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This question is worded sloppy. How close is "just below"? Generic answer: any crystal (periodic arrangement of atoms) has a bandstructure with allowed bands and forbidden bands (band gaps). Metals have zero band gap around the Fermi energy (meaning the Fermi energy lies in a band), therefore they are always conductors. Insulators have a large band gap, ...


The difference between Fermi energy and Fermi level is described in a previously asked question. To summarize, you're correct that the Fermi level is the energy at which (in a 0K system) all of the lower energy states are occupied while all of the higher energy states are unoccupied. For a system not at 0K, the Fermi energy is the energy state that has a 50% ...

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