Swanepoel method for estimating the film thickness and complex index of refraction by using only the lower envelope: Special case

Abstract

Over the last few decades, a large number of research papers on the optical properties of thin films have been published, and significant efforts have been made to supply a mathematical formulation that can describe the transmittance (T(λ)) and reflectance (R(λ)) of various optical systems. Swanepoel suggested a straightforward analysis using the upper (TM) and lower (Tm) envelopes of measured transmittance. He suggested a good correlation between the index of refraction (n), Tm, and absorbance (x) in the form of (Tm=16n2sx/(A+Bx+Cx2) where s, A, B, and C parameters are given in the text). He solved this equation to determine the value of the refractive index (see eq. (9) in Ref.1). Here comes the question why we do not resolve the equation to determine the value of the absorption coefficient?In this investigation the author tries to estimate both the film refractive index (n), absorbance (x) based only on the values of Tm and without any dependence on the film thickness (t). Also, a new analysis to find the film thickness precisely is based on the interference fringes main equation (2 nt = mλ).