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I started doing lab work with nanoindenter on project my teaching assistant got from uni. We are trying to get thickness of thin film (Titanium dioxide) placed on Silicon substrate. My idea was to measure hardness of that bilayer and determine at what depth hardness starts to change siginificantly,but with that method I don't get any results since hardness of these materials is similar.

Is there other way to approach this experiment, or better question, is there some article which deals with same/similar problem?

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If the thin film is transparent, the customary tool used to nondestructively measure its thickness quite accurately is called an ellipsometer.

If the thin film is not transparent, you can instead cleave the sample in cross-section, thin it down, and put it in a transmission electron microscope and measure it that way.

niels nielsen
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For a transparent film, a spectrophotometer is widely used, among other tools. For any film, SEM of the cross section may be sufficient to obtain the thickness. See here, for example.