band gap. Our results provide some guidance for improving electronic structure of ZnO using the GGA+U approach.