Electronic structure and spectroscopic properties were calculated for the O vacancy, in various charge states, in the monoclinic phase. Periodic and embedded cluster calculations, using density functional theory and a hybrid density functional, reproduced the band-gap of this material with good accuracy and predicted the positions of the 1-electron energy levels corresponding to 5 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 active states, were calculated. The relationship of the calculated properties to the metrology of vacancies was considered using spectroscopic ellipsometry, electron spin resonance and electrical stress measurements.

Spectroscopic Properties of Oxygen Vacancies in Monoclinic HfO2 Calculated with Periodic and Embedded Cluster Density Functional Theory. D.M.Ramo, J.L.Gavartin, A.L.Shluger, G.Bersuker: Physical Review B, 2007, 75[20], 205336 (12pp)