First-principles calculations were used to study the effects of neutral and 2+ charged O vacancies upon the dielectric properties of crystalline HfO2. In agreement with previous results, the neutral vacancy was found to be more stable on 4-fold coordinated sites, while the charged vacancy was more stable on 3-fold-coordinated sites. For both vacancy positions, HfO2 remained insulating no matter whether the vacancy was neutral, or in the 2+ charge state. The dynamic matrix, Born effective charges and electronic dielectric tensor were calculated for each structure. With one O vacancy per 64 oxygen atoms, the static dielectric constant increased by 1 to 2% for neutral vacancies and was suppressed by 1 to 3% for 2+ charged vacancies; with the larger changes occurring for 3-fold coordinated vacancies. The exact result in the case of a charged vacancy depended upon how the neutralizing charge, required for macroscopic charge neutrality, was modeled. The increase in the static dielectric constant for neutral O vacancies arose from an enhancement of the electronic dielectric response due to a pair of electrons which occupied an easily polarizable F-center defect state. The suppression of the static dielectric constant for charged O vacancies was due to phonon hardening, which reduced the ionic response. No evidence was found for a characteristic localized phonon, induced by O vacancies, that could be detected using infra-red or Raman spectroscopy.

Influence of Oxygen Vacancies on the Dielectric Properties of Hafnia - First-Principles Calculations. E.Cockayne: Physical Review B, 2007, 75[9], 094103 (8pp)