Simple method for the determination of optical parameters of inhomogeneous thin films

In this work, we propose a new method for the determination of the optical parameters of an inhomogeneous thin optical film deposited on a substrate of finite thickness. The method can be applied successfully, if the following hyphotheses are satisfied: the film exhibits small optical inhomogeneities throughout the thickness (less than 5%), smooth refractive index profiles, weak absorption (extinction coefficient ≤ 0.02) and negligible diffuse light scattering. Useful formulae are derived describing the effects of refractive-index inhomogeneity and absorption not only on the transmittance and reflectance extrema but also for any other wavelength value. This allows us to calculate the refractive index inhomogeneity and to subtract its contribution from the measured transmittance and reflectance curves starting from approximate refraction index and film thickness values. In this way, it is possible to obtain the transmittance and reflectance spectra of a homogeneous film whose optical parameters are the mean values of those of the inhomogeneous film. These new transmittance and reflectance curves can be easily processed with any computer program for the determination of the optical parameters and film thickness based on the homogeneous thin film optical model.