Fast analytical inversion of s-transmittance data of weakly absorbing films on transparent substrates

We present a two-step analytical inversion of s-polarized transmittance data of weakly absorbing films on transparent substrates using an important relation between the s-transmittances τ (film alone), τ1 (substrate alone) and T (film on substrate). This relation allows to calculate τ from the measured quantities τ1 and T. Instead of a direct determination of the optical constants n, k from the measured s-transmittance, we firstly calculate the real and imaginary parts η and γ of the normal component of the wave vector q in the film. Analytical formulae are derived for the calculation of these quantities from the envelopes of the transmittance τ of the film at oblique incidence. The optical constants are then easily determined analytically again from η and γ. We tested the formulae to investigate the accuracy of the deduced values of the optical constants for different cases of refractive index ratio of film to substrate and show that they are well-suited for implementation in real-time inline monitoring systems for film deposition.