Theoretical Study on Interactions between Oxygen Vacancy and Doped Rare-Earth Elements in Barium Titanate

We performed first-principles theoretical calculations to examine the interactions between oxygen vacancy (V \text{O ) and rare-earth (RE) elements in barium titanate (BaTiO 3 ), in order to clarify the mechanism of V \text{O trapping by RE dopants, which affects the insulating reliability of BaTiO 3 -based multilayer ceramic capacitors (MLCC). It was found that V \text{O is stabilized at the first and second nearest O sites of RE at Ba site (RE \text{Ba ), and at the second nearest O site of RE at Ti site (RE \text{Ti ). The structural relaxations on bond lengths of RE \text{Ba --O and RE \text{Ti --O in BaTiO 3 , which are brought about by the existence of V \text{O at the above sites, decrease the total energy, and thus V \text{O is stabilized. Furthermore, we revealed that the stability of V \text{O increases with decreasing solution stability of RE dopants in BaTiO 3 . Accordingly, we concluded that RE dopants with higher solution energy in BaTiO 3 efficiently trap V \text{O , and thus the insulation reliability of MLCC is improved.