Band gap
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Reverted edits by [[Special:Contributions/Jamesrei|Jamesrei]] ([[User talk:Jamesrei|talk]]) to last version by Dicklyon
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 [[Electrical insulation|insulator]]s and [[semiconductor]]s, 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==
[[Image:Bandgap_in_semiconductor.svg|right|thumb|250px|Semiconductor [[Electronic band structure|band structure]].]]
In semiconductors and insulators, [[electron]]s are confined to a number of [[Electronic band structure|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]]; electrons are able to jump from one band to another.
The [[electrical conductivity|conductivity]] of [[intrinsic semiconductor]]s 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 [[alloy]]s, 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 transistor]]s (HBTs), [[laser diode]]s and [[solar cells]].
The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as 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 gaps depend on temperature because of [[thermal expansion]]. Band gaps also depend on pressure. Band gaps can be either [[Direct bandgap|direct]] or [[indirect bandgap]]s, depending on the [[band structure]].
=== Mathematical interpretation ===
Classically, the ratio of probabilities that two states with an energy difference ''ΔE'' will be occupied by an electron is given by the [[Boltzmann factor]]:
:<math>e^{\left(\frac{-\Delta E}{kT}\right)}</math>
where:
:e is the [[exponential function]]
:<math>\, \Delta E</math> is the energy difference
:<math>\, k</math> is [[Boltzmann's constant]]
:<math>\, T</math> is [[temperature]]
At the [[Fermi level]] (or [[chemical potential]]), the probability of a state being occupied is ½. If the Fermi level is in the middle of a band gap of 1 eV, this ratio is ''e'' <sup>-20</sup> or about 2.0•10<sup>-9</sup> at the room-temperature thermal energy of 25.9 meV.
=== List of band gaps ===
{| class="wikitable"
|-
! Material !! Symbol !! Band gap ([[electron volt|eV]]) @ 300[[kelvin|K]]
|-
| [[Silicon]]
| Si
| 1.11 <ref name="Streetman">{{cite book|last=Streetman|first=Ben G.|coauthors=Sanjay Banerjee|title=Solid State electronic Devices|edition=5th edition|year=2000|publisher=[[Prentice Hall]]|location=[[New Jersey]]|isbn=0-13-025538-6|pages=524}}</ref>
|-
| [[Germanium]]
| Ge
| 0.67 <ref name="Streetman" />
|-
| [[Silicon carbide]]
| SiC
| 2.86 <ref name="Streetman" />
|-
| [[Aluminum phosphide]]
| AlP
| 2.45 <ref name="Streetman" />
|-
| [[Aluminium arsenide]]
| AlAs
| 2.16 <ref name="Streetman" />
|-
| [[Aluminium antimonide]]
| AlSb
| 1.6 <ref name="Streetman" />
|-
| [[Aluminium nitride]]
| AlN
| 6.3
|-
| [[Diamond]]
| C
| 5.5
|-
| [[Gallium(III) phosphide]]
| GaP
| 2.26 <ref name="Streetman" />
|-
| [[Gallium(III) arsenide]]
| GaAs
| 1.43 <ref name="Streetman" />
|-
| [[Gallium(III) nitride]]
| GaN
| 3.4 <ref name="Streetman" />
|-
| [[Gallium(II) sulfide]]
| GaS
| 2.5 (@ 295 K)
|-
| [[Gallium antimonide]]
| GaSb
| 0.7 <ref name="Streetman" />
|-
| [[Indium(III) phosphide]]
| InP
| 1.35 <ref name="Streetman" />
|-
| [[Indium(III) arsenide]]
| InAs
| 0.36 <ref name="Streetman" />
|-
| [[Zinc sulfide]]
| ZnS
| 3.6 <ref name="Streetman" />
|-
| [[Zinc selenide]]
| ZnSe
| 2.7 <ref name="Streetman" />
|-
| [[Zinc telluride]]
| ZnTe
| 2.25 <ref name="Streetman" />
|-
| [[Cadmium sulfide]]
| CdS
| 2.42 <ref name="Streetman" />
|-
| [[Cadmium selenide]]
| CdSe
| 1.73 <ref name="Streetman" />
|-
| [[Cadmium telluride]]
| CdTe
| 1.49 <ref name="Madelung">{{cite book|last=Madelung|first=Otfried|title=Semiconductors - Basic Data|edition=2nd rev. ed.|year=1996|publisher=[[Springer-Verlag]]|location=[[Berlin Heidelberg New York]]|isbn=3-540-60883-4}}</ref>
|-
| [[Lead(II) sulfide]]
| PbS
| 0.37 <ref name="Streetman" />
|-
| [[Lead(II) selenide]]
| PbSe
| 0.27 <ref name="Streetman" />
|-
| [[Lead(II) telluride]]
| PbTe
| 0.29 <ref name="Streetman" />
|}
== In photonics and phononics ==
In [[photonics]] band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a [[photonic crystal]].
Similar physics applies to [[phonon]]s in a [[phononic crystal]].
==References==
<references/>
==See also==
===Chemicals===
*[[Aluminium gallium arsenide]]
*[[Boron nitride]]
*[[Indium gallium arsenide]]
*[[Gallium arsenide]]
*[[Germanium]]
*[[Metallic hydrogen]]
===[[List of electronics topics]]===
*[[Electronics]]
*[[Bandgap voltage reference]]
*[[Condensed matter physics]]
*[[Direct bandgap]]
*[[Electrical conduction]]
*[[Electron hole]]
*[[Field-effect transistor|Field effect transistor]]
*[[Indirect bandgap]]
*[[Photodiode]]
*[[Photoresistor]]
*[[Photovoltaics]]
*[[Solar cell]]
*[[Solid state physics]]
*[[Semiconductor]]
*[[Semiconductor device]]s
*[[Strongly correlated material]]
*[[Valence band]]
==References==
{{reflist}}
==External links==
[[Category:Condensed matter physics]]
[[Category:Semiconductors]]
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