Ellipsometry of transparent films on transparent substrates

Abstract

For an ambient-film-substrate system, where all media are transparent, homogeneous and isotropic, we show that: (1) The parallel polarization p acts as an ideal reference, in the sense that its reflection coefficient is strictly constant while that of the perpendicular polarization s varies as the film thickness changes, at an angle of incidence φ 0 such that csc 2φ 0 = ( N 0 N 1 ) 2 + ( N 0 N 2 ) 2 , where N 0, n 1 and N 2 are the refractive indices of the ambient, film, and substrate, respectively. (2) It follows from (1) that the locus in the complex plane of the ratio of reflection coefficients ρ = tan ψ e jΔ (the polar curve) becomes exactly a circle. (3) The rate of change of the relative phase shift Δ with respect to film thickness d, starting from d = 0, is maximum when the film refractive index equals the geometric mean of the substrate and ambient refractive indices, i.e., N 1 = (N 0N 2) 1 2 . We discuss the effect on this latter condition of maximum delta sensitivity of small substrate absorption.