Modified Envelope Method for Obtaining Optical Properties of Weakly Absorbing Thin Films and Its Application to Thin Films of Pb(Zr,Ti)O3 Solid Solutions

A modified envelope method, which includes the consideration of the light intensity loss from the back surface of the substrate, was developed and shown to be a simple and convenient tool for obtaining the optical properties and the thickness of the film by using the transmission spectra alone in the medium and weak absorption regions. In the near-optical band gap region, both the transmission and the reflection spectra were used to calculate the optical constants of the films. This technique was applied to the thin films of PZT solid solutions across the entire composition range. The film thickness derived from the envelope method was cross-checked by a computer simulation method and was found to have an accuracy better than 2%. In addition, the refractive indices were fitted to a simple Sellmeier-type equation for determining the dispersion constants for PZT films. The valid wavelength range of these dispersion relations was from 350 to 2000 nm. The refractive index of the PZT films decreased linearly with increasing zirconium content. On the other hand, the optical band gap energy of the PZT films increased with increasing zirconium content.