Thickness determination by Fourier transform

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Thickness determination by Fourier transform

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In the case of thickness determination by model fitting it is sometimes useful to obtain a good starting value for the thickness. This is in particular important in the case of thick layers.

If the spectrum exhibits pronounced interference patterns, and the refractive index of the deposited material is more or less constant, one can get a good approximation for the thickness from the Fourier transform of the spectrum. Here is an example:

If n is the refractive index of the layer, the peaks in the reflectance have a periodicity of 1/(2*n*d) where d is the layer thickness. The Fourier transform (power spectrum) of this spectrum shows a peak at the optical thickness 2*n*d:

Knowing the value of n one can compute from the peak position of the optical thickness the geometric thickness d.

 

The menu command Actions|FFT thickness analysis of the spectrum window performs the analysis explained above. You are asked for the spectral range to be used for the periodicity analysis (wavenumber minimum and maximum, number of data points) and the expected geometrical thickness range (minimum, maximum) as well as for the refractive index (constant, real): For the choices 1000 ... 6000 1/cm with 2048 data points and a thickness range 3 ... 50 microns with n=2.0 SCOUT computes the power spectrum and searches for the highest peak in the specified thickness range. The obtained thickness is 7.88 microns.

Once you have specified the parameters for the FFT thickness analysis, you can load new spectra and do the same analysis with the command Actions|Repeat FFT thickness analysis. In this case there are no questions about parameters but the previous ones are used once more.