Perfecting the dispersion model free characterization of a thin film on a substrate specimen from its normal incidence interference transmittance spectrum

Abstract

An algorithm is proposed for perfecting the envelope method (EM) for characterization of a thin film on a substrate specimen from its normal incidence interference transmittance spectrum T(λ). It takes into account the partial coherence of light propagating through the film, due to light scattering mainly associated with roughness of the surface film/air, in the computations of both the smoothed transmittance spectrum Tsm(λ) and the extinction coefficient k(λ) of the film. The algorithm includes enhanced computation of the envelopes T+(λ) and T-(λ) of Tsm(λ), and adjustment of points T+(λt) and T-(λt) in spectral regions of substrate non-transparency as λt are the wavelengths of the tangency points between Tsm(λ) and its envelopes. The average thickness d¯ and the non-uniformity ∆d of the film are computed by EM based optimization procedure, followed by obtaining the refractive index n(λ) of the film by optimized curve fitting over approximated values n0(λt) of n(λt) without employing a dispersion model. It is demonstrated that k(λ) is determined more accurately from Tsm(λ), based on computing its coherent light approximation k0(λ) and partially coherent light correction Δk(λ), rather than the commonly used computation of k(λ) from T+(λ). Two a-Si films with dissimilar thicknesses are characterized by the proposed algorithm; as there are published characterization results for the same films computed by two spectroscopic ellipsometry related methods, and two EMs, selected as most likely to provide accurate characterization of the films. Comparing the characterization accuracy for the proposed algorithm with the characterization accuracy for the best of these published results shows that using the proposed algorithm leads to significantly more accurate characterization of both a-Si films. Accurate characterization is achieved even in a case of T(λ) influenced by residual gas absorption during its measurement, by employing both Tsm(λ) and T+(λ) in the computation of k(λ). The presented results indicate that using the proposed algorithm has a capacity for providing most accurate characterization of almost every dielectric or semiconductor film with d¯ = [300,5000] nm on a substrate, only from T(λ), compared to all the other methods for characterization of such films only from T(λ).