Energetics of donor-doping, metal vacancies, and oxygen-loss in A-site Rare-Earth-doped BaTiO₃

The energetics of La-doping in BaTiO₃ are reported for both (electronic) donor-doping with the creation of Ti³⁺ cations and ionic doping with the creation of Ti vacancies. The experiments (for samples prepared in air) and simulations demonstrate that ionic doping is the preferred mechanism for all concentrations of La-doping. The apparent disagreement with electrical conduction of these ionic doped samples is explained by subsequent oxygen-loss, which leads to the creation of Ti³⁺ cations. Simulations show that oxygen-loss is much more favorable in the ionic-doped system than undoped BaTiO₃ due to the unique local structure created around the defect site. These findings resolve the so-called “donor-doping” anomaly in BaTiO₃ and explain the source of semiconductivity in positive temperature coefficient of resistance (PTCR) BaTiO₃ thermistors.