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If while calculating a band gap, the band just below the Fermi level touches the Fermi level, can we say the material is semiconducting?

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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, where electrons usually can not be excited into the conduction band.

Semiconductors lie right in between. Commonly semiconductors are defined, where (a significant amount of) electrons is excited thermally into the conduction band. This definition may have changed with the rise of wide bandgap materials like III-N semiconductors.

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