Fermi Level Pinning In Co-Doped Batio3: Part Ii. Defect Chemistry Models

A first-principles informed grand canonical defect chemistry model capable of accounting for non-stoichiometry and partial equilibration of different sub-lattices is developed and used to study Mg and Mn doped, and (Mg+Y) and (Mn+Y) co-doped BaTiO3 to elucidate the role of Mn and Y in improving the resistivity and resistance degradation of BaTiO3 as observed by Ryu et al. in Part I of this series of papers. The model qualitatively captures the behavior of the samples in all conditions, reproducing the observed carrier plateau and increased resistivity of (Mn+Y) co-doped BaTiO3, and expected trends in the concentrations of free oxygen vacancies with doping. These trends reflect the observed differences in degradation characteristics, and help explain the substantially improved degradation resistance of the (Mn+Y) co-doped samples. Our model adds to the mechanism proposed by Yeoh et al. that the Fermi level is pinned by the multivalent character of Mn-Ti in (Mn+Y) co-doped BaTiO3 by giving insight into the role of barium vacancies, the site preferences of the dopants, and defect complexes in this mechanism. These insights provide a set of criteria in the search for sets of co-dopants with similar behaviors.