Microstructural and optical investigations of sol-gel derived ferroelectric BaTiO₃ nanocrystalline films determined by spectroscopic ellipsometry

Ferroelectric BaTiO₃ nanocrystalline films (BTNFs) with the crystalline sizes of about 30 nm were grown on Pt/Ti/SiO₂/Si substrates by a modified sol-gel method. Spectroscopic ellipsometry (SE) was used to characterize the films in the photon energy range of 1.5-5.0 eV with a five-phase layered model (air/surface rough layer/BaTiO₃/interface layer/Pt). The optical properties in the transparent and absorption regions have been investigated with the Forouhi-Bloomer dispersion relation. With the aid of the structural and dielectric function models, the microstructure and electronic structure of the BTNFs can be readily obtained. It was found that the refractive index reaches the value of 2.20 in the transparent region. Based on the Sellmeier dispersion analysis, the single-oscillator energy is about 4.7 eV for the BTNFs. The long wavelength refractive index n (0) can be estimated to about 2.00 at zero point. The direct optical band gap energy approaches approximately 4.2 eV and Urbach band tail energy is 262 ± 2 and 268 ± 1 meV respectively with increasing crystalline size. A higher band gap observed can be owing to the known quantum confinement effect in the nanocrystalline formation and different fraction of amorphous and crystalline components. The theoretical analysis based on the effective mass approximation theory is well used to explain these experimental data.