Temperature dependent optical properties of Mn doped (Pb,Sr) TiO ₃ ferroelectric films in absorption region: Electron-phonon interaction

The 2 mol % Mn doped Pb_0.5 Sr_0.5 TiO₃ films were fabricated on sapphire substrates by chemical solution deposition. The complex dielectric functions and optical parameters of the films determined by transmittance spectroscopy in a broad temperature range of 80-500 K were investigated. Apparent thermally-driven band-gap energy shrinkage, line-width of interband electron transition broadening and the Urbach band tail behaviors were observed. The results can be mainly correlated with the renormalization of electronic band structure and band-gap energy due to the electron-phonon interaction, which is well established in terms of the Bose-Einstein model.