Influence of Oxygen Vacancies on the Dielectric Properties of Hafnia
Eric J. Cockayne
First-principles calculations were used to study the effects of neutral and 2+ charged oxygen vacancies on the dielectric properties of crystalline HfO2. In agreement with previous results, the neutral vacancy is more stable on the 4-fold coordinated site, while the charged vacancy is more stable on a 3-fold coordinated site. For both vacancy positions, HfO2 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 ks is increased by 1% to 2% for neutral vacancies and suppressed by 1% to 3% for 2+ charged vacancies, with the larger changes for 3-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 ks 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 ks for charged oxygen vacancies is due to phonon hardening, which reduces the ionic response.
Physical Review B (Condensed Matter and Materials Physics)