We have calculated the electronic structure and spectroscopic properties of the oxygen vacancy in different charge states in the monoclinic phase of $\mathrm{Hf}{\mathrm{O}}_2$. Periodic and embedded cluster calculations using density functional theory and a hybrid density functional reproduce the band gap of this material with good accuracy and predict the positions of the one-electron energy levels corresponding to five charge states of the vacancy in the band gap. The optical transition energies as well as optical and thermal ionization energies into the conduction band for all vacancy charge states and the $g$ tensor for electron spin resonance (ESR) active states are calculated. We discuss the relation of the calculated properties to metrology of vacancies using spectroscopic ellipsometry, ESR, and electrical stress measurements.

• Received 22 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.205336