Effects of Ionic Doping on the Behaviors of Oxygen Vacancies in HfO2 and ZrO2: A First Principles Study

The effects of metallic ion (Al, Ti, or La) doping in HfO
₂
or ZrO
₂
on the behaviors of oxygen vacancies (V
₀
) such as the formation energy, density of states, and migration energy were investigated by using first principles calculations. The calculations show that, 1) the doping causes an upward shift of deep V
₀
levels; 2) dopant radius has a weak impact on the relaxed formation energy of V
₀
(E
_j

^v
) but a significant impact on the unrelaxed E
_f

^v
; 3) the relaxed formation energy E
_f

^v
of V
₀
is remarkably reduced by trivalent ion (Al or La) doping compared to by tetravalent ion (Ti) doping; 4) Al, Ti, or La doping impacts the migration barriers of V
₀
along different directions.