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Strictly from the definition of the Fermi level as the highest energy occupied at zero temperature, it seems that in the presence of a band gap the Fermi level (Ef) could be placed fairly arbitrarily anywhere between the conduction (Ec) and valence (Ev) bands, since the density of states is zero in that region.

At least, that's what I always thought.

What if I apply a constant voltage V to the sample? When V reaches Ec-Ef I should start getting a current even at zero temperature, and so measure Ec-Ef.

Of course, the difference between the Ec-Ev could be measured in many ways, for example, absorption spectra.

And so, Ef can be determined!

Am I right? If so, I'd be glad to hear what is the physics involved in determining Ef... How is it defined if not by the Fermi-Dirac distribution?

P.S

I know the Ef usually appears in the middle of the band gap in the literature. As I said, I think it is arbitrary in undoped materials, and would be glad to be taught otherwise.

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# Location of Fermi level in semiconductors

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