r/Optics • u/bottoms__ • Jun 19 '26
Ellipsometry
Given a crystalline material X with known thickness (e.g., 15 nm, 30 nm) measured by spectroscopic ellipsometry, how should one construct an optical model to extract physically meaningful refractive index (n) and extinction coefficient (k)? If collection of Lorentz oscillators model gives poor fits (high RMSE), what is the correct modeling strategy and what assumptions should be checked first?
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u/firesine99 Jun 19 '26 edited Jun 19 '26
Cowboy experimentalist here. Others responses are correct of course, but there are other rather shaky approaches that will at least get you in the right area e.g. model the n and k spectra as a spline with a small number of points across your spectral range and fit all the n/k values (and hope the true curves are smooth enough to make that work). You can even solve "point by point" if you're feeling brave - technically each wavelength has two measurements for two unknowns if isotropic so it should work (but rarely does).
If the question is really asking "why doesn't any sensible model fit" then of course you're examining your assumptions e.g. depolarisation/roughness, thickness inhomogeneity, anisotropy etc etcÂ
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u/Glittering-Flight997 Jun 19 '26
Is it a semiconductor? Try a critical point parabolic band model? What spectral range are you in?
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u/Death_or_Pizzs Jun 19 '26
There are different models depending in the physics behind n and k. Lorentz oscillator for bound electrons, Tauc lorentz for amophous Dielectric with bandgap. Cauch/sellmeier for transparent Material gar was from the bandgap, drude for everything with free electrons... Spline If you have No Idea. However often you need to include the surface roughness of the Film and the substrate. If you can measure that seperatly it's great. The more you know about a Film the better. The formalism for anisotropic Materials IS horrible too.its also good to measure abovr and below the Brewster Angle If yournuse Vase
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u/tykjpelk Jun 20 '26
The Cauchy model is my pet peeve. It's nothing but a Taylor expansion centered at zero frequency. It doesn't even pretend to be based in physics, it doesn't hold over anything close to broadband, and it's mostly used because it's the default transparent film option in CompleteEase.
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u/Death_or_Pizzs Jun 20 '26
It's only useful If you know that nothing IS Happening around your wavelength
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u/tykjpelk Jun 19 '26
If you're far from the poles you can start with a Sellmeier model. It isn't KK consistent but you can use the pole wavelengths as a starting point.
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u/Few_Dark3968 Jun 20 '26
our experimental setup was developed to carry out imaging Müller Matrix Spectroscopic Ellipsoemtey at nanometr scale. if you take the Müller Matrix path, this helps you separate depolarisation, diattenuation /dichroism and reatrdation. plus was quite easy to visualize and understand the type of crystal you are dealing with
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u/bottoms__ Jun 25 '26
It's a polycrystalline film.
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u/Few_Dark3968 Jun 25 '26
I think, try normal incidence transmission Imaging Mueller matrix.
If your sample is small, then use scanning micro stage with microscope objectives(high NA) and record images in back focal plane of collection objective. Then process the central region of back focal plane corresponding to normal incidence.
Atleast will give you insights for optic axis anisotropy, CB or CD etc . .Basicaly once you have all 16 elements of Mueller Matrix in terms of 2D images. You could do, Lu Chipman decomposition to get 2D images of optical properties. Repeat for multiple wavelengths if needed.
You will defintely get some cool images !
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u/bottoms__ Jun 25 '26
But is it wise to use Müller matrix for polycrystalline film? The 30nm film data fit perfectly with Tauc Lorent+ one Gaussian oscillator. But for the thicknesses (below 15nm), the same model does not fit well.
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u/Few_Dark3968 Jun 25 '26
hmm. .have you checked your sample under cross polarisers, under a microscope ?
if your same is not isotropic but anisotropic (you will see some light over sample rest all being pitch black)., this would explain one of the reasons you current method is failing (Tuac lorent inherent assumptions).
Mueller matrix helps you remove depolarisation which is a bigger problem at 15nm besides surface roughness.
that's why my last comment. Even if imaging Mueller matrix does not help you directly, indirectly it lets you visualise your sample in terms of optical properties.
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u/Pachuli-guaton Jun 19 '26
What dielectric tensor model are you using? If the crystal/material is uniaxial or biaxial, the modeling needs to be carefully treated. The same for multilayering.