The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence

Abstract

The derivation of the components n and k of the complex refractive index of a thin film from measurements, at normal incidence, of reflectance R and transmittance T is complicated by the existence of multiple solutions of the relevant equations. It is shown that, although use of Tomlin's expressions for (1 ± R)/T rather than Heavens's explicit formulae for R and T separately simplifies the problem, it is still necessary to consider very carefully the multiple solutions. A procedure is given for determining the correct solutions for n and k, and also for accurately fixing the film thickness, provided that the film is a homogeneous single layer on a substrate. Some experimental results have not yielded to this treatment and in these cases it has been found necessary to assume the presence of a surface layer (often, but not necessarily, an oxide layer) and to make use of the equations in the preceding paper which relate to a double layer on a substrate. It is shown how this may be done in such a way as to obtain the correct dispersion curve for the material, together with its thickness, and that of the surface layer.