In the
solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...
of
semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s, carrier generation and carrier recombination are processes by which mobile
charge carrier
In 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. The term is used ...
s (
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 kn ...
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 radiatio ...
semiconductor device
A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material (primarily silicon, germanium, and gallium arsenide, as well as organic semiconductors) for its function. Its conductivity li ...
s, such as
photodiode
A photodiode is a light-sensitive semiconductor diode. It produces current when it absorbs photons.
The package of a photodiode allows light (or infrared or ultraviolet radiation, or X-rays) to reach the sensitive part of the device. The packag ...
s,
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 (cor ...
s and
laser diode
file:Laser diode chip.jpg, The laser diode chip removed and placed on the eye of a needle for scale
A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a di ...
s. 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 bipolar ...
s and p-n junction
diode
A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diode ...
s.
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
In solid-state physics, the electronic band structure (or simply 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 (called ''band gaps'' or '' ...
determined by the crystal properties of the material. Energy distribution among electrons is described by the
Fermi level
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 ''E''F
for brevity. The Fermi level does not include the work required to remove ...
and the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
of the electrons. At
absolute zero
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
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 (in ...
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
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 ...
''. 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 kn ...
s,
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 ...
, 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
In solid-state physics crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the associated wave vectors \mathbf of this lattice, according to
:_ \equiv \hbar
(where \hba ...
, 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
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
, a material at
thermal equilibrium
Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
will have generation and recombination rates that are balanced so that the net
charge carrier
In 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. The term is used ...
density remains constant. The resulting probability of occupation of energy states in each energy band is given by
Fermi–Dirac statistics
Fermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac di ...
.
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.,