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solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how th ...
, the valence band and conduction band are the bands closest to the
Fermi level The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''µ'' or ''E''F for brevity. The Fermi level does not include the work required to remove ...
, and thus determine the
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
of the solid. In nonmetals, the valence band is the highest range of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
energies in which electrons are normally present at
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibra ...
temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the
electronic band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called '' band gaps'' or ...
of a material, the valence band is located below the Fermi level, while the conduction band is located above it. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.


Band gap

In semiconductors and insulators the two bands are separated by a band gap, while in
semimetals A semimetal is a material with a very small overlap between the bottom of the conduction band and the top of the valence band. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, or metals. ...
the bands overlap. A band gap is an energy range in a solid where no electron states can exist due to the quantization of energy. Within the concept of bands, the energy gap between the valence band and the conduction band is the band gap. Electrical conductivity of non-metals is determined by the susceptibility of electrons to be excited from the valence band to the conduction band.


Electrical conductivity


''Semiconductor band structure''
''See electrical conduction and
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way ...
for a more detailed description of band structure.''
In solids, the ability of electrons to act as
charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term i ...
s depends on the availability of vacant electronic states. This allows the electrons to increase their energy (i.e., accelerate) when an electric field is applied. Similarly, holes (empty states) in the almost filled valence band also allow for conductivity. As such, the
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
of a solid depends on its capability to flow electrons from the valence to the conduction band. Hence, in the case of a semimetal with an overlap region, the electrical conductivity is high. If there is a small band gap (Eg), then the flow of electrons from valence to conduction band is possible only if an external energy (thermal, etc.) is supplied; these groups with small Eg are called semiconductors. If the Eg is sufficiently high, then the flow of electrons from valence to conduction band becomes negligible under normal conditions; these groups are called insulators. There is some conductivity in semiconductors, however. This is due to thermal excitation—some of the electrons get enough energy to jump the band gap in one go. Once they are in the conduction band, they can conduct electricity, as can the hole they left behind in the valence band. The hole is an empty state that allows electrons in the valence band some degree of freedom.


Band edge shifts of semiconductor nanoparticles

The edge shifting of size-dependent conduction and/or valence band is a phenomenon being studied in the field of semiconductor nanocrystals. The radius limit of occurrence of the semiconductor nanocrystal is the effective Bohr radius of the nanocrystal. The conduction and/or valence band edges shift to higher energy levels under this radius limit due to discrete optical transitions when semiconductor nanocrystal is restricted by the exciton. As a result of this edge shifting, the size of the conduction and/or valence band is decreased. This size-dependent edge shifting of conduction and/or valence band can provide plenty of useful information regarding the size or concentration of the semiconductor nanoparticles or band structures.


See also

* Electrical conduction for more information about conduction in solids, and another description of band structure. *
Fermi sea A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions we ...
* HOMO/LUMO *
Semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way ...
for a full explanation of the band structure of materials. * Valleytronics


References


Citations


General references

* * * {{cite web , last=Nave , first=Carl R. (Rod) , date=1999 , title=Band Theory for Solids , url=http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html , publisher=Hyperphysics , access-date=8 December 2021


External links


Direct Band Gap Energy Calculator
Electronic band structures