Defect Clustering in Rare-Earth-Doped BaTiO₃ and SrTiO₃ and Its Influence on Dopant Incorporation

Rare-earth (RE) doping of BaTiO₃ and SrTiO₃ has received tremendous research attention in recent decades. Although RE doping has been a particularly popular topic, little or no attention has been given to the contribution from different defect arrangements. In this study, we use a proven interatomic potential model to calculate the binding energies of different RE donor defect (Ba/Sr site doping) configurations in BaTiO₃ and SrTiO₃. We consider two standard donor defect mechanisms, namely, charge compensation from Ba/Sr vacancies or Ti vacancies. Consistently stronger negative binding energies are calculated for SrTiO₃ compared to BaTiO₃. We also show that SrTiO₃ can accept a larger range of RE ion sizes at the divalent cation site than BaTiO₃. This is highlighted by the simple trend of increasing binding energy with decreasing RE ion size found for the defect configurations with a Ti vacancy in SrTiO₃. Conversely, defect clustering in BaTiO₃ can cause significant strain on the lattice, resulting in positive binding energies. Our results show that one standard defect arrangement per incorporation mechanism cannot be applied to all dopants. We clearly show that the lowest energy defect configuration is dependent on both the dopant and host material. The consequences of these findings for the overall defect incorporation energetics in BaTiO₃ and SrTiO₃ are also presented.