Optimization of the graphical method of Swanepoel for characterization of thin film on substrate specimens from their transmittance spectrum

Abstract

The accuracy of the popular graphical method of Swanepoel (SGM) for the characterization of a thin film on a substrate specimen from its interference transmittance spectrum depends on the subjective choice of four characterization parameters: the slope of the graph, the order number for the longest wavelength extremum, and the two numbers of the extrema used for the calculation approximations of the average film thickness. Here, an error metric is introduced for estimating the accuracy of SGM characterization. An algorithm is proposed for the optimization of SGM, named the OGM algorithm, based on the minimization of this error metric. Its execution provides optimized values of the four characterization parameters, and the respective computation of the most accurate film characteristics achievable within the framework of SGM. Moreover, substrate absorption is accounted for, unlike in the classical SGM, which is beneficial when using modern UV/visible/NIR spectrophotometers due to the relatively larger amount of absorption in the commonly used glass substrates for wavelengths above 1700 nm. A significant increase in the accuracy of the film characteristics is obtained employing the OGM algorithm compared to the SGM algorithm for two model specimens. Such improvements in accuracy increase with increasing film absorption. The results of the film characterization by the OGM algorithm are presented for two specimens containing RF-magnetron-sputtered a-Si films with disparate film thicknesses. The computed average film thicknesses are within 1.1% of the respective film thicknesses measured by SEM for both films. Achieving such high film characterization accuracy is particularly significant for the film with a computed average thickness of 3934 nm, since we are not aware of any other film with such a large thickness that has been characterized by SGM.

Optical-Electrical Properties and Thickness Analysis of TiO2 Thin Films Obtained by Magnetron Sputtering

“…The films deposited after 120 min showed a higher number of interference fringes. Therefore, the Swanepoel Method for determining its thickness was applied only to these films, since this method requires a higher number of fringes to produce reliable results [19]. This standard is suitable for TiO 2 film applications as semiconductors due to low Bandgap values.…”

“…First, the films must be thin, that is, their thickness must be many orders of magnitude less than the thickness of the substrate that holds it [19]. The substrate must be transparent in the region of analysis, that is, resulting in a region of weak and medium absorption in the transmittance graph [19]. For the application of the Swanepoel method, the transmittance graph must present interference fringes.…”

“…The great challenge of this computational method is to provide precise values of thickness in analyzes of optical transmittance spectra, mainly when the samples are considerably thin films and with a high value of optical absorption coefficient [28]. Theoretical methods, based on different mathematical devices, are recurrent in the literature [7,13,19,[28][29][30][31][32] seek to obtain the lowest percentage of error concerning the determination of thickness.…”

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

“…An expression about the refractive index of a uniform film on a non-transparent substrate was presented in [ 35 ]: as T u+ ( λ ) and T u− ( λ ) are the upper and lower envelopes of the smoothed transmittance spectrum of the respective specimen with uniform film.…”

“…Based on using FOM from Equation (7), it was shown in [ 28 ] that the OEM provides more accurate film characterization compared to the FEM and the IEM, for all specimens studied there. Furthermore, FOM s were compared in [ 34 ] for characterizations of sputtered a-Si thin films with dissimilar average thicknesses by the OEM, the optimizing graphical method (OGM) [ 35 ], the Tauc–Lorentz–Urbach model method (TLUM) [ 36 ], and the Cody–Lorentz–Urbach model method (CLUM) [ 37 ]. These four film characterization methods were selected as most likely to provide accurate characterization of the a-Si films.…”