Vacancy and interstitial defects in hafnia

We have performed plane wave density functional theory calculations of atomic and molecular interstitial defects and oxygen vacancies in monoclinic hafnia $({\mathrm{HfO}}_{2}).$ The atomic structures of singly and doubly positively charged oxygen vacancies, and singly and doubly negatively charged interstitial oxygen atoms and molecules are investigated. We also consider hafnium vacancies, substitutional zirconium, and an oxygen vacancy paired with substitutional zirconium in hafnia. Our results predict that atomic oxygen incorporation is energetically favored over molecular incorporation, and that charged defect species are more stable than neutral species when electrons are available from the hafnia conduction band. The calculated positions of defect levels with respect to the bottom of the silicon conduction band demonstrate that interstitial oxygen atoms and molecules and positively charged oxygen vacancies can trap electrons from silicon.