Oxygen Vacancy in ZnO-$w$ Phase: Pseudohybrid Hubbard Density Functional Study

TL;DR

This paper investigates the effects of including Hubbard corrections for oxygen 2p orbitals in ZnO, revealing significant impacts on electronic properties and defect states, especially around oxygen vacancies, through ab initio calculations.

Contribution

It introduces a pseudohybrid Hubbard density functional approach with corrections for both Zn 3d and O 2p orbitals, providing new insights into defect states in ZnO.

Findings

U_O-2p significantly affects lattice constants and bandgap.

Localized defect states are primarily influenced by nearby Zn atoms.

Hubbard correction alters the overlap of defect states with conduction bands.

Abstract

The study of zinc oxide, within the homogeneous electron gas approximation, results in overhybridization of zinc $3d$ shell with oxygen $2p$ shell, a problem shown for most transition metal chalcogenides. This problem can be partially overcome by using LDA+$U$ (or, GGA+$U$) methodology. However, in contrast to the zinc $3d$ orbital, Hubbard type correction is typically excluded for the oxygen $2p$ orbital. In this work, we provide results of electronic structure calculations of an oxygen vacancy in ZnO supercell from ab initio perspective, with two Hubbard type corrections, $U_{\mathrm{Zn}-3d}$ and $U_{\mathrm{O}-2p}$. The results of our numerical simulations clearly reveal that the account of $U_{\mathrm{O}-2p}$ has a significant impact on the properties of bulk ZnO, in particular the relaxed lattice constants, effective mass of charge carriers as well as the bandgap. For a set of validated values of $U_{\mathrm{Zn}-3d}$ and $U_{\mathrm{O}-2p}$ we demonstrate the appearance of a localized state associated with the oxygen vacancy positioned in the bandgap of the ZnO supercell. Our numerical findings suggest that the defect state is characterized by the highest overlap with the conduction band states as obtained in the calculations with no Hubbard-type correction included. We argue that the electronic density of the defect state is primarily determined by Zn atoms closest to the vacancy.