I have a glass coated with a transparent conductive oxide (TCO), and I need to know the refractive index of this material coating.
Can I use a simple ellipsometer for this without knowing of the layer thickness?
Yes and no. You need to fit the ellipsometry data with an optical model that will fit the refractive index AND the thickness to the data. However, in order to get a reasonable fit you should provide the software with a sensible starting value for at least one of the two, ideally for both.
It also goes without saying that you can only really determine the refractive index at wavelengths that your ellipsometer measures at (beyond that you have to trust the optical model), and measuring at multiple angles improves the fit.
But why do I need the layer thickness at all? Can't I shine a beam from the backside, through the glass to the TCO layer, and then change the angle until I hit total interal reflection?
Interesting thought. I suppose you could do that. Since the beam hits the air/glass and the glass/film interface before entering the film, so you will always get some reflection. You could detect total internal reflection if the interference fringes disappear at a certain angle, because those require light that was in the film to leave the film. So your approach works, provided the interference fringes are present when total internal reflection does not occur.
That said, your accuracy is limited by how well you know the refractive index of the glass and how accurately you can set the angle of incidence. My guess would be a standard measurement with model fitting would be more accurate.
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