I have a reflectance spectra which was acquired by the perpendicular incidence of light. The reflectance spectra were taken on film/SiO2/Si stack. The data is in the frequency domain and thus I only have the amplitude data. I need to calculate n and k value from it.
At first, I have taken n and k as unknown and used transfer matrix to back calculate the values by minimizing the error of calculated and simulated reflectance results. But this process gives multiple solution points.
I am wondering if anyone has any solution.
Dear Sandipta,
I think one of the possibilities for solving your problem is to use ellipsometry in reflection. Indeed, if you know the geometry and composition of your sample, this is the standard way to obtain n and k from a system. If you are not familiar with ellipsometry, the best way is to start from a tutorial:
https://www.jawoollam.com/resources/ellipsometry-tutorial/what-is-ellipsometry
this one has been prepared by a leading company realizing ellipsometry systems.
All the best for your project,
Roberto
Thanks Prof. Roberto for the reply. I am aware of the ellipsometry measurement, but the size of the thin film is very less and it does not cover the spot size of the incident light. So, we have measured the reflectance spectra of a vertical incident light, where the spot size is very less to the sample. This experiment provides only amplitude of the reflection spectra. I would love to know if you have any alternative solution.
Dear Sandipta
Yes, application of an ellipsometry can give you solution. Otherwise, if you don't have ellipsometer, you can try to recover n,k data from fit reflectivity spectra by a calculated model. This is not simple, but after analysis of such results you can obtain reasonable approximation. You can see similar example in my publication:
https://www.researchgate.net/publication/7697624_Scattering_and_reflective_properties_of_ordered_mesoporous_silica_films
Good luck
Article Scattering and reflective properties of ordered mesoporous s...
Hi, Sandipa,
In your back calculations, you also need to make sure that the pair of n and k constants satisfies the sum rule, i.e. the Kramer-Kronig transformation. If you know n in all frequencies (0 to infinity), you can calculate the k from n by Kramer-Kronig transformation. In actual experiments, one do not have data at all frequencies so there has to be some approximations or empirical modelling. I suggest you read through the following paper by Dr. A. B. Kuzmenko, he also has a software (free, called RefFIT) that does exactly what you wanted to do.
https://arxiv.org/abs/cond-mat/0503565
https://sites.google.com/site/homepageofalexeybkuzmenko/software
I also has done some studies, comparing various curving fitting methods, using matlab. You can download the codes from Mathworks File exchange website.
https://au.mathworks.com/matlabcentral/fileexchange/61550-spectral-curvefitting-of-dielectric-constants
And Good luck
Article Kuzmenko, A. B. Kramers-Kronig constrained variational analy...
Code Spectral curve fitting of dielectric constants
Dear Ruzi and Valery,
Thank you for the reply. I shall look into the process.
I am following the publication https://www.osapublishing.org/ao/abstract.cfm?uri=ao-29-22-3207. My data is almost same. I am stuck in eqn 4 where w'-w is there. if the w' and w have same length then I could not calculate the n from k since at one point log(#/0) is coming which is undefined. I shall be thankful if you could help me to solve this section.
Dear Sandipta, your problem is challenging due to strong possibility to find non-unique solutions that can satisfied initial reflectance spectra. By the way, this is also correct about ellipsometry method: you can find several models that can satisfied your experimentally measured parameters. Direct conclusion is following: you must verify found solutions with some independent methods to have possibility of right choice. Article you have cited did not proposed such verification.
hi, Sandipta.
Again, you need to understand the Kramer-Kronig trnasformations, which is the equation (4) in that paper. As I mentioned, there are various codes you can use to calculate the transformation. The details, you can find in the following paper.
https://www.osapublishing.org/as/abstract.cfm?uri=as-42-6-952
Article Comparison Among Several Numerical Integration Methods for K...
Hi all,
Somehow I have collected the reflectance data at the different angle by ellipsometry measurement. Now Can you help me how can I figure out the n-k value?
Additionally, I think I need to fit the data with some model. I would love to know which model I should choose.
I have 3 liquid form material samples. Distilled water, and cell cuture mediums.
How I can do elissometry for thses samples that are not thin films. Is available a setup for liquid samples?
Is there any method I do the liquide samples between the thin film lams?
I think you can use quartz substrate. However, I am just curious why you want to do ellipsometry of a liquid sample?
Roy, actually, as a bench mark for a spectroscopic MATLAB code of Kramers-kroning , I save the reflectance spectra of these liquides as three samples. Could you please let me know how exactly I can use quartz substrate for liquid maintaning during elipsometry?
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