Negative oxygen vacancies in HfO${}_2$ as charge traps in high-k stacks

We calculated the optical excitation and thermal ionization energies of oxygen vacancies in m-HfO${}_2$ using atomic basis sets, a non-local density functional and periodic supercell. The thermal ionization energies of negatively charged V${}^{-}$ and V${}^{2-}$ centres are consistent with values obtained by the electrical measurements. The results suggest that negative oxygen vacancies are the likely candidates for intrinsic electron traps in the hafnum-based gate stack devices.