Editing Band gap (section)

==In semiconductor physics==
[[File:Bandgap in semiconductor.svg|right|thumb|Semiconductor [[Electronic band structure|band structure]].]]
Every solid has its own characteristic [[electronic band structure|energy-band structure]]. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials.
Depending on the dimension, the band structure and spectroscopy can vary. The different types of dimensions are as listed: one dimension, two dimensions, and three dimensions.<ref name=":0">{{Cite book |last=Cox |first=P.A. |title=The Electronic Structure and Chemistry of Solids |year=1987 |pages=102–114}}</ref>

In semiconductors and insulators, [[electron]]s are confined to a number of [[Electronic band structure|bands]] of energy, and forbidden from other regions because there are no allowable electronic states for them to occupy. 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 a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. This required energy is an [[Intrinsic and extrinsic properties|intrinsic]] characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a [[phonon]] (heat) or a [[photon]] (light).

A [[semiconductor]] is a material with an intermediate-sized, non-zero band gap that behaves as an insulator at T=0K, 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 there is no longer a bandgap with forbidden regions of electronic states.

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 and the [[electron hole]]s that are left off when such an excitation occurs.

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 [[Aluminium gallium arsenide|GaAlAs]], [[Indium gallium arsenide|InGaAs]], and [[Aluminium indium arsenide|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.

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 4 eV,<ref name="Solid State Devices and Technology">{{cite book |title=Solid State Devices and Technology, 3rd Edition |last1=Babu|first1=V. Suresh |year= 2010 |publisher=Peason }}</ref> 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.

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 |last1=Ünlü |first1=Hilmi |title=A thermodynamic model for determining pressure and temperature effects on the bandgap energies and other properties of some semiconductors |journal=Solid-State Electronics |date=September 1992 |volume=35 |issue=9 |pages=1343–1352 |doi=10.1016/0038-1101(92)90170-H |bibcode = 1992SSEle..35.1343U |doi-access=free }}</ref> The relationship between band gap energy and temperature can be described by [[Y. P. Varshni|Varshni]]'s empirical expression (named after [[Y. P. Varshni]]),
: <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>{{cite journal |last1=Varshni |first1=Y.P. |title=Temperature dependence of the energy gap in semiconductors |journal=Physica |date=January 1967 |volume=34 |issue=1 |pages=149–154 |doi=10.1016/0031-8914(67)90062-6 |bibcode=1967Phy....34..149V }}</ref>

Furthermore, lattice vibrations increase with temperature, which increases the effect of electron scattering. Additionally, the number of charge carriers within a semiconductor will increase, as more carriers have the energy required to cross the band-gap threshold and so conductivity of semiconductors also increases with increasing temperature.<ref name=":03">{{Cite book |last=Cox |first=P. A. |url=https://www.worldcat.org/oclc/14213060 |title=The electronic structure and chemistry of solids |date=1987 |publisher=Oxford University Press |isbn=0-19-855204-1 |location=Oxford [Oxfordshire] |oclc=14213060}}</ref> The external pressure also influences the electronic structure of semiconductors and, therefore, their optical band gaps.<ref name="Pankove">{{cite book | last=Pankove|first=J.I. | title=Optical processes in semiconductors | chapter=Chapters 1-3 | year=1971 | publisher=Dover | isbn=0-486-60275-3 }}</ref>

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”] {{Webarchive|url=https://web.archive.org/web/20090206143216/http://www.evidenttech.com/quantum-dots-explained/quantum-dot-glossary.html |date=2009-02-06 }}. Evidenttech.com. Retrieved on 2013-04-03.</ref> It is also known as [[quantum confinement effect]].

Band gaps can be either [[Direct and indirect bandgaps|direct or indirect]], depending on the [[electronic band structure]] of the material.<ref name="Pankove" /><ref name="Yu&Cardona">{{cite book |title=Fundamentals of semiconductors |last1=Yu|first1=P.Y. |last2=Cardona|first2=M. |year=1996  | chapter=Chapter 6 |publisher=Springer | isbn=3-540-61461-3 }}</ref><ref name="Fox">{{cite book |title=Optical properties of solids |last1=Fox|first1=M. | year=2008  | chapter=Chapters 1–3 |publisher=Oxford Univ. Press | isbn=978-0-19-850613-3 }}</ref>

It was mentioned earlier that the dimensions have different band structure and spectroscopy. For non-metallic solids, which are one dimensional, have optical properties that are dependent on the electronic transitions between valence and conduction bands. In addition, the spectroscopic transition probability is between the initial and final orbital and it depends on the integral.<ref name=":0" /> φ<sub>i</sub> is the initial orbital, φ<sub>f</sub> is the final orbital, ʃ φ<sub>f</sub><sup>*</sup>ûεφ<sub>i</sub> is the integral, ε is the electric vector, and u is the dipole moment.<ref name=":0" />

Two-dimensional structures of solids behave because of the overlap of atomic orbitals.<ref name=":0" /> The simplest two-dimensional crystal contains identical atoms arranged on a square lattice.<ref name=":0" /> Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential, which produces a gap between bands. The behavior of the one-dimensional situations does not occur for two-dimensional cases because there are extra freedoms of motion. Furthermore, a bandgap can be produced with strong periodic potential for two-dimensional and three-dimensional cases.<ref name=":0" />

===Direct and indirect band gap===
{{main|Direct and indirect bandgaps}}
Based on their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy.<ref name="Pankove"/><ref name="Yu&Cardona"/><ref name="Fox"/><ref>{{Cite book |last1=Böer |first1=K.W. |author-link=Karl Wolfgang Boer |title=Semiconductor Physics |last2=Pohl |first2=U.W. |author-link2=Udo W. Pohl |date=2023 |publisher=Springer |isbn=9783031182853}}</ref> For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and [[phonon]] must both be involved in a transition from the valence band top to the conduction band bottom, involving a [[Direct and indirect band gaps|momentum change]]. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for [[photovoltaics]] (PVs), [[light-emitting diode]]s (LEDs), and [[laser diode]]s;<ref name="Sze">{{cite book |title=Physics of semiconductor devices |last1=Sze|first1=S.M. |year=1981 |chapter=Chapters 12–14|publisher=John Wiley & Sons | isbn=0471056618 }}</ref> however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.

===Light-emitting diodes and laser diodes===
{{main|Light-emitting diode}}
LEDs and [[laser diode]]s usually emit photons with energy close to and slightly larger than the band gap of the semiconductor material from which they are made. Therefore, as the band gap energy increases, the LED or laser color changes from infrared to red, through the rainbow to violet, then to UV.<ref>{{cite journal |last1=Dean |first1=K J |title=Waves and Fields in Optoelectronics: Prentice-Hall Series in Solid State Physical Electronics |journal=Physics Bulletin |date=August 1984 |volume=35 |issue=8 |pages=339 |doi=10.1088/0031-9112/35/8/023 }}</ref>

===Photovoltaic cells===
{{main | Solar cell}}
[[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 band gap. If the band gap 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 band gap, and  the rest is wasted.<ref name="Goetzberger">{{cite book |title=Crystalline silicon solar cells |last1=Goetzberger|first1=A. |last2=Knobloch|first2=J. |last3=Voss|first3=B. |year=1998  |publisher=John Wiley & Sons | isbn=0-471-97144-8 }}</ref> The semiconductors commonly used in commercial solar cells have band gaps near the peak of this curve, as it occurs in silicon-based cells. The Shockley–Queisser limit has been exceeded experimentally by combining materials with different band gap energies to make, for example, [[tandem solar cell]]s.]]

The optical band gap (see below) determines what portion of the solar spectrum a [[photovoltaics|photovoltaic cell]] absorbs.<ref name="Goetzberger" /> Strictly, a  semiconductor will not absorb photons of energy less than the band gap; whereas most of the photons with energies exceeding the band gap will generate heat. Neither of them contribute to the efficiency of a solar cell. One way to circumvent this problem is based on the so-called photon management concept, in which case the solar spectrum is modified to match the absorption profile of the solar cell.<ref name="Zanatta1">{{cite journal |last1=Zanatta |first1=A.R. | title= The Shockley-Queisser limit and the conversion efficiency of silicon-based solar cells |journal=Results Opt. |date=December 2022 |volume=9 |pages=100320–7pp |doi=10.1016/j.rio.2022.100320 |doi-access=free |bibcode=2022ResOp...900320Z }}</ref>

===List of band gaps===
Below are band gap values for some selected materials.<ref name="Tropf">{{cite book |title= Electro-Optics Handbook |last1=Tropf|first1=W.J. |last2=Harris|first2=T.J. |last3=Thomas|first3=M.E. |year=2000  | chapter=11 |publisher=McGraw-Hill | isbn= 9780070687165 }}</ref> For a comprehensive list of band gaps in semiconductors, see [[List of semiconductor materials]].

{| class="wikitable sortable"
|-
! [[Group (periodic table)#CAS and old IUPAC|Group]] !! Material !! Symbol !! Band gap ([[electron volt|eV]]) @ 302[[kelvin|K]] !! Reference
|-
| III–V
| [[Aluminium nitride]]
| AlN
| 6.0
| <ref name="FenebergLeute2010">{{cite journal |last1=Feneberg |first1=Martin |last2=Leute |first2=Robert A. R. |last3=Neuschl |first3=Benjamin |last4=Thonke |first4=Klaus |last5=Bickermann |first5=Matthias |title=High-excitation and high-resolution photoluminescence spectra of bulk AlN |journal=Physical Review B |date=16 August 2010 |volume=82 |issue=7 |pages=075208 |doi=10.1103/PhysRevB.82.075208 |bibcode=2010PhRvB..82g5208F }}</ref>

|-
| IV
| [[Diamond]]
| [[Carbon|C]]
| 5.5
| <ref name="Kittel7">{{cite book |title=[[Introduction to Solid State Physics (Kittel book)|Introduction to Solid State Physics]], 7th Edition |last1=Kittel |first1=Charles |author-link1=Charles Kittel |year= <!--replace this comment with the publication year--> |publisher=Wiley }}</ref>
|-
| IV
| [[Silicon]]
| Si
| 1.14
| <ref name="Streetman" /><ref name="Pankove"/><ref name="Zanatta2">{{cite journal |last1=Zanatta |first1=A.R. | title= Revisiting the optical bandgap of semiconductors and the proposal of a unified methodology to its determination |journal=Scientific Reports |date=August 2019 |volume=9 |issue=1 |pages=11225–12pp |doi=10.1038/s41598-019-47670-y |doi-access=free |pmid=31375719 |pmc=6677798 |bibcode=2019NatSR...911225Z }}</ref>
|-
| IV
| [[Germanium]]
| Ge
| 0.67
| <ref name="Streetman">{{cite book|last=Streetman|first=Ben G.|author2=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><ref name="Pankove" /><ref name="Zanatta2" />
|-
| III–V
| [[Gallium nitride]]
| GaN
| 3.4
| <ref name="Streetman" /><ref name="Pankove"/><ref name="Zanatta2" />
|-
| III–V
| [[Gallium phosphide]]
| GaP
| 2.26
| <ref name="Streetman" /><ref name="Pankove" /><ref name="Zanatta2" />
|-
| III–V
| [[Gallium arsenide]]
| GaAs
| 1.43
| <ref name="Streetman" /><ref name="Pankove" /><ref name="Zanatta2" />
|-
| IV–V
| [[Silicon nitride]]
| Si<sub>3</sub>N<sub>4</sub>
| 5
| <ref name="Bauer1977">{{cite journal |last1=Bauer |first1=J. |title=Optical properties, band gap, and surface roughness of Si3N4 |journal=Physica Status Solidi A |date=1977 |volume=39 |issue=2 |pages=411–418|doi=10.1002/pssa.2210390205 |bibcode=1977PSSAR..39..411B }}</ref>
|-
| IV–VI
| [[Lead(II) sulfide]]
| PbS
| 0.37
| <ref name="Streetman" /><ref name="Pankove"/>
|-
| IV–VI
| [[Silicon dioxide]]
| SiO<sub>2</sub>
| 9
| <ref name="Vella">{{cite journal|title=Unraveling exciton dynamics in amorphous silicon dioxide: Interpretation of the optical features from 8 to 11 eV|year=2011|last1=Vella|first1=E.|last2=Messina|first2=F.|last3=Cannas|first3=M.|last4=Boscaino|first4=R.|journal=Physical Review B|volume=83|issue=17|page=174201|doi=10.1103/PhysRevB.83.174201|bibcode = 2011PhRvB..83q4201V |s2cid=121793038 |url=http://bib-pubdb1.desy.de/search?p=id:%22PHPPUBDB-22952%22}}</ref>
|-
|
| [[Copper(I) oxide]]
| Cu<sub>2</sub>O
| 2.1
| <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>
|}