Comparative study of the accuracy of characterization of thin films a-Si on glass substrates from their interference normal incidence transmittance spectrum by the Tauc-Lorentz-Urbach, the Cody-Lorentz-Urbach, the optimized envelopes and the optimized graphical methods

Two RF magnetron sputtered a-Si thin films one of them several times thicker than the other are characterized by four methods. Since most literature data indicate presence of Urbach tails in the bandgap of a-Si, the two inverse synthesis methods based on the Tauc-Lorentz-Urbach model (TLUM) and the Cody-Lorentz-Urbach model (CLUM) are employed. It is clarified that the conventional envelope methods tend to overestimate the average thickness ${\overline{d}}_f,$ and to underestimate the refractive index n _f(λ) of the film. Therefore, the recently proposed optimized envelope method (OEM) and the optimized graphical method (OGM) are also employed. The accuracies of characterizations by these four methods are compared using a figure of merit (FOM), representing RMS deviation of the computed transmittance spe_ctrum T _c(λ) obtained using the computed film characteristics, from the measured transmittance spectrum T(λ) of the specimen. The most accurate characterization of the thinner film is achieved by OEM, providing average film thicknesses ${\overline{d}}_f$ = 785 nm, its thickness non-uniformity Δd_f = 23.5 nm, and FOM = 2.63 × 10⁻³. Although absorbance data for this film show that its band tails can be approximated as exponential (Urbach tails), the FOMs for the respective TLUM and CLUM characterizations are more than 38% larger than for OEM. The most accurate characterization of the thicker film is achieved again by OEM, providing ${\overline{d}}_f$ = 3939.1 nm, Δd_f = 53.1 nm, and FOM = 6.99 × 10⁻³. TLUM and CLUM fail to characterize the thicker film with acceptable accuracy, which is attributed to presence of non-exponential band tail, revealed by absorbance data for this film. The superior performance of OEM is explained considering that it does not assume particular band tails shapes, unlike TLUM and CLUM, neither it uses existence of a wide spectral region of film transparency as an initial approximation, unlike OGM. This inherent flexibility, and the demonstrated here exceptional accuracy of OEM, make it suitable for very accurate characterization of different types of thin films, including doped films and organic films. (paper)