Quantitative study of band structure in BaTiO₃ particles with vacant ionic sites

Levels of the conduction band minimum and the valence band maximum in ion-deficient BaTiO₃ particles were investigated with optical band gap and ionization energy measurements. Though it is known that the quantification of the band structure in an insulator is difficult, due to the poor electrical conductivity of BaTiO₃, systematic variation in the band energy levels was found that correlated with the introduction of vacancies. Photoelectron yield spectroscopy provided direct observation of the occupancy level of electrons, which is altered by the presence of oxygen and barium vacancies. In addition, the conduction band deviation from the vacuum level was determined by optical reflectance spectroscopy. Our results show that: (1) Introduction of oxygen vacancies forms a donor level below the conduction band. (2) The conduction band is shifted to a lower level by a larger number of oxygen vacancies, while the valence band also shifts to a lower level, due to the reduction in the density of O 2p orbitals. (3) Introduction of barium vacancies widens the band gap. Since barium vacancies can induce a small number of oxygen vacancies with accompanying charge compensation, this behavior suppresses any large formation of donor levels in the gap states, indicating that cation vacancies can control the number of both donor and acceptor levels.