Dear Colleaguse,
We are trying to simulate the XRR nanolayers to get information about the density parameters of PS films on Si substrate.
And I found that no matter how I adjusted the parameters of PS film and the substrate, I could not make the first half of the fitted image match the shape of the data. I tried to change the density of the Si substrate, but to get a better fitting curve would more than double the density of the substrate, which I don't think is right.
Does anyone have an idea of where is the problem, and what we have to change/modify to get a better simulation?
Thanks in advance.
Dear Zhijing Hu ,
I think, you have already identified the critical 'point' in the mismatch of the calculated and the 'measured' angular dependence of the reflectivity.
It is the cut-off of the reflectivity; i.e. the critical angle of total reflection, which is proportional to the square root of the density of your PS layer.
I do not know your x-ray wavelength (or photon energy); so I am not able to estimate your critical angle via your q-scale.
So, a) please share the estimated value of the critical angle of total reflection...
It must be in the range of a very few mrad*) ?
Please compare this small value with the precision (uncertainty) of your angular scale in the experimental XRR pattern. It is not an easy task to provide a 'perfect' offset-free experimental angular scale**).
So, b) you should play around with an angular offset in the measured XRR pattern and see how you can solve your issue with reasonable densities of PS and Si...
c) A way to decrease the influence of an angular offset is to use a far larger x-ray wavelength lambda; you know that the critical angle is proportional to lambda...
*) please note, that 1mrad is a tiny little angle equal to a lateral displacement
of 1mm at 1m distance
**) for example, a simple tiny height misalignment of the sample will cause a shift of the angular scale...
Good luck and
best regards
G.M.
Dear Gerhard Martens
Thank you so much for your explanation fitstly.And Merry Christmas to you.
We use the reflectometer was equipped with a Cu source,so λ = 1.54 Å.I think the critical angle of PS is 0.1538°.（I'm not sure bc I fond the date in the leterature(REFLEX: a program for the analysis of specular X-ray and neutron reflectivity data)）
So maybe I need to change the "tthoff" value when I simulate the XRR nanolayers right?I also want to make sure whether the tthoff value will change for the same batch of samples. Thank you again in advance.
Sincerely,Zhijing Hu
Dear Zhijing Hu ,
thanks for feedback and merry Christmas to you and your family...
You are right, for 1,54 A in wavelength and a density of about 1g/cm³ for PS you will end up at about 0,15° for the critical angle phic (~2,6mrad).
The q-value will be about ~0,022/A (=(4*pi/lambda)*phic), which is close to the cut-off of your thin red curve.
Please play around with the theta-offset of the XRR pattern (I do not know whether it is abbreviated as "tthoff")...
Assuming a q-difference of 0,025/A in the cut-offs between the measurement and the simulation, one will expect a theta-offset of about 3mrad, which to my opinion is a quite large value...
Good luck and
best regards
G.M.
For better understanding you can read this book, "X-Ray Scattering from Soft-Matter Thin Films" by Metin Tolan.
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