Band gap

In solid state physics and related applied fields, the band gap, also called an energy gap or stop band, is a region where a particle or quasiparticle is forbidden from propagating. For insulators and semiconductors, the band gap generally refers to the energy difference between the top of the valence band and the bottom of the conduction band.

In semiconductor physics

Semiconductor band structure.

In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden from other regions. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band, where electrons are able to jump from one band to another. The other gaps are between bands are between a pair of filled or a pair of empty bands, which are unimportant to the properties of the semiconductor.

The conductivity of intrinsic semiconductors is strongly dependent on the band gap. The only available carriers for conduction are the electrons which have enough thermal energy to be excited across the band gap.

Band gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), laser diodes and solar cells.

The distinction between semiconductors and insulators is a matter of convention. One approach is to consider semiconductors a type of insulator with a low band gap. Insulators with a higher band gap, usually greater than 3 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. Electron mobility also plays a role in determining a material's informal classification.

Band gap decreases with increasing temperature, in a process related to thermal expansion. Special purpose integrated circuits such as the DS1621 exploit this property to perform accurate temperature measurements. Band gap also depends on pressure. Bandgaps can be either direct or indirect bandgaps, depending on the band structure.

Mathematical interpretation

Template:Rewrite-section The probability that a state of energy, $E_{0}$, will be occupied by an electron is derived from Fermi-Dirac statistics. An approximation, called the Boltzmann approximation, is valid if the energy of the state $E_{0}>>E_{F}$, where $E_{F}$ is the Fermi energy. The Boltzman approximation is given by:

$e^{\left({\frac {-E_{g}}{kT}}\right)}$

where:

e is the exponential function

E_g is the band gap energy

k is Boltzmann's constant

T is temperature

Conductivity is undesirable, and larger band gap materials give better performance. In infrared photodiodes, a small band gap semiconductor is used to allow detection of low-energy photons.