I'm trying to calculate the band gap of two samples of Al2O3: an amorphous and a crystalline. I've read that Tauc's plot method is employed to determine the band gap of amorphous semiconductors, however, I didn't find a way to calculate the gap of crystalline thin films.
First, you need to look at "Handbook Of Optical Constants of Solids" by Palik, where you can find the [n,k] of sapphire (crystalline Al2O3). The Eg is about 8 eV. So unless you have access to the very hard UV, you will not be able to measure its bandbap. A typical spectrometer goes down to 250 nm (or about 5 eV), so you are well out of range of its Eg.
2nd, Reflectance [R] is not typically used to measure Eg. Assuming that you are limited to 250 nm wavelength, then you will see the normal dispersion of [R] increasing (for shorter wavelengths). This is not much help in identifying the Eg. Instead, transmittance [T] is used. Using [T], you first compute the Absorbance, Abs = -log10(To/T). Then using the sample thickness (t), you compute the absorption constant, alpha = Abs/(t x log10(e)), which is what is normally used in the Tauc plot. BUT for all this to work, you really do need to measure [T] for wavelengths down to about 100 nm.
There are different versions of the Tauc plot, depending on "direct-allowed", "direct forbidden", "indirect allowed", and "indirect forbidden", which should cover any crystalline optical edge.
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