Electronic band structure

Electronic band structure refers to very closely spaced energy levels available to electrons in solids by virtue of the small separation between atoms composing a solid. The small spacing of atoms means that the energy levels found in isolated atoms are disturbed by neighboring atoms, causing shifts in these energy levels. Thus, a single energy level for each of N atoms becomes a band of N closely spaced energy levels in a solid composed of these N atoms. These bands of allowed energies are separated in energy by energy gaps where no levels exist.

Material classification by band theory
According to the occupancy of these bands, a material may be an insulator if all the levels in one band are filled, and all those levels in higher energy bands are unoccupied. The filled band cannot conduct, because the electron configuration is fixed, having occupied all the available energy levels. If a band is only partially filled, the material will conduct and be a metal. The partially filled band can conduct, by shifting occupancy of the levels within the band in response to an external field. If the highest energy completely filled band is not widely separated from the next highest unoccupied band (that is, the intervening energy gap separating the bands is small), the electrons in the filled band can gain sufficient energy by heating to leave this lower-energy filled band (creating holes) and occupy the lower levels of the higher-energy band, making the material a semiconductor. The semiconductor can conduct because the unoccupied levels in the lower band can shift occupancy under a field (hole conduction) and the electrons in the partially occupied higher band can conduct by shifting energy levels within this band (electron conduction). Evidently, the number of holes and the number of higher-energy-band electrons is very sensitive to temperature, and more importantly, to any external field itself. This last property of semiconductors is the source of practical applications of semiconductors such as silicon in integrated circuits. The devices in these circuits control the conductivity of semiconductors using applied voltages, to achieve switching and modulation of signals.