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Hybrid functional calculations reveal the Zn-O divacancy in ZnO, consistingof adjacent Zn and O vacancies, as an electrically active defect exhibitingcharge states ranging from $2+$ to $2-$ within the band gap. Notably, thedivacancy retains key features of the monovacancies, namely thenegative-\textit{U} behavior of the O vacancy, and the polaronic nature of theZn vacancy. The thermodynamic charge-state transition levels associated withthe negative-\textit{U} behavior $\varepsilon$($0$/$2-$),$\varepsilon$($-$/$2-$) and $\varepsilon$($0$/$-$) are predicted to occur at0.22, 0.42 and 0.02 eV below the conduction band minimum, respectively,resulting in \textit{U} = $-$0.40 eV. These transition levels are moved closerto the conduction band and the magnitude of \textit{U} is lowered compared tothe values for the O vacancy. Further, the interaction with hydrogen has beenexplored, where it is shown that the divacancy can accommodate up to three Hatoms. The first two H atoms prefer to terminate O dangling bonds at the Znvacancy, while the geometrical location of the third depends on the Fermi-levelposition. The calculated electrical properties of the divacancy are inexcellent agreement with those reported for the E4 center observed bydeep-level transient spectroscopy, challenging the O vacancy as a candidate forthis level.

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