Band gap
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Insolid-state physicsandsolid-state chemistry,aband gap,also called abandgaporenergy gap,is an energy range in a solid where noelectronic statesexist. In graphs of theelectronic band structureof solids, the band gap refers to the energy difference (often expressed inelectronvolts) between the top of thevalence bandand the bottom of theconduction bandininsulatorsandsemiconductors.It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron (and theelectron holein the valence band) are free to move within the crystal lattice and serve as charge carriers to conductelectric current.It is closely related to theHOMO/LUMO gapin chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band (mostly full) to the conduction band (mostly empty), then currentcanflow (seecarrier generation and recombination). Therefore, the band gap is a major factor determining theelectrical conductivityof a solid. Substances having large band gaps (also called "wide" band gaps) are generallyinsulators,those with small band gaps (also called "narrow" band gaps) aresemiconductor,andconductorseither have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.
In semiconductor physics
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Every solid has its own characteristicenergy-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.[1]
In semiconductors and insulators,electronsare confined to a number ofbandsof 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 anintrinsiccharacteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either aphonon(heat) or aphoton(light).
Asemiconductoris 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 aninsulator.Inconductors,the valence and conduction bands may overlap, so there is no longer a bandgap with forbidden regions of electronic states.
Theconductivityofintrinsic semiconductorsis 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 theelectron holesthat 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 semiconductoralloys,such asGaAlAs,InGaAs,andInAlAs.It is also possible to construct layered materials with alternating compositions by techniques likemolecular-beam epitaxy.These methods are exploited in the design ofheterojunction bipolar transistors(HBTs),laser diodesandsolar 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 narrow band gap. Insulators with a larger band gap, usually greater than 4 eV,[2]are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions.Electron mobilityalso 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 latticephononsand the free electrons and holes will also affect the band gap to a smaller extent.[3]The relationship between band gap energy and temperature can be described byVarshni's empirical expression (named afterY. P. Varshni),
- ,whereEg(0), α and β are material constants.[4]
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.[5]The external pressure also influences the electronic structure of semiconductors and, therefore, their optical band gaps.[6]
In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In aquantum dotcrystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band.[7]It is also known asquantum confinement effect.
Band gaps can be eitherdirect or indirect,depending on theelectronic band structureof the material.[6][8][9]
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.[1]φiis the initial orbital, φfis the final orbital, ʃ φf*ûεφiis the integral, ε is the electric vector, and u is the dipole moment.[1]
Two-dimensional structures of solids behave because of the overlap of atomic orbitals.[1]The simplest two-dimensional crystal contains identical atoms arranged on a square lattice.[1]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.[1]
Direct and indirect band gap
[edit]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.[6][8][9]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 andphononmust both be involved in a transition from the valence band top to the conduction band bottom, involving amomentum change.Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited forphotovoltaics(PVs),light-emitting diodes(LEDs), andlaser diodes;[10]however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.
Light-emitting diodes and laser diodes
[edit]LEDs andlaser diodesusually 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.[11]
Photovoltaic cells
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The optical band gap (see below) determines what portion of the solar spectrum aphotovoltaic cellabsorbs.[12]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.[13]
List of band gaps
[edit]Below are band gap values for some selected materials.[14]For a comprehensive list of band gaps in semiconductors, seeList of semiconductor materials.
Group | Material | Symbol | Band gap (eV) @ 302K | Reference |
---|---|---|---|---|
III–V | Aluminium nitride | AlN | 6.0 | [15] |
IV | Diamond | C | 5.5 | [16] |
IV | Silicon | Si | 1.14 | [17][6][18] |
IV | Germanium | Ge | 0.67 | [17][6][18] |
III–V | Gallium nitride | GaN | 3.4 | [17][6][18] |
III–V | Gallium phosphide | GaP | 2.26 | [17][6][18] |
III–V | Gallium arsenide | GaAs | 1.43 | [17][6][18] |
IV–V | Silicon nitride | Si3N4 | 5 | [19] |
IV–VI | Lead(II) sulfide | PbS | 0.37 | [17][6] |
IV–VI | Silicon dioxide | SiO2 | 9 | [20] |
Copper(I) oxide | Cu2O | 2.1 | [21] |
Optical versus electronic bandgap
[edit]In materials with a largeexcitonbinding 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 band gap" and "electronic 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 isnotbound together. The optical bandgap is at lower energy than the transport gap.
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, includingorganic semiconductorsandsingle-walled carbon nanotubes,the distinction may be significant.
Band gaps for other quasi-particles
[edit]Inphotonics,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 aphotonic crystal.The concept ofhyperuniformity[22]has broadened the range of photonic band gap materials, beyond photonic crystals. By applying the technique insupersymmetric quantum mechanics,a new class of optical disordered materials has been suggested,[23]which support band gaps perfectly equivalent to those ofcrystalsorquasicrystals.
Similar physics applies tophononsin aphononic crystal.[24]
Materials
[edit]List of electronics topics
[edit]- Electronics
- Bandgap voltage reference
- Condensed matter physics
- Direct and indirect bandgaps
- Electrical conduction
- Electron hole
- Field-effect transistor
- Light-emitting diode
- Photodiode
- Photoresistor
- Photovoltaics
- Solar cell
- Solid state physics
- Semiconductor
- Semiconductor devices
- Strongly correlated material
- Valence band
See also
[edit]- Wide-bandgap semiconductors
- Band bending
- Spectral density
- Pseudogap
- Tauc plot
- Moss–Burstein effect
- Urbach energy
References
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- ^Varshni, Y.P. (January 1967). "Temperature dependence of the energy gap in semiconductors".Physica.34(1): 149–154.Bibcode:1967Phy....34..149V.doi:10.1016/0031-8914(67)90062-6.
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- ^abGoetzberger, A.; Knobloch, J.; Voss, B. (1998).Crystalline silicon solar cells.John Wiley & Sons.ISBN0-471-97144-8.
- ^Zanatta, A.R. (December 2022). "The Shockley-Queisser limit and the conversion efficiency of silicon-based solar cells".Results Opt.9:100320–7pp.doi:10.1016/j.rio.2022.100320.
- ^Tropf, W.J.; Harris, T.J.; Thomas, M.E. (2000). "11".Electro-Optics Handbook.McGraw-Hill.ISBN9780070687165.
- ^Feneberg, Martin; Leute, Robert A. R.; Neuschl, Benjamin; Thonke, Klaus; Bickermann, Matthias (16 August 2010). "High-excitation and high-resolution photoluminescence spectra of bulk AlN".Physical Review B.82(7): 075208.Bibcode:2010PhRvB..82g5208F.doi:10.1103/PhysRevB.82.075208.
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- ^abcdeZanatta, A.R. (August 2019)."Revisiting the optical bandgap of semiconductors and the proposal of a unified methodology to its determination".Scientific Reports.9:11225–12pp.doi:10.1038/s41598-019-47670-y.PMC6677798.PMID31375719.
- ^Bauer, J. (1977). "Optical properties, band gap, and surface roughness of Si3N4".Physica Status Solidi A.39(2): 411–418.Bibcode:1977PSSAR..39..411B.doi:10.1002/pssa.2210390205.
- ^Vella, E.; Messina, F.; Cannas, M.; Boscaino, R. (2011)."Unraveling exciton dynamics in amorphous silicon dioxide: Interpretation of the optical features from 8 to 11 eV".Physical Review B.83(17): 174201.Bibcode:2011PhRvB..83q4201V.doi:10.1103/PhysRevB.83.174201.S2CID121793038.
- ^Baumeister, P.W. (1961). "Optical Absorption of Cuprous Oxide".Physical Review.121(2): 359.Bibcode:1961PhRv..121..359B.doi:10.1103/PhysRev.121.359.
- ^Xie, R.; Long, G. G.; Weigand, S. J.; Moss, S. C.; Carvalho, T.; Roorda, S.; Hejna, M.; Torquato, S.; Steinhardt, P. J. (29 July 2013)."Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor".Proceedings of the National Academy of Sciences.110(33): 13250–13254.Bibcode:2013PNAS..11013250X.doi:10.1073/pnas.1220106110.PMC3746861.PMID23898166.
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External links
[edit]- Direct Band Gap Energy Calculator
- Moriarty, Philip."Energy Gap (and what makes glass transparent?)".Sixty Symbols.Brady Haranfor theUniversity of Nottingham.