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| {{about|solid state physics|voltage control circuitry in electronics|Bandgap voltage reference}}
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| {{about|the electronic bandgap found in semiconductors|the photonic band gap|photonic crystal}}
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| In [[solid-state physics]], a '''band gap''', also called an '''energy gap''' or '''bandgap''', is an [[energy range]] in a [[solid]] where no [[electron]] states can exist. In graphs of the [[electronic band structure]] of solids, the band gap generally refers to the energy difference (in [[electron volt]]s) between the top of the [[valence band]] and the bottom of the [[conduction band]] in [[Electrical insulation|insulators]] and [[semiconductor]]s. This is equivalent to the energy required to free an [[Valence shell|outer shell]] [[Valence electron|electron]] from its orbit about the [[Atomic nucleus|nucleus]] to become a mobile [[charge carrier]], able to move freely within the solid material, so the band gap is a major factor determining the [[electrical conductivity]] of a solid. Substances with large band gaps are generally [[insulator (electrical)|insulators]], those with smaller band gaps are [[semiconductor]]s, while [[Electrical conductor|conductors]] either have very small band gaps or none, because the valence and conduction bands overlap.
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| ==In semiconductor physics==
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| [[File:Bandgap in semiconductor.svg|right|thumb|Semiconductor [[Electronic band structure|band structure]].]]
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| Every solid has its own characteristic energy-band structure. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials.
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| 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. However, in order for an electron to jump from a valence band to a conduction band, it requires a specific minimum amount of energy for the transition. The required energy differs with different materials. Electrons can gain enough energy to jump to the conduction band by absorbing either a [[phonon]] (heat) or a [[photon]] (light).
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| A [[semiconductor]] is a material with a small but non-zero band gap that behaves as an insulator at absolute zero but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point. In contrast, a material with a large band gap is an [[Electrical insulator|insulator]]. In [[Electrical conductor|conductors]], the valence and conduction bands may overlap, so they may not have a band gap.
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| The [[electrical conductivity|conductivity]] of [[intrinsic semiconductor]]s is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap.
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| 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 cell]]s.
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| 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 narrow band gap. Insulators with a larger band gap, usually greater than 3 eV,{{Citation needed|reason=this value can be disputed|date=May 2010}} 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.
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| The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice [[phonon]]s and the free electrons and holes will also affect the band gap to a smaller extent.<ref>{{cite journal|author=H. Unlu|title=A Thermodynamic Model for Determining Pressure and Temperature Effects on the Bandgap Energies and other Properties of some Semiconductors|journal=Solid State Electronics|volume=35|pages=1343–1352|year=1992|doi=10.1016/0038-1101(92)90170-H|bibcode = 1992SSEle..35.1343U|issue=9 }}</ref> The relationship between band gap energy and temperature can be described by [[Y. P. Varshni|Varshni]]'s empirical expression,
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| :<math>E_g(T)=E_g(0)-\frac{\alpha T^2}{T+\beta}</math>, where ''E<sub>g</sub>''(0), α and β are material constants.<ref>[http://ece-www.colorado.edu/~bart/book/eband5.htm Temperature dependence of the energy bandgap]. Ece-www.colorado.edu. Retrieved on 2013-04-03.</ref>
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| In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In a [[quantum dot]] crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band.<ref>[http://www.evidenttech.com/quantum-dots-explained/quantum-dot-glossary.html “Evident Technologies”]. Evidenttech.com. Retrieved on 2013-04-03.</ref> It is also known as [[quantum confinement effect]].
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| Band gaps also depend on pressure. Band gaps can be either [[Direct and indirect bandgaps|direct or indirect]], depending on the [[electronic band structure]].
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| ===Mathematical interpretation===
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| 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]]:
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| :<math>e^{\left(\frac{-\Delta E}{kT}\right)}</math>
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| where:
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| * Δ''E'' is the energy difference
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| * ''k'' is [[Boltzmann's constant]]
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| * ''T'' is [[temperature]].
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| 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.
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| ===Photovoltaic cells===
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| [[File:ShockleyQueisserFullCurve.svg|thumb|The [[Shockley–Queisser limit]] gives the maximum possible efficiency of a single junction solar cell under un-concentrated sunlight, as a function of the semiconductor bandgap. If the bandgap is too high, most daylight photons cannot be absorbed; if it is too low, then most photons have much more energy than necessary to excite electrons across the bandgap, and the rest is wasted. The semiconductors commonly used in commercial solar cells have bandgaps near the peak of this curve, for example silicon (1.1eV) or [[CdTe]] (1.5eV). The Shockley–Queisser limit has been exceeded experimentally by combining materials with different band gap energies to make [[tandem solar cell]]s.]]
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| The optical band gap (see below) determines what portion of the solar spectrum a [[Solar cell|photovoltaic cell]] absorbs.<ref>[http://www.nrel.gov/csc/proj_nanoscale_material.html Nanoscale Material Design]. Nrel.gov. Retrieved on 2013-04-03.</ref> A luminescent solar converter uses a [[Luminescence|luminescent]] medium to downconvert photons with energies above the band gap to photon energies closer to the band gap of the semiconductor comprising the solar cell.<ref>[http://socrates.berkeley.edu/~kammen/C226/Berkeley-C226-EnergyConversionFilms.pdf Nanocrystalline luminescent solar converters], 2004</ref>
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| ===List of band gaps===
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| Below are band gap values for some selected materials. For a comprehensive list of band gaps in semiconductors, see [[List of semiconductor materials]].
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| {| class="wikitable sortable"
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| ! [[Group_(periodic_table)#CAS_and_old_IUPAC|Group]] !! Material !! Symbol !! Band gap ([[electron volt|eV]]) @ 302[[kelvin|K]] !! Reference
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| |-
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| | IV
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| | [[Diamond]]
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| | [[Carbon|C]]
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| | 5.5
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| | <ref name="Kittel7">{{cite isbn|0471111813}}</ref>
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| |-
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| | IV
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| | [[Silicon]]
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| | Si
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| | 1.11
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| | <ref name="Streetman" />
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| |-
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| | IV
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| | [[Germanium]]
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| | Ge
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| | 0.67
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| | <ref name="Streetman">{{cite book|last=Streetman|first=Ben G.|coauthors=Sanjay Banerjee|title=Solid State electronic Devices|edition=5th|year=2000|publisher=[[Prentice Hall]]|location=[[New Jersey]]|isbn=0-13-025538-6|page=524}}</ref>
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| |-
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| | III–V
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| | [[Gallium(III) nitride]]
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| | GaN
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| | 3.4
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| | <ref name="Streetman" />
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| |-
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| | III–V
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| | [[Gallium(III) phosphide]]
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| | GaP
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| | 2.26
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| | <ref name="Streetman" />
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| |-
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| | III–V
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| | [[Gallium(III) arsenide]]
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| | GaAs
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| | 1.43
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| | <ref name="Streetman" />
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| |-
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| | IV–V
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| | [[Silicon nitride]]
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| | Si<sub>3</sub>N<sub>4</sub>
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| | 5
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| |-
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| | IV–VI
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| | [[Lead(II) sulfide]]
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| | PbS
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| | 0.37
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| | <ref name="Streetman" />
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| |-
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| | IV–VI
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| | [[Silicon dioxide]]
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| | SiO<sub>2</sub>
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| | 9
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| |-
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| | [[Copper(I) oxide]]
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| | Cu<sub>2</sub>O
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| | 2.1
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| | <ref name="Baumeister">{{cite journal|title=Optical Absorption of Cuprous Oxide|year=1961|last1=Baumeister|first1=P.W.|journal=Physical Review|volume=121|page=359|doi=10.1103/PhysRev.121.359|bibcode = 1961PhRv..121..359B|issue=2 }}</ref>
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| |}
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| ==Optical versus electronic bandgap==
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| In materials with a large [[exciton]] binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical bandgap" and "electrical band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is ''not'' bound together. (The optical bandgap is at a lower energy than the transport gap.)
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| In almost all inorganic semiconductors, such as silicon, gallium arsenide, etc., there is very little interaction between electrons and holes (very small exciton binding energy), and therefore the optical and electronic bandgap are essentially identical, and the distinction between them is ignored. However, in some systems, including [[organic semiconductors]], the distinction may be significant.
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| ==In photonics and phononics==
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| 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]].
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| Similar physics applies to [[phonon]]s in a [[phononic crystal]].
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| ==Materials==
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| {{colbegin|3}}
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| * [[Aluminium gallium arsenide]]
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| * [[Boron nitride]]
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| * [[Indium gallium arsenide]]
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| * [[Indium arsenide]]
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| * [[Gallium arsenide]]
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| * [[Gallium nitride]]
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| * [[Germanium]]
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| * [[Metallic hydrogen]]
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| {{colend}}
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| ===List of electronics topics===
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| {{colbegin|3}}
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| * [[Electronics]]
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| * [[Bandgap voltage reference]]
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| * [[Condensed matter physics]]
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| * [[Direct and indirect bandgaps]]
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| * [[Electrical conduction]]
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| * [[Electron hole]]
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| * [[Field-effect transistor]]
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| * [[Photodiode]]
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| * [[Photoresistor]]
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| * [[Photovoltaics]]
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| * [[Solar cell]]
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| * [[Solid state physics]]
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| * [[Semiconductor]]
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| * [[Semiconductor device]]s
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| * [[Strongly correlated material]]
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| * [[Valence band]]
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| {{colend}}
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| ==See also==
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| * [[Wide bandgap semiconductors]]
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| * [[Band bending]]
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| * [[Spectral density]]
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| * [[Pseudogap]]
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| ==References==
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| {{reflist|35em}}
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| ==External links==
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| * [http://www.ee.byu.edu/cleanroom/EW_ternary.phtml Direct Band Gap Energy Calculator]
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| * {{cite web|last=Moriarty|first=Philip|title=Energy Gap (and what makes glass transparent?)|url=http://www.sixtysymbols.com/videos/energygap.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]}}
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| {{DEFAULTSORT:Band Gap}}
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| [[Category:Electron states]]
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| [[Category:Electronic band structures]]
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| [[fr:Bande interdite]]
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| [[ko:띠간격]]
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