Negative oxygen vacancies in $HfO2$ as charge traps in high-$k$ stacks

The optical excitation and thermal ionization energies of oxygen vacancies in $m-HfO2$ are calculated using a non-local density functional theory with atomic basis sets and periodic supercell. The thermal ionization energies of negatively charged $V−$ and $V2−$ centers are consistent with values obtained by the electrical measurements. The results suggest that negative oxygen vacancies are essentially polaronic in origin. They are likely candidates for intrinsic shallow electron traps in the hafnium based gate stack devices.