First principles study of defect-induced electronic properties across temperature-dependent phases of BaTiO₃

Barium titanate (BaTiO₃) undergoes a sequence of temperature-driven structural phase transitions that greatly influence its electronic structure. In this work, first-principles density functional theory calculations are employed to provide a systematic, phase-resolved investigation of native vacancies across the four equilibrium bulk phases of BaTiO₃ - rhombohedral, orthorhombic, tetragonal, and cubic. Evolution depending on structural symmetry is observed for the band structure, with a progressive bandgap reduction from the low-symmetry rhombohedral phase to the high-symmetry cubic phase. The introduction of vacancies generates distinct defect states within the bandgap, accompanied by characteristic Fermi-level shifts that reflect donor and acceptor-like electronic behavior. Formation energy calculations show that oxygen vacancies are energetically favored in all phases, indicating their primary role in modifying the electronic properties of BaTiO₃. Optical absorption spectrum reveals corresponding defect-induced low-energy transitions, while phonon analysis confirms the dynamic stability of the structures. These results clarify the relationship between crystal symmetry, defect energetics, and electronic structure in BaTiO₃ and thus offer predictive insight into its temperature-dependent electronic behavior.