In the
solid-state physics of
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, carrier generation and carrier recombination are processes by which mobile
charge carriers (
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 no ...
s and
electron hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...
s) are created and eliminated. Carrier generation and recombination processes are fundamental to the operation of many
optoelectronic
Optoelectronics (or optronics) is the study and application of electronic devices and systems that find, detect and control light, usually considered a sub-field of photonics. In this context, ''light'' often includes invisible forms of radiat ...
semiconductor devices, such as
photodiodes,
light-emitting diode
A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (co ...
s and
laser diodes. They are also critical to a full analysis of
p-n junction devices such as
bipolar junction transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipola ...
s and p-n junction
diodes.
The electron–hole pair is the fundamental unit of generation and recombination in
inorganic semiconductors, corresponding to an electron transitioning between the valence band and the conduction band where generation of electron is a transition from the valence band to the conduction band and recombination leads to a reverse transition.
Overview
Like other solids, semiconductor materials have an
electronic band structure determined by the crystal properties of the material. Energy distribution among electrons is described by the
Fermi level and 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 ...
of the electrons. At
absolute zero temperature, all of the electrons have energy below the Fermi level; but at non-zero temperatures the energy levels are filled following a Fermi-Dirac distribution.
In undoped semiconductors the Fermi level lies in the middle of a ''forbidden band'' or
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 ( ...
between two ''allowed bands'' called 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 ...
'' and the ''
conduction band''. The valence band, immediately below the forbidden band, is normally very nearly completely occupied. The conduction band, above the Fermi level, is normally nearly completely empty. Because the valence band is so nearly full, its electrons are not mobile, and cannot flow as electric current.
However, if an electron in the valence band acquires enough energy to reach the conduction band (as a result of interaction with other
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 no ...
s,
holes, photons, or the
vibrating crystal lattice itself), it can flow freely among the nearly empty conduction band energy states. Furthermore, it will also leave behind a hole that can flow as current exactly like a physical charged particle.
Carrier generation describes processes by which electrons gain energy and move from the valence band to the conduction band, producing two mobile carriers; while recombination describes processes by which a conduction band electron loses energy and re-occupies the energy state of an electron hole in the valence band.
These processes must conserve both quantized energy and
crystal momentum, and the
vibrating lattice plays a large role in conserving momentum as, in collisions, photons can transfer very little momentum in relation to their energy.
Relation between generation and recombination
Recombination and generation are always happening in semiconductors, both optically and thermally. As predicted by
thermodynamics, a material at
thermal equilibrium will have generation and recombination rates that are balanced so that the net
charge carrier density remains constant. The resulting probability of occupation of energy states in each energy band is given by
Fermi–Dirac statistics.
The product of the
electron and hole densities (
and
) is a constant
at equilibrium, maintained by recombination and generation occurring at equal rates. When there is a surplus of carriers (i.e.,
), the rate of recombination becomes greater than the rate of generation, driving the system back towards equilibrium. Likewise, when there is a deficit of carriers (i.e.,