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 HfO₂ or ZrO₂ on the behaviors of oxygen vacancies (V₀) 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 V₀ levels; 2) dopant radius has a weak impact on the relaxed formation energy of V₀ (E_j ^v) but a significant impact on the unrelaxed E_f ^v; 3) the relaxed formation energy E_f ^v of V₀ 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 V₀ along different directions.