Calculation of the thickness and optical constants of lead titanate thin films grown on MgO from their transmission spectra

In this paper, the optical constants and thickness of thin lead titanate (PbTiO_3) films are investigated. The studied films are grown by pulsed laser deposition on MgO substrate. The interference modulated transmission spectra T(λ) at normal incidence were obtained in the spectral region from 300 nm up to 1000 nm. The presented films have been characterized using the extremes of the interference fringes in accordance with the straightforward method proposed by Swanepoel which is applied to derive the real and imaginary parts of the complex index of refraction and also the film thickness. We have therefore determined the dispersion of the real part of the refractive index, the absorption and extinction coefficients. Furthermore, the energy band gap has been determined from the absorption coefficient values using the direct transition model proposed by Tauc.