The transport of electrical charge through some substance. Only metals conduct electricity well; conduction is by means of the free electrons in the electron gas characteristic of metal structure. Ionic and covalently bound solids are insulators; but ionic solids such as salt (sodium chloride) conduct when dissolved in water, as the electrically charged ions become free to move. In semiconductors, the low electrical conductivity is due to a small number of electrons acquiring sufficient energy to become released into the body of the material in a way similar to conduction electrons in metals. The spaces vacated by the electrons (holes) behave as positively charged particles, and also contribute to conduction. Conduction in semi-conductors may be altered by doping - the introduction of impurities to provide more holes and electrons.
Conduction in metals and resistors is well described by Ohm's Law, which states that the current is proportional to the applied electric field. The ease with which current density (current per area) j appears in a material is measured by the conductivity σ, defined as:
j = σ Eor its reciprocal resistivity ρ:
j = E / ρIn linear anisotropic materials, σ and ρ are tensors.
Solids (including insulating solids)
In crystalline solids, atoms interact with their neighbors, and the energy levels of the electrons in isolated atoms turn into bands. Electrons, being fermions, follow the Pauli exclusion principle, meaning that two electrons in the same interacting system cannot occupy the same state, which further means that their four quantum numbers have to be different. Thus electrons in a solid fill up the energy bands up to a certain level, called the Fermi energy. Bands which are completely full of electrons cannot conduct electricity, because there is no state of nearby energy to which the electrons can jump.
Metals
Metals are good conductors because they have unfilled space in the valence energy band. In the absence of an electric field, there exist electrons travelling in all directions and many different velocities up to the Fermi velocity (the velocity of electrons at the Fermi energy). When an electric field is applied, a slight imbalance develops and mobile electrons flow. Electrons in this band can be accelerated by the field because there are plenty of nearby unfilled states in the band.
Resistance comes about in a metal because of the scattering of electrons from defects in the lattice or by phonons. The conductivity is then given by the formula
where n is the density of conduction electrons, e is the electron charge, and m is the electron mass.
Semiconductors
A solid with filled bands is an insulator, but at finite temperature, electrons can be thermally excited from the valence band to the next highest, the conduction band. The fraction of electrons excited in this way depends on the temperature and the band gap, the energy difference between the two bands. Exciting these electrons into the conduction band leaves behind positively charged holes in the valence band, which can also conduct electricity. Donor (n-type) impurities have extra valence electrons with energies very close to the conduction band which can be easily thermally excited to the conduction band. Acceptor (p-type) impurities capture electrons from the valence band, allowing the easy formation of holes.
Electrolytes
Electric currents in electrolytes are flows of electrically charged atoms (ions). If the conditions are right, redox reactions will take place at the electrode surfaces, releasing electrons from the chlorine, and allow electrons to be absorbed into the sodium. In these materials, currents of electricity are composed of moving protons (as opposed to the moving electrons found in metals).
Gases and plasmas
In air, and other ordinary gases below the breakdown field, the dominant source of electrical conduction is via a relatively small number of mobile ions produced by radioactive gases, ultraviolet light, or cosmic rays. However, once the applied electric field approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown. The breakdown process forms a plasma that contains a significant number of mobile electrons and positive ions, causing it to behave as an electrical conductor.
Plasma is the state of matter where some of the electrons in a gas are stripped or "ionized" from their molecules or atoms. Due to their lower mass, the electrons in a plasma accelerate more quickly in response to an electric field than the heavier positive ions, and hence carry the bulk of the current. However, metal electrode surfaces can cause a region of the vacuum to become conductive by injecting free electrons or ions through either field emission or thermionic emission. Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum. Externally heated electrodes are often used to generate an electron cloud as in the filament or indirectly heated cathode of vacuum tubes. Cold electrodes can also spontaneously produce electron clouds via thermionic emission when small incandescent regions (called cathode spots or anode spots) are formed.
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