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

Authors:
  • RDR E Denton
    R E Denton
  • RCR D Campbell
    R D Campbell
  • STS G Tomlin
    S G Tomlin
Publisher website
Google Scholar
Abstract
The derivation of the componentsnandkof the complex refractive index of a thin film from measurements, at normal incidence, of reflectanceRand transmittanceTis complicated by the existence of multiple solutions of the relevant equations. It is shown that, although use of Tomlin's expressions for (1 ±R)/Trather than Heavens's explicit formulae forRandTseparately simplifies the problem, it is still necessary to consider very carefully the multiple solutions. A procedure is given for determining the correct solutions fornandk, 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.