Conduction band in the context of "Electronic state"

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 (often expressed in electronvolts) 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 (and the electron hole in the valence band) 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 (mostly full) to the conduction band (mostly empty), then current can flow (see carrier generation and recombination). Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps (also called "wide" band gaps) are generally insulators, those with small band gaps (also called "narrow" band gaps) are semiconductors, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.

It is possible to produce laser induced insulator-metal transitions which have already been experimentally observed in some condensed matter systems, like thin films of C₆₀, doped manganites, or in vanadium sesquioxide V₂O₃. These are special cases of the more general metal-to-nonmetal transitions phenomena which were intensively studied in the last decades. A one-dimensional analytic model of laser induced distortion of band structure was presented for a spatially periodic (cosine) potential. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger co-moving frame. The solutions can be given with the help of the Mathieu functions.

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 (electron donor dopant/excited electrons) is equal to p (electron acceptor dopant/vacant holes that act as positive charges).

The electrical conductivity of chemically pure semiconductors can still be affected by crystallographic defects of technological origin (like vacancies), some of which can behave similar to dopants. Their effect can often be neglected, though, and the number of electrons in the conduction band is then exactly equal to the number of holes in the valence band. The conduction of current of intrinsic semiconductor is enabled purely by electron excitation across the band-gap, which is usually small at room temperature except for narrow-bandgap semiconductors, like Hg
_0.8Cd
_0.2Te.

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.

The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as an elementary excitation primarily in condensed matter, such as insulators, semiconductors, some metals, and in some liquids. It transports energy without transporting net electric charge.

An exciton can form when an electron from the valence band of a crystal is promoted in energy to the conduction band, for instance when a material absorbs a photon. Promoting the electron to the conduction band leaves a positively charged hole in the valence band. Here 'hole' represents the unoccupied quantum mechanical electron state with a positive charge, an analogue in crystal of a positron. Because of the attractive Coulomb force between the electron and the hole, a bound state is formed, akin to that of the electron and proton in a hydrogen atom or the electron and positron in positronium. Excitons are composite bosons since they are formed from two fermions which are the electron and the hole.

Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic in nanotechnology and materials science. When a quantum dot is illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conduction band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the discrete energy levels of the quantum dot in the conduction band and the valence band.

In other words, a quantum dot can be defined as a structure on a semiconductor which is capable of confining electrons in three dimensions, enabling the ability to define discrete energy levels. The quantum dots are tiny crystals that can behave as individual atoms, and their properties can be manipulated.

In semiconductors, 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 characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are different, the material has an "indirect gap". The band gap is called "direct" if the crystal momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.

Examples of direct bandgap materials include hydrogenated amorphous silicon and some III–V materials such as InAs and GaAs. Indirect bandgap materials include crystalline silicon and Ge. Some III–V materials are indirect bandgap as well, for example AlSb.

Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from a material placed in an electrostatic field. The most common context is field emission from a solid surface into a vacuum. However, field emission can take place from solid or liquid surfaces, into a vacuum, a fluid (e.g. air), or any non-conducting or weakly conducting dielectric. The field-induced promotion of electrons from the valence to conduction band of semiconductors (the Zener effect) can also be regarded as a form of field emission.

Field emission in pure metals occurs in high electric fields: the gradients are typically higher than 1 gigavolt per metre and strongly dependent upon the work function. While electron sources based on field emission have a number of applications, field emission is most commonly an undesirable primary source of vacuum breakdown and electrical discharge phenomena, which engineers work to prevent. Examples of applications for surface field emission include the construction of bright electron sources for high-resolution electron microscopes or the discharge of induced charges from spacecraft. Devices that eliminate induced charges are termed charge-neutralizers.

A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than a semiconductor. Unlike non-degenerate semiconductors, these kinds of semiconductor do not obey the law of mass action, which relates intrinsic carrier concentration with temperature and bandgap.

At moderate doping levels, the dopant atoms create individual doping levels that can often be considered as localized states that can donate electrons or holes by thermal promotion (or an optical transition) to the conduction or valence bands respectively. At high enough impurity concentrations, the individual impurity atoms may become close enough neighbors that their doping levels merge into an impurity band and the behavior of such a system ceases to show the typical traits of a semiconductor, e.g. its increase in conductivity with temperature. On the other hand, a degenerate semiconductor still has far fewer charge carriers than a true metal so that its behavior is in many ways intermediary between semiconductor and metal.