A semimetal is a material with a very small overlap between the bottom of the
conduction band
Band or BAND may refer to:
Places
*Bánd, a village in Hungary
*Band, Iran, a village in Urmia County, West Azerbaijan Province, Iran
* Band, Mureș, a commune in Romania
*Band-e Majid Khan, a village in Bukan County, West Azerbaijan Province, I ...
and the top of the
valence band
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in w ...
.
According to
electronic band theory, solids can be classified as
insulators
Insulator may refer to:
* Insulator (electricity), a substance that resists electricity
** Pin insulator, a device that isolates a wire from a physical support such as a pin on a utility pole
** Strain insulator, a device that is designed to work ...
,
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. ...
s, semimetals, or
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
s. In insulators and semiconductors the filled valence band is separated from an empty conduction band by a
band gap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference ( ...
. For insulators, the magnitude of the band gap is larger (e.g., > 4
eV) than that of a semiconductor (e.g., < 4 eV). Because of the slight overlap between the conduction and valence bands, semimetals have no band gap and a negligible
density of states
In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states i ...
at the
Fermi level. A metal, by contrast, has an appreciable density of states at the Fermi level because the conduction band is partially filled.
Temperature dependency
The insulating/semiconducting states differ from the semimetallic/metallic states in the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
dependency of their
electrical conductivity. With a metal, the conductivity decreases with increases in temperature (due to increasing interaction of electrons with
phonons (lattice vibrations)). With an insulator or semiconductor (which have two types of charge carriers –
holes
A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of en ...
and electrons), both the carrier mobilities and carrier concentrations will contribute to the conductivity and these have different temperature dependencies. Ultimately, it is observed that the conductivity of insulators and semiconductors increase with initial increases in temperature above
absolute zero (as more electrons are shifted to the conduction band), before decreasing with intermediate temperatures and then, once again, increasing with still higher temperatures. The semimetallic state is similar to the metallic state but in semimetals both holes and electrons contribute to electrical conduction. With some semimetals, like
arsenic
Arsenic is a chemical element with the symbol As and atomic number 33. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Arsenic is a metalloid. It has various allotropes, ...
and
antimony
Antimony is a chemical element with the symbol Sb (from la, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony compounds have been known since ancient t ...
, there is a temperature-independent carrier density below room temperature (as in metals) while, in
bismuth
Bismuth is a chemical element with the symbol Bi and atomic number 83. It is a post-transition metal and one of the pnictogens, with chemical properties resembling its lighter group 15 siblings arsenic and antimony. Elemental bismuth occurs ...
, this is true at very low temperatures but at higher temperatures the carrier density increases with temperature giving rise to a semimetal-semiconductor transition. A semimetal also differs from an insulator or semiconductor in that a semimetal's conductivity is always non-zero, whereas a semiconductor has zero conductivity at zero temperature and insulators have zero conductivity even at ambient temperatures (due to a wider band gap).
Classification
To classify semiconductors and semimetals, the energies of their filled and empty bands must be plotted against the
crystal momentum of conduction electrons. According to the
Bloch theorem
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who d ...
the conduction of electrons depends on the periodicity of the crystal lattice in different directions.
In a semimetal, the bottom of the conduction band is typically situated in a different part of momentum space (at a different
k-vector) than the top of the valence band. One could say that a semimetal is a
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. ...
with a negative
indirect bandgap
In semiconductor physics, the band gap of a semiconductor can be of two basic types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterize ...
, although they are seldom described in those terms.
Classification of a material either as a semiconductor or a semimetal can become tricky when it has extremely small or slightly negative band-gaps. The well-known compound Fe
2VAl for example, was historically thought of as a semi-metal (with a negative gap ~ -0.1 eV) for over two decades before it was actually shown to be a small-gap (~ 0.03 eV) semiconductor using self-consistent analysis of the transport properties, electrical resistivity and
Seebeck coefficient
The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material ...
. Commonly used experimental techniques to investigate band-gap can be sensitive to many things such as the size of the band-gap, electronic structure features (direct versus indirect gap) and also the number of free charge carriers (which can frequently depend on synthesis conditions). Band-gap obtained from transport property modeling is essentially independent of such factors. Theoretical techniques to calculate the electronic structure on the other hand can often underestimate band-gap.
Schematic
![Semimetal-en](https://upload.wikimedia.org/wikipedia/commons/3/33/Semimetal-en.svg)
Schematically, the figure shows
The figure is schematic, showing only the lowest-energy conduction band and the highest-energy valence band in one dimension of
momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension.
Position space (also real space or coordinate space) is the set of all ''position vectors'' r in space, and h ...
(or k-space). In typical solids, k-space is three-dimensional, and there are an infinite number of bands.
Unlike a regular
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
, semimetals have charge carriers of both types (holes and electrons), so that one could also argue that they should be called 'double-metals' rather than semimetals. However, the charge carriers typically occur in much smaller numbers than in a real metal. In this respect they resemble
degenerate semiconductor
A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than as a semiconductor. Unlike non-degenerate semiconductors, these kind of semiconductor do not obey law of mass act ...
s more closely. This explains why the electrical properties of semimetals are partway between those of metals and
semiconductors.
Physical properties
As semimetals have fewer charge carriers than metals, they typically have lower
electrical
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
and
thermal conductivities. They also have small effective masses for both holes and electrons because the overlap in energy is usually the result of the fact that both energy bands are broad. In addition they typically show high
diamagnetic
Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
susceptibilities and high lattice
dielectric constants.
Classic semimetals
The classic semimetallic elements are
arsenic
Arsenic is a chemical element with the symbol As and atomic number 33. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Arsenic is a metalloid. It has various allotropes, ...
,
antimony
Antimony is a chemical element with the symbol Sb (from la, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony compounds have been known since ancient t ...
,
bismuth
Bismuth is a chemical element with the symbol Bi and atomic number 83. It is a post-transition metal and one of the pnictogens, with chemical properties resembling its lighter group 15 siblings arsenic and antimony. Elemental bismuth occurs ...
, α-
tin
Tin is a chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal.
Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent, t ...
(gray tin) and
graphite
Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on lar ...
, an
allotrope of
carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon mak ...
. The first two (As, Sb) are also considered
metalloids
A metalloid is a type of chemical element which has a preponderance of properties in between, or that are a mixture of, those of metals and nonmetals. There is no standard definition of a metalloid and no complete agreement on which elements are ...
but the terms semimetal and metalloid are not synonymous. Semimetals, in contrast to metalloids, can also be
chemical compound
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
s, such as
mercury telluride
Mercury telluride (HgTe) is a binary chemical compound of mercury and tellurium. It is a semi-metal related to the II-VI group of semiconductor materials. Alternative names are mercuric telluride and mercury(II) telluride.
HgTe occurs in nature ...
(HgTe), and
tin
Tin is a chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal.
Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent, t ...
,
bismuth
Bismuth is a chemical element with the symbol Bi and atomic number 83. It is a post-transition metal and one of the pnictogens, with chemical properties resembling its lighter group 15 siblings arsenic and antimony. Elemental bismuth occurs ...
, and
graphite
Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on lar ...
are typically not considered metalloids.
Transient semimetal states have been reported at extreme conditions. It has been recently shown that some
conductive polymers
Conductive polymers or, more precisely, intrinsically conducting polymers (ICPs) are organic polymers that conduct electricity. Such compounds may have metallic conductivity or can be semiconductors. The biggest advantage of conductive polymers ...
can behave as semimetals.
See also
*
Charge-transfer insulators
*
Half-metal
A half-metal is any substance that acts as a conductor to electrons of one spin orientation, but as an insulator or semiconductor to those of the opposite orientation. Although all half-metals are ferromagnetic (or ferrimagnetic), most ferromag ...
*
Hubbard model
*
Mott insulator
Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band ...
*
Solid-state physics
References
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