Band gap

The energy range separating a solid’s occupied valence states from its conduction states. Its size helps determine whether the solid behaves as an insulator, semiconductor, or conductor.

Electronic band structure: The relationship between electron energy and crystal momentum in a solid. The band gap is the separation between regions of this structure.
Semiconductor: A material whose electrical conductivity can be controlled by doping, temperature, light, or electric fields. A moderate band gap lets practical energy inputs generate mobile carriers.
Direct band gap: A semiconductor band gap whose valence-band maximum and conduction-band minimum occur at the same crystal momentum. Direct transitions can emit or absorb light efficiently without a momentum-changing phonon.
Bloch's theorem: A theorem stating that electron wavefunctions in a periodic potential are plane waves multiplied by functions with the lattice periodicity. Periodic crystal potentials produce the energy bands whose edges define the gap.
Silicon: A crystalline chemical element widely used as the foundation of modern semiconductor electronics. Its indirect gap shapes its weak light emission and dominance in electronic devices.
Valence band: The highest energy band occupied by electrons at absolute zero in a semiconductor or insulator. Its upper edge forms one boundary of the gap.
Doping (semiconductors): The deliberate addition of impurities to a semiconductor to control its charge-carrier concentration. Dopants add levels near the band edges without usually changing the host gap substantially.
Indirect band gap: A semiconductor band gap whose valence-band maximum and conduction-band minimum occur at different crystal momenta. A phonon is generally needed to conserve momentum during band-edge optical transitions.
Brillouin zone: A primitive cell in reciprocal space that contains the distinct crystal momenta of a periodic lattice. Band extrema are located at points in this zone.
Gallium arsenide: A compound semiconductor made from gallium and arsenic, used in high-speed and optoelectronic devices. Its direct gap makes it effective for light-emitting and laser applications.

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