On the use of fast Fourier transform for optical layer thickness determination

Autor: Michael Quinten
Rok vydání: 2019
Předmět:
Zdroj: SN Applied Sciences. 1
ISSN: 2523-3971
2523-3963
DOI: 10.1007/s42452-019-0866-9
Popis: Thin film thickness determination with a reflectometer is a fast and pretty cheap method that can be applied on many thin and thick films that are transparent or semitransparent in the considered spectral range. For evaluation of the reflectance spectrum either nonlinear regression analysis is used for very thin films or fast Fourier transform (FFT) for films thicker than approximately 1 µm. Using FFT for layer thickness determination there are some special facts to consider in contrast to the common use of FFT in signal processing. First of all, the sampling points are in general not equidistant as the wavelengths of the used spectrometer are not equidistant. Next the number of sampling points may be different from a power of 2. The reason is that the measured spectral range may be restricted by the user. And finally the analogues in layer thickness determination to the independent parameters “time” and “frequency” in signal processing are not independent of each other. The reason is the dispersion of the refractive index of the layer material that causes unwanted Moire effects in the reflectance spectrum. All these deviations lead to additional sources for errors in the thickness determination beyond those error sources that are well-known from common FFT applications in signal processing. In this paper we discuss how these deviations affect the thickness determination and present a solution for the main problem caused by the dispersion of the refractive index. Further improvements of the FFT result in combination with a grid search algorithm and a nonlinear regression are presented and discussed. Finally we present with structured samples and highly doped semiconductors two specific applications of FFT on layer thickness determination.
Databáze: OpenAIRE
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