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So, the Fermi level in crystals is pretty easy to understand. Been using it and talking about it in terms of the highest occupied level forever. However, I'm now reading about disordered systems. A lot of researchers mention the existence of empty states randomly distributed above and below the Fermi level. But isn't the Fermi level necessarily the energy at which all energies below are filled states?

EDIT: So I suppose chemical potential is the more correct term to use (instead of Fermi energy) because not at T = 0. Anyways, consider this quote: "the localized gap states near $E_F$ are spread in energy with singly occupied gap states below $E_F$, doubly occupied states lying above $E_F$, and empty states distributed randomly."

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It's difficult without context to know exactly what you have in mind, but that definition of $E_F$ really only holds at zero temperature -- at any $T>0$ states above the (nominal) Fermi level are thermally occupied. – wsc Mar 2 '11 at 1:18
    
Please mention a context and refer to a specific source to make the question clearer. For example, what is the source of the quotation? – Philosophiæ Naturalis Dec 15 '15 at 16:17

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