Valence and conduction bands

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Filling of the electronic states in various types of materials at equilibrium. Here, height is energy while width is the density of available states for a certain energy in the material listed. The shade follows the Fermi-Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level EF lies inside at least one band.
In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes. "intrin." indicates intrinsic semiconductors.
edit Band filling diagram.svg
Filling of the electronic states in various types of materials at equilibrium. Here, height is energy while width is the density of available states for a certain energy in the material listed. The shade follows the Fermi–Dirac distribution (black: all states filled, white: no state filled). In metals and semimetals the Fermi level EF lies inside at least one band.
In insulators and semiconductors the Fermi level is inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes. "intrin." indicates intrinsic semiconductors.

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 which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a semiconducting material, the valence band is located below the Fermi level, while the conduction band is located above it.

Contents

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 conductors 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. [1] 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 (lots of bands 2).svg
Semiconductor band structure
See electrical conduction and semiconductor for a more detailed description of band structure.

In solids, the ability of electrons to act as charge carriers 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 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. [2]

See also

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<span class="mw-page-title-main">Electric current</span> Flow of electric charge

An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons.

<span class="mw-page-title-main">Metallic bonding</span> Type of chemical bond in metals

Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and lustre.

A semiconductor is a material that is between the conductor and insulator in ability to conduct electrical current. In many cases their conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common semiconductor and is used in laser diodes, solar cells, microwave-frequency integrated circuits, and others. Silicon is a critical element for fabricating most electronic circuits.

Electrical resistivity is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

<span class="mw-page-title-main">Band gap</span> Energy range in a solid where no electron states exist

In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO/LUMO gap in 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 to the conduction band, then current can flow. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps are generally insulators, those with small band gaps are semiconductor, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.

<span class="mw-page-title-main">Electron hole</span> Conceptual opposite of an electron

In physics, chemistry, and electronic engineering, an electron hole is a quasiparticle denoting the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole's location.

<span class="mw-page-title-main">Fermi level</span> Quantity in solid state thermodynamics

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 EF for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from. A precise understanding of the Fermi level—how it relates to electronic band structure in determining electronic properties; how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics.

In solid state 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. In a conducting medium, an electric field can exert force on these free particles, causing a net motion of the particles through the medium; this is what constitutes an electric current. The electron and the proton are the elementary charge carriers, each carrying one elementary charge (e), of the same magnitude and opposite sign.

<span class="mw-page-title-main">Valence electron</span> Electron in the outer shell of an atoms energy levels

In chemistry and physics, valence electrons are electrons in the outermost shell of an atom, and that can participate in the formation of a chemical bond if the outermost shell is not closed. In a single covalent bond, a shared pair forms with both atoms in the bond each contributing one valence electron.

In solid-state physics, the electronic 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.

<span class="mw-page-title-main">Semimetal</span> Metal with a small negative indirect band-gap

A semimetal is a material with a small energy overlap between the bottom of the conduction band and the top of the valence band, but they do not overlap in momentum space. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, or metals. In insulators and semiconductors the filled valence band is separated from an empty conduction band by a band gap. For insulators, the magnitude of the band gap is larger than that of a semiconductor. Because of the slight overlap between the conduction and valence bands, semimetals have no band gap and a small density of states 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.

<span class="mw-page-title-main">Doping (semiconductor)</span> Intentional introduction of impurities into an intrinsic semiconductor

In semiconductor production, doping is the intentional introduction of impurities into an intrinsic (undoped) semiconductor for the purpose of modulating its electrical, optical and structural properties. The doped material is referred to as an extrinsic semiconductor.

In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.

An intrinsic semiconductor, also called a pure semiconductor, undoped semiconductor or i-type semiconductor, is a semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p. This may be the case even after doping the semiconductor, though only if it is doped with both donors and acceptors equally. In this case, n = p still holds, and the semiconductor remains intrinsic, though doped. This means that some conductors are both intrinsic as well as extrinsic but only if n is equal to p.

<span class="mw-page-title-main">Mott insulator</span> Materials classically predicted to be conductors, that are actually insulators

Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators. These insulators fail to be correctly described by band theories of solids due to their strong electron–electron interactions, which are not considered in conventional band theory. A Mott transition is a transition from a metal to an insulator, driven by the strong interactions between electrons. One of the simplest models that can capture Mott transition is the Hubbard model.

Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m−3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.

<span class="mw-page-title-main">Band diagram</span> Diagram plotting electron energy levels

In solid-state physics of semiconductors, a band diagram is a diagram plotting various key electron energy levels as a function of some spatial dimension, which is often denoted x. These diagrams help to explain the operation of many kinds of semiconductor devices and to visualize how bands change with position. The bands may be coloured to distinguish level filling.

A quasi Fermi level is a term used in quantum mechanics and especially in solid state physics for the Fermi level that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from equilibrium. This displacement could be caused by the application of an external voltage, or by exposure to light of energy , which alter the populations of electrons in the conduction band and valence band. Since recombination rate tends to be much slower than the energy relaxation rate within each band, the conduction band and valence band can each have an individual population that is internally in equilibrium, even though the bands are not in equilibrium with respect to exchange of electrons. The displacement from equilibrium is such that the carrier populations can no longer be described by a single Fermi level, however it is possible to describe using concept of separate quasi-Fermi levels for each band.

In electronics and semiconductor physics, the law of mass action relates the concentrations of free electrons and electron holes under thermal equilibrium. It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration . The intrinsic carrier concentration is a function of temperature.

<span class="mw-page-title-main">Field effect (semiconductor)</span>

In physics, the field effect refers to the modulation of the electrical conductivity of a material by the application of an external electric field.

References

Citations

  1. Cox, P. A. (1987). The electronic structure and chemistry of solids. Oxford [Oxfordshire]: Oxford University Press. ISBN   0-19-855204-1. OCLC   14213060.
  2. Jasieniak, Jacek; Califano, Marco; Watkins, Scott E. (2011-06-22). "Size-Dependent Valence and Conduction Band-Edge Energies of Semiconductor Nanocrystals" . ACS Nano. 5 (7): 5888–5902. doi:10.1021/nn201681s. ISSN   1936-0851. PMID   21662980.

General references