Abstract
This study reports on the determination of the optical constants of a lead-free ferroelectric material, Na0.5Bi0.5TiO3. The optical transmission measurements were carried out in the 300–3000 nm wavelength range, on a 100-oriented Na0.5Bi0.5TiO3 thin film, epitaxially grown by laser ablation on a 100MgO single crystal substrate. Applying the “method of the envelopes,” developed by Manifacier et al. J. Phys. E 9, 1002 1976 and by Swanepoel J. Phys. E 16, 1214 1983, the analysis of the observed interference fringes allowed extracting some optical data for Na0.5Bi0.5TiO3, namely the linear refractive and extinction indices n and k, the absorption coefficient , and as well the nature direct or indirect transition and value of the optical band gap. It was found that n=2.321 and the transmission data suggested a 3.30 eV indirect transition. Our experimental results are thus in opposition to the few data reported so far for Na0.5Bi0.5TiO3, where a direct transition was evoked. Therefore, we have confronted the optical transmission data to supplementary diffuse reflectance and ellipsometry measurements, and finally, to first principles calculations. The diffuse reflectance data, collected for Na0.5Bi0.5TiO3 powders, indicate a 3.26 eV optical band gap. In addition, the ellipsometry measurements reveal a refractive index of 2.346 at 2.066 m, an energy gap of 3.20 eV, and also confirm the thickness of the layer. These additional data are then in very good agreement with the data derived from the optical transmission measurements. Finally, first principles calculations were carried out in the framework of the density functional theory for the three Na0.5Bi0.5TiO3 polymorphs i.e., rhombohedral, tetragonal, and cubic. For each polymorph, in order to consider the Na/Bi disorder on the perovskite A-site, three different Na/Bi distributions within the unit cell were investigated, leading to nine atomic configurations. The electronic structure of these nine configurations was then calculated after geometry optimization and only one of them did not converge. These calculations complete the above experimental data, as six electronic structures over eight presented an indirect band gap, with a band gap energy Eg falling in the 3.90–4.60 eV energy range. The latter value is higher than the experimental ones but is definitely more compatible with the energy band gap expected for ferroelectric oxide materials.