Theoretical and experimental studies of formation and migration of oxygen vacancies in BaMxTi1−xO3 (M = Zr, Ge)

The formation and migration energies of oxygen vacancies in pure BaTiO3, and BaMxTi1−xO3 (M = Zr, Ge) are calculated by first-principles calculations to understand the effect of doping on the reliability of multilayer ceramic capacitors (MLCCs). The formation and migration energies of oxygen vacancies are found to be larger in BaZrxTi1−xO3 than in BaTiO3. This finding could be one of the possible reasons behind the improved reliability of Zr-doped MLCCs materials. On the other hand, by substituting Ge, the migration energy of BaGexTi1−xO3 becomes larger than that of BaTiO3. This is despite the smaller oxygen vacancy formation energy in BaGexTi1−xO3 than in BaTiO3. Even though Zr and Ge are tetravalent in BaMxTi1−xO3, their valence states are different after the formation of oxygen vacancies, providing an explanation for the differences in vacancy formation and migration energies between BaZrxTi1−xO3 and BaGexTi1−xO3. Our theoretical results are further confirmed by experiments on these model systems.