Optical analysis of absorbing thin films: application to ternary chalcopyrite semiconductors.

The refractive index n and the absorption coefficient a of radio frequency sputtered CuGaSe(2) and CuInSe(2) thin films were obtained by means of transmissivity (T) and reflectivity (R) measurements at normal incidence. The optical properties were determined from the rigorous expressions for the transmission and the reflection in an air/film/(glass)substrate/air multilayer system. The solutions to this system of equations are not unique, and the physically meaningful solution is identified by trying different thicknesses in the numerical approach. Usually, nonacceptable n dispersion curves are found for all thicknesses. To be able to obtain a good n dispersion curve and, therefore, a correct absorption coefficient, we propose a simple modification of the equations for R and T through a factor called the coherence factor (CF). Because of the surface roughness and the nonuniformity of n and alpha, the light rays that reflect internally in the interface between the substrate and the film have a random difference in opt cal path. The CF accounts for this effect. This modification leads to an unambiguous and accurate determination of the optical properties and thickness of thin films for all wavelengths where transmission is not negligible. The CF is shown to be greatly dependent on the thickness of the film. This method can be used even when the R and T spectra do not have interference fringes. This method is applied successfully to the optical analyses, in the 0.4-2.5-mum wavelength range, of CuInSe(2) and CuGaSe(2) ternary chalcopyrite thin films deposited onto glass substrates by radio-frequency sputtering.