When polarized light is reflected from a film-covered surface, the variations in Δ and Ψ with the film thickness d are given by the exact equation of ellipsometry. Δ is the change in the difference between the phases of the parallel (p) and the perpendicular (s) components of the polarized light on reflection, and Ψ is the arc tangent of the factor by which the amplitude ratio of the p and s components changes on reflection. A first-order calculation of the exact equation is presented from which the two Archer equations for Δ and Ψ (which are more accurate than those derived by Drude), relating their variations with the film thickness d, have been derived. Until now, both of these equations have been considered to be valid only in the thin-film region by most of the authors except Burge and Bennett who questioned the usefulness of the linear approximation for Ψ. It is shown that the Archer equation for Ψ is not valid in the thin-film region and a new generalized equation for Ψ is derived which is valid not only in the thin-film region (~100 Å) but also in certain ranges of the thick-film region. Further, a generalized approximate equation for Δ has also been derived which holds in the thin-film as well as in certain ranges of the thick-film regions. Experimental data to check the validity of the generalized approximate equation for Δ in the thick-film region are presented.
A. N. SAXENA, "Changes in the Phase and Amplitude of Polarized Light Reflected from a Film-Covered Surface and Their Relations with the Film Thickness," J. Opt. Soc. Am. 55, 1061-1067 (1965)