When N ≈ 10²² atoms bond into a crystal, overlapping atomic orbitals split into levels spaced by roughly 10⁻²² eV that form quasi-continuous energy bands.
In metals and semimetals the Fermi level lies inside at least one band, whereas in insulators and semiconductors it sits inside a forbidden band gap between the valence and conduction bands.
Band gaps are classified as direct when the conduction-band minimum and valence-band maximum share the same wavevector k (as in GaAs) or indirect when they differ (as in silicon and germanium).