Negative-U and polaronic behavior of the Zn-O divacancy in ZnO

Hybrid functional calculations reveal the Zn-O divacancy in ZnO, consisting of adjacent Zn and O vacancies, as an electrically active defect exhibiting charge states ranging from $2+$ to $2-$ within the band gap. Notably, the divacancy retains key features of the monovacancies, namely the negative-\textit{U} behavior of the O vacancy, and the polaronic nature of the Zn vacancy. The thermodynamic charge-state transition levels associated with the negative-\textit{U} behavior $\varepsilon$($0$/$2-$), $\varepsilon$($-$/$2-$) and $\varepsilon$($0$/$-$) are predicted to occur at 0.22, 0.42 and 0.02 eV below the conduction band minimum, respectively, resulting in \textit{U} = $-$0.40 eV. These transition levels are moved closer to the conduction band and the magnitude of \textit{U} is lowered compared to the values for the O vacancy. Further, the interaction with hydrogen has been explored, where it is shown that the divacancy can accommodate up to three H atoms. The first two H atoms prefer to terminate O dangling bonds at the Zn vacancy, while the geometrical location of the third depends on the Fermi-level position. The calculated electrical properties of the divacancy are in excellent agreement with those reported for the E4 center observed by deep-level transient spectroscopy, challenging the O vacancy as a candidate for this level.