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

Optical Characterization of AsxTe100−x Films Grown by Plasma Deposition Based on the Advanced Optimizing Envelope Method

“…In an advanced version of the OEM (AOEM) [ 29 ] was pointed out that partial coherence of light, due to both light scattering from the film and finite slit width, results in slight shrinkage of the interference pattern. To offset these effects, it was proposed in [ 29 ] that the smoothed spectrum T sm ( λ ) should be computed by “external smoothing” of T ( λ ), to correspond to the coherence of light passing through the film assumed in Equation (1), instead of the commonly used “internal smoothing” of T ( λ ).…”

“…The envelopes T + ( λ ) and T − ( λ ) of T sm ( λ ) were computed in [ 29 ] by combining the advantages of including extra points for the interpolation of both envelopes [ 30 ], with these of using iterations [ 31 ], however, implying substrate transparency for all λ . Moreover, points T + ( λ t ) and T − ( λ t ) were adjusted in the spectral region with x s ( λ ) < 1 to take into account the substrate non-transparency there [ 29 ].…”

“…The envelopes T + ( λ ) and T − ( λ ) of T sm ( λ ) were computed in [ 29 ] by combining the advantages of including extra points for the interpolation of both envelopes [ 30 ], with these of using iterations [ 31 ], however, implying substrate transparency for all λ . Moreover, points T + ( λ t ) and T − ( λ t ) were adjusted in the spectral region with x s ( λ ) < 1 to take into account the substrate non-transparency there [ 29 ]. The following accurate formula for the envelope T + ( λ ) was also presented in [ 29 ]: where Equations (1) and (2) have been derived assuming n 2 ( λ ) > n s 2 ( λ ) >> k 2 ( λ ) and n s 2 ( λ ) >> k s 2 ( λ ) [ 27 ], as these relationships are usually satisfied in the UV/VIS/NIR spectral region for a thin dielectric or semiconductor film with = (300,5000) nm on a glass substrate [ 24 ].…”

“…Main advantage of the envelope methods (EM) is that they do not employ and dispersion model, as a result of using the interference fringes equation [ 19 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]: …”

“…The AOEM is executed in two stages, as at the end of its first stage are computed both the average thickness , and the thickness non-uniformity ∆d ≥ 0 of the film over the light spot, as well as the first interference order m 1 (max( λ t )) [ 28 , 29 ]. This is achieved by minimization of an error metric.…”