Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra

Thickness inhomogeneities in thin films have a large influence on their optical transmission and reflection spectra. If not taken into account, this may lead to rather large calculated values for the absorption coefficient or the erroneous presence of an absorption-band tail, as well as to significant errors in the calculated values of the refractive index and the film thickness. The effect of thickness variation on the optical reflection spectrum of a thin dielectric film covering a thick non-absorbing substrate, is analysed in detail in this paper, and analytical expressions are presented for such a reflection spectrum and its upper and lower envelopes. A method is suggested for determining the refractive index n(lambda) and the extinction coefficient k(lambda), as well as the average thickness and the thickness variation, of a thin dielectric film with variable thickness, by using only the two envelopes of the corresponding shrunk reflection spectrum. This method is used for the geometrical and optical. characterization of thermally-evaporated amorphous chalcogenide films, deposited on glass substrates.