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.