Based on the first-principles calculations, the authors study defect-defect interactions between cation vacancies in rutile TiO2 and monoclinic HfO2. It was found that vacancies were greatly stabilized at small separations because of a large reconstruction of nearby oxygen atoms that have two broken bonds. As a result, O-O bonds resembling O2 or O3 molecules were formed near the divacancy site. The defect levels originated from anti-bonding states of O p-orbitals were identified within the energy gap, which could affect leakage currents and the density of trapped charges of oxides substantially.

Pairing of Cation Vacancies and Gap-State Creation in TiO2 and HfO2. Ahn, H.S., Han, S., Hwang, C.S.: Applied Physics Letters, 2007, 90[25], 252908