Quasiparticle Excitations and Charge Transition Levels of Oxygen   Vacancies in Hafnia
  We calculate the quasiparticle defect states and charge transition levels of oxygen vacancies in monoclinic hafnia. The charge transition levels, although they are thermodynamic quantities, can be critically dependent on the band gap owing to localized defect states. These quasiparticle defect level effects are treated using the first principle GW approximation to the self energy. We show that the quality and reliability of the results may be evaluated by calculating the same transition level via two physical paths and that it is important to include the necessary electrostatic corrections in a supercell calculation. Contrary to many previous reports, the oxygen vacancies in monoclinic hafnia are found to be a positive U center, where U is the defect electron addition energy. We identify a physical partitioning of U in terms of an electronic and structural relaxation part. 
Manish Jain, James R. Chelikowsky and Steven G. Louie
cond-mat.mtrl-sci