Influence of oxygen vacancies on the dielectric properties of hafnia: First-principles calculations

Abstract

First-principles calculations were used to study the effects of neutral and $2+$ charged oxygen vacancies on the dielectric properties of crystalline $\mathrm{Hf}{\mathrm{O}}_{2}$. In agreement with previous results, the neutral vacancy is more stable on four fold-coordinated site, while the charged vacancy is more stable on a three fold-coordinated site. For both vacancy positions, $\mathrm{Hf}{\mathrm{O}}_{2}$ remains insulating whether the vacancy is neutral or in the $2+$ charge state. The dynamical matrix, Born effective charges, and electronic dielectric tensor were calculated for each structure. With one oxygen vacancy per 64 oxygen atoms, the static dielectric constant ${\ensuremath{\kappa}}_{s}$ is increased by 1%--2% for neutral vacancies and suppressed by 1%--3% for $2+$ charged vacancies, with the larger changes for three fold-coordinated vacancies. The exact result in the case of a charged vacancy depends on how the neutralizing charge necessary for macroscopic charge neutrality is modeled. The increase in ${\ensuremath{\kappa}}_{s}$ for neutral oxygen vacancies arises from an enhancement of the electronic dielectric response due to a pair of electrons occupying an easily polarizable $F$-center defect state. The suppression in ${\ensuremath{\kappa}}_{s}$ for charged oxygen vacancies is due to phonon hardening, which reduces the ionic response. No evidence is found for characteristic localized phonons induced by oxygen vacancies that could be detected by infrared or Raman spectroscopy.