A method for calculating the complex refractive index of inhomogeneous thin films

Abstract

We calculate the complex refractive index of inhomogeneous thin films using the transfer matrix method and reflection/transmission measurements. To this end we have developed a model for both the 3D distribution of inhomogeneities inside thin films and for light propagation through the inhomogeneities. The model involves splitting the light into contributions from the homogeneous section of the film (modelled coherently) and the inhomogeneous sections (modelled incoherently). Measurements of the film implied an isotropic inhomogeneity distribution, which was replicated in the simulation. The model for light propagation inside a film was implemented into a transfer matrix program allowing for the evaluation of the reflection and transmission of the thin film on a substrate. Using this result and experimental data for the reflection and transmission, the complex refractive index, n + ik, of an inhomogeneous CuInSe2 film was calculated. The resulting n and k were in much closer agreement to the n and k for a homogeneous CuInSe2 film than those for the standard transfer matrix approach applied to the data of the inhomogeneous sample. The n value at short wavelengths deviates from the homogeneous value suggesting a breakdown of the scalar scattering theory for short wavelengths.