I want to estimate the film thickness from the XRD measurement. I have fitted the XRD spectra using Origin Lab and I have extracted the integrated intensity, peak position, FWHM and intensity. Please, kindly guide me on how to calculate the film thickness from the available data
Dear Martin C. Eze ,
a) The only parameter, in which the film thickness is involved, is the peak height (or better the peak integral). However in films orientation/texture artifacts also affect the peak heights/integrals. (Crystallite size as well as stress/strain will also affect the peak heights; thus one should use the peak integral instead).
b) The absolute intensity itself depends on various other parameters, so a reference or calibration measurement is necessary. From a reference, such as an XRD pattern of a sufficiently thick film, having the same crystallographic properties compared to your thin film you may derive the film thickness d from the following expression:
I(d)/Imax = 1-exp(-2µ*d/sin(theta))
For a derivation please see my answer at:
https://www.researchgate.net/post/Why_XRD_peak_intensity_increases_with_the_films_thickness_Is_there_any_fixed_relation_between_XRD_peak_intensity_and_thickness
But as I mentioned above, you cannot exclude orientation artifacts in the film, so this method is not very reliable.
c) When you have got diffraction peaks from your substrate you might be able to derive the film thickness via the attenuation of the substrate peaks.
However, also here there is a need for a reference: the XRD pattern of the substrate sample prior to film deposition. Please make sure that the fixing of the substrate and fixing of the substrate+film is the same in position*) and orientation.
You may easily calculate the decrease of the substrate peaks with increasing film thickness d as:
I/I0= exp(-2µ*d/sin(theta)) , with µ as the linear x-ray attenuation coefficient of the film material
*) in lateral (x,y) and in height (z) position
Thank you, Gerhard. Since my substrate is glass, probably option (b) will be more suitable as glasses do not have peaks.
Dear Martin C. Eze ,
option b) is critical due to the preferred orientation/texture issues.
Thickness measurements are done via the measured angular dependence of the X-ray reflection in the vicinity of the critical angle of total reflection.
Please google for 'x-ray reflectometry XRR' and 'Kiessig fringes'.
For a short introduction please have a look at:
https://en.wikipedia.org/wiki/X-ray_reflectivity
One of the early papers in this field is:
L. G. Parratt; Surface Studies of Solids by Total Reflection of X-Rays;
Phys. Rev. 95 (2), pp. 359-369 (1954).
I will send you this paper via RG messenger...
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