Non-radiative Recombination
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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 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 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 radiat ...
semiconductor devices, 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 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 diode pumped directly with e ...
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 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''. 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, 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 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 (n and p) is a constant (n_o p_o=n_i^2) at equilibrium, maintained by recombination and generation occurring at equal rates. When there is a surplus of carriers (i.e., n p>n_i^2), 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., n p), the generation rate becomes greater than the recombination rate, again driving the system back towards equilibrium. As the electron moves from one energy band to another, the energy and momentum that it has lost or gained must go to or come from the other particles involved in the process (e.g.
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
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 ...
, or the system of vibrating lattice atoms).


Carrier generation

When light interacts with a material, it can either be absorbed (generating a pair of free carriers or an exciton) or it can ''stimulate'' a recombination event. The generated photon has similar properties to the one responsible for the event. Absorption is the active process in
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,
solar cell A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
s and other semiconductor
photodetector Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation. There is a wide variety of photodetectors which may be classified by mechanism of detection, such as Photoelectric effect, photoelectric or photoc ...
s, while stimulated emission is the principle of operation in
laser diode 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 diode pumped directly with e ...
s. Besides light excitation, carriers in semiconductors can also be generated by an external electric field, for example in
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
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
s. When light with sufficient energy hits a semiconductor, it can excite electrons across the band gap. This generates additional charge carriers, temporarily lowering the electrical resistance of materials. This higher conductivity in the presence of light is known as
photoconductivity Photoconductivity is an optical and electrical phenomenon in which a material becomes more electrically conductive due to the absorption of electromagnetic radiation such as visible light, ultraviolet light, infrared light, or gamma radiation ...
. This conversion of light into electricity is widely used in
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.


Recombination mechanisms

Carrier recombination can happen through multiple relaxation channels. The main ones are band-to-band recombination, Shockley–Read–Hall (SRH) trap-assisted recombination,
Auger recombination In the solid-state physics of semiconductors, carrier generation and carrier recombination are processes by which mobile charge carriers (electrons and electron holes) are created and eliminated. Carrier generation and recombination processes are ...
and surface recombination. These decay channels can be separated into radiative and non-radiative. The latter occurs when the excess energy is converted into heat by
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
emission after the mean lifetime \tau_, whereas in the former at least part of the energy is released by light emission or
luminescence Luminescence is spontaneous emission of light by a substance not resulting from heat; or "cold light". It is thus a form of cold-body radiation. It can be caused by chemical reactions, electrical energy, subatomic motions or stress on a crys ...
after a radiative lifetime \tau_. The carrier lifetime \tau is then obtained from the rate of both type of events according to: \frac=\frac+\frac From which we can also define the internal quantum efficiency or quantum yield, \eta as: \eta = \frac =\frac \leq 1.


Radiative recombination


Band-to-band radiative recombination

''Band-to-band recombination'' is the name for the process of electrons jumping down from the conduction band to the valence band in a radiative manner. During band-to-band recombination, a form of spontaneous emission, the energy absorbed by a material is released in the form of photons. Generally these photons contain the same or
less Less or LESS may refer to: fewer than,: not as much. Computing * less (Unix), a Unix utility program * Less (stylesheet language), a dynamic stylesheet language * Large-Scale Scrum (LeSS), a product development framework that extends Scrum Othe ...
energy than those initially absorbed. This effect is how
LEDs 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 ...
create light. Because the photon carries relatively little
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
, radiative recombination is significant only in
direct bandgap In semiconductor physics, 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 characteriz ...
materials. This process is also known as ''bimolecular recombination'.'' This type of recombination depends on the density of electrons and holes in the excited state, denoted by n(t) and p(t) respectively. Let us represent the radiative recombination as R_r and the carrier generation rate as G. Total generation is the sum of thermal generation G0 and generation due to light shining on the semiconductor GL: G = G_0 + G_L Here we will consider the case in which there is no illumination on the semiconductor. Therefore G_L = 0 and G = G_0 , and we can express the change in carrier density as a function of time as = G-R_r = G_0 - R_r Because the rate of recombination is affected by both the concentration of free electrons and the concentration of holes that are available to them, we know that Rr should be proportional to np: R_r \propto np and we add a proportionality constant Br to eliminate the \propto sign: R_r=B_r np If the semiconductor is in thermal equilibrium, the rate at which electrons and holes recombine must be balanced by the rate at which they are generated by the spontaneous transition of an electron from the valence band to the conduction band. The recombination rate R_0 must be exactly balanced by the thermal generation rate G_0. Therefore: R_0 = G_0 = B_r n_0 p_0 where n_0 and p_0 are the equilibrium carrier densities. Using the mass action law np=n_i^2,with n_i being the intrinsic carrier density, we can rewrite it as R_0 = G_0 = B_r n_0 p_0= B_r n_i^2 The non-equilibrium carrier densities are given by n= n_0+ \Delta n, p= p_0+ \Delta p Then the new recombination rate R_\text becomes, R_\text = R_r-G_0 = B_rnp-G_0 = B_r(n_0 + \Delta n)(p_0 + \Delta p)-G_0 Because n_0 \gg\Delta n and p_0 \gg \Delta p, we can say that \Delta n\Delta p \approx 0 R_\text= B_r(n_0 + \Delta n)(p_0 + \Delta p)-G_0 = B_r(n_0p_0 + \Delta n p_0 +\Delta p n_0) - B_r n_i^2 R_\text= B_r(n_i^2 + \Delta n p_0 +\Delta p n_0- n_i^2) R_\text= B_r(\Delta n p_0 +\Delta p n_0) In an n-type semiconductor, p_0 \ll n_0 and \Delta p \ll n_0 thus R_ \approx B_r\Delta p n_0 Net recombination is the rate at which excess holes \Delta p disappear \frac = - R_\text \approx - B_r\Delta p n_0 Solve this differential equation to get a standard exponential decay \Delta p = p_e^ where pmax is the maximum excess hole concentration when t = 0. (It can be proved that p_=\frac, but here we will not discuss that). When t = \frac, all of the excess holes will have disappeared. Therefore, we can define the lifetime of the excess holes in the material \tau_p = \frac So the lifetime of the minority carrier is dependent upon the majority carrier concentration.


Stimulated emission

''Stimulated emission'' is a process in which an incident photon interacts with an excited electron causing it to recombine and emit a photon with the same properties of the incident one, in terms of
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
,
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
, polarization, and direction of travel. Stimulated emission together with the principle of
population inversion In science, specifically statistical mechanics, a population inversion occurs while a system (such as a group of atoms or molecules) exists in a state in which more members of the system are in higher, excited states than in lower, unexcited energy ...
are at the heart of operation of
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
s and
maser A maser (, an acronym for microwave amplification by stimulated emission of radiation) is a device that produces coherent electromagnetic waves through amplification by stimulated emission. The first maser was built by Charles H. Townes, Ja ...
s. It has been shown by
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
at the beginning of the twentieth century that if the excited and the ground level are non degenerate then the absorption rate W_and the stimulated emission rate W_are the same. Else if level 1 and level 2 are g_1-fold and g_2-fold degenerate respectively, the new relation is:g_1 W_= g_2 W_.


Trap emission

''Trap emission'' is a multistep process wherein a carrier falls into defect-related wavestates in the middle of the bandgap. A ''trap'' is a defect capable of holding a carrier. The trap emission process recombines electrons with holes and emits photons to conserve energy. Due to the multistep nature of trap emission, a phonon is also often emitted. Trap emission can proceed by use of bulk defects or surface defects.


Non-radiative recombination

Non-radiative recombination is a process in phosphors and
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, whereby charge carriers recombine releasing
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s instead of photons. Non-radiative recombination in optoelectronics and phosphors is an unwanted process, lowering the light generation efficiency and increasing heat losses. Non-radiative life time is the average time before an
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 ...
in the conduction band of a
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 ...
recombines with a
hole 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 ...
. It is an important parameter in
optoelectronics 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 ...
where
radiative recombination In the solid-state physics of semiconductors, carrier generation and carrier recombination are processes by which mobile charge carriers (electrons and electron holes) are created and eliminated. Carrier generation and recombination processes are ...
is required to produce a photon; if the non-radiative life time is shorter than the radiative, a carrier is more likely to recombine non-radiatively. This results in low internal quantum efficiency.


Shockley–Read–Hall (SRH)

In ''Shockley-Read-Hall recombination'' (''SRH''), also called ''trap-assisted recombination'', the electron in transition between bands passes through a new energy state (localized state) created within the
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 ...
by a
dopant A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optical properties. The amount of dopant necessary to cause changes is typically very low. When ...
or a
defect A defect is a physical, functional, or aesthetic attribute of a product or service that exhibits that the product or service failed to meet one of the desired specifications. Defect, defects or defected may also refer to: Examples * Angular defec ...
in the
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
; such energy states are called ''traps''. Non-radiative recombination occurs primarily at such sites. The energy is exchanged in the form of lattice vibration, a phonon exchanging thermal energy with the material. Since traps can absorb differences in
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
between the carriers, SRH is the dominant recombination process in
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
and other
indirect bandgap In semiconductor physics, 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 characterize ...
materials. However, trap-assisted recombination can also dominate in
direct bandgap In semiconductor physics, 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 characteriz ...
materials under conditions of very low carrier densities (very low level injection) or in materials with high density of traps such as
perovskites A perovskite is any material with a crystal structure following the formula ABX3, which was first discovered as the mineral called perovskite, which consists of calcium titanium oxide (CaTiO3). The mineral was first discovered in the Ural mou ...
. The process is named after
William Shockley William Bradford Shockley Jr. (February 13, 1910 – August 12, 1989) was an American physicist and inventor. He was the manager of a research group at Bell Labs that included John Bardeen and Walter Brattain. The three scientists were jointly ...
,
William Thornton Read William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of Eng ...
and Robert N. Hall, who published it in 1952.


Types of traps


= Electron traps vs. hole traps

= Even though all the recombination events can be described in terms of electron movements, it is common to visualize the different processes in terms of excited electron and the electron ''holes'' they leave behind. In this context, if trap levels are close to the conduction band, they can temporarily immobilize excited electrons or in other words, they are ''electron traps''. On the other hand, if their energy lies close to 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 ...
they become ''hole traps.''


=Shallow traps vs. deep traps

= The distinction between shallow and deep traps is commonly made depending on how close electron traps are to the conduction band and how close hole traps are to the valence band. If the difference between trap and band is smaller than the thermal energy kBT it is often said that it is a ''shallow trap''. Alternatively, if the difference is larger than the thermal energy, it is called a
deep trap ''Deep Trap'' () (previously known as ''Exchange'') is a 2015 South Korean crime thriller film starring Ma Dong-seok, Jo Han-sun and Kim Min-kyung, and directed by Kwon Hyung-jin. Based on an actual SNS crime, it depicts the terror experienced by ...
. This difference is useful because shallow traps can be emptied more easily and thus are often not as detrimental to the performance of optoelectronic devices.


SRH model

In the SRH model, four things can happen involving trap levels: * An electron in the conduction band can be trapped in an intragap state. * An electron can be emitted into the conduction band from a trap level. * A hole in the valence band can be captured by a trap. This is analogous to a filled trap releasing an electron into the valence band. * A captured hole can be released into the valence band. Analogous to the capture of an electron from the valence band. When carrier recombination occurs through traps, we can replace the valence
density of states In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states i ...
by that of the intragap state. The term p(n)is replaced by the density of trapped electrons/holes N_t(1-f_t). R_=B_n n N_t (1-f_t) Where N_t is the density of trap states and f_t is the probability of that occupied state. Considering a material containing both types of traps, we can define two trapping coefficients B_n, B_p and two de-trapping coefficients G_n, G_p. In equilibrium, both trapping and de-trapping should be balanced and R_=G_). Then, the four rates as a function of f_tbecome: \begin R_=B_nnN_(1-f_t)& G_n=B_n n_t N_t f_t \\ R_=B_p p N_t f_t&G_p=B_p p_t N_t (1-f_t) \end Where n_t and p_t are the electron and hole densities when the
quasi Fermi level A quasi Fermi level (also called imref, which is "fermi" spelled backwards) is a term used in quantum mechanics and especially in solid state physics for the Fermi level (chemical potential of electrons) that describes the population of electrons ...
matches the trap energy. In steady-state condition, the net recombination rate of electrons should match the net recombination rate for holes, in other words: R_-G_n =R_-G_p. This eliminates the occupation probability f_t and leads to the Shockley-Read-Hall expression for the trap-assisted recombination: R=\frac Where the average lifetime for electrons and holes are defined as: \tau_n=\frac,\quad \tau_p=\frac.


Auger recombination

In ''Auger recombination'' the energy is given to a third carrier which is excited to a higher energy level without moving to another energy band. After the interaction, the third carrier normally loses its excess energy to thermal vibrations. Since this process is a three-particle interaction, it is normally only significant in non-equilibrium conditions when the carrier density is very high. The
Auger effect The Auger effect or Auger−Meitner effect is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom. When a core electron is removed, leaving a vacancy, an ...
process is not easily produced, because the third particle would have to begin the process in the unstable high-energy state. In thermal equilibrium the Auger recombination R_A and thermal generation rate G_0 equal each other R_ = G_0 = C_n n_0^2 p_0 + C_p n_0 p_0^2 where C_n,C_p are the Auger capture probabilities. The non-equilibrium Auger recombination rate r_A and resulting net recombination rate U_A under steady-state conditions are r_A = C_n n^2 p + C_p n p^2 \,, \quad R_A = r_A-G_0 = C_n \left( n^2p-n_0^2 p_0 \right) + C_p \left( np^2- n_0 p_0^2 \right) \,. The Auger lifetime \tau_A is given by \tau_A = \frac = \frac \,. The mechanism causing LED efficiency drop was identified in 2007 as Auger recombination, which met with a mixed reaction.Stevenson, Richard (August 2009
"The LED's Dark Secret: Solid-state lighting won't supplant the lightbulb until it can overcome the mysterious malady known as droop"
IEEE Spectrum
In 2013, an experimental study claimed to have identified Auger recombination as the cause of efficiency droop. However, it remains disputed whether the amount of Auger loss found in this study is sufficient to explain the droop. Other frequently quoted evidence against Auger as the main droop-causing mechanism is the low-temperature dependence of this mechanism, which is the opposite of that found for the drop.


Surface recombination

Trap-assisted recombination at the surface of a semiconductor is referred to as surface recombination. This occurs when traps at or near the surface or interface of the semiconductor form due to dangling bonds caused by the sudden discontinuation of the semiconductor crystal. Surface recombination is characterized by surface recombination velocity which depends on the density of surface defects. In applications such as solar cells, surface recombination may be the dominant mechanism of recombination due to the collection and extraction of free carriers at the surface. In some applications of solar cells, a layer of transparent material with a large band gap, also known as a window layer, is used to minimize surface recombination. Passivation techniques are also employed to minimize surface recombination.


Langevin recombination

For free carriers in low-mobility systems, the recombination rate is often described with the Langevin recombination rate. The model is often used for disordered systems such as organic materials (and is hence relevant for
organic solar cell An organic solar cell (OSC) or plastic solar cell is a type of photovoltaic that uses organic electronics, a branch of electronics that deals with conductive organic polymers or small organic molecules, for light absorption and charge transport t ...
s) and other such systems. The Langevin recombination strength is defined as \gamma = \tfrac\mu.


See also

*
Cage effect In chemistry, the cage effect (also known as geminate recombination) describes how the properties of a molecule are affected by its surroundings. First introduced by Franck and Rabinowitch in 1934, the cage effect suggests that instead of actin ...
*
Auger effect The Auger effect or Auger−Meitner effect is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom. When a core electron is removed, leaving a vacancy, an ...


References

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Further reading

* N.W. Ashcroft and N.D. Mermin, ''Solid State Physics'', Brooks Cole, 1976


External links


PV Lighthouse Recombination Calculator

PV Lighthouse Band Gap CalculatorPV Education
Semiconductors Optoelectronics Charge carriers