Band theory is a quantum model in solid state physics which gives the possible energies for electrons in a solid and gives an understanding of electrical conductivity. It comes from the theory of molecular orbitals.
In a solid the allowed energy levels are confined to a band of which the width, of the order of an electron volt, depends on the crystal and the overlap of the atomic orbitals.
Solids have a band structure: there are allowed energy bands and forbidden energy bands. The energy bands are filled according to Fermi-Dirac statistics: it is shown that at 0 K the electrons occupy all the energy levels lower than the Fermi level. Its value is characteristic of the crystal being considered.
The valance band and the conduction band are then highlighted.
Band structures in an insulator, a semiconductor and a solid. Credits: energies2demain.com, contrat creativecommons.org/licenses/by-nc-sa/2.0/fr/