The Ministry of Silly Walks

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https://en.wikipedia.org/wiki/The_Ministry_of_Silly_Walks

John Cleese as a civil servant in the halls of the Ministry

Typical silly walk gait with instructions.

"The Ministry of Silly Walks" is a sketch from the Monty Python comedy troupe's television show Monty Python's Flying Circus, series 2, episode 1, which is entitled "Face the Press". The episode first aired on 15 September 1970. A shortened version of the sketch was performed for Monty Python Live at the Hollywood Bowl.

A satire on bureaucratic inefficiency, the sketch involves John Cleese as a bowler-hatted civil servant in a fictitious British government ministry responsible for developing silly walks through grants. Cleese, throughout the sketch, walks in a variety of silly ways. It is these various silly walks, more than the dialogue, that have earned the sketch its popularity. Cleese has cited the physical comedy of Max Wall, probably in character as Professor Wallofski, as important to its conception.

Ben Beaumont-Thomas in The Guardian writes, "Cleese is utterly deadpan as he takes the stereotypical bowler-hatted political drone and ruthlessly skewers him. All the self-importance, bureaucratic inefficiency and laughable circuitousness of Whitehall is summed up in one balletic extension of his slender leg."

According to research, published in British Medical Journal a 'silly walk' would take about 2.5 times as much energy as normal walking.

Sketch

The sketch as originally depicted in the series begins with John Cleese playing Mr. Teabag, a civil servant who, after purchasing The Times from the newsagent in the previous sketch, walks through the streets of London (at the crossing of Thorpebank Road and Dunraven Road) in a very peculiar manner. He eventually arrives at his place of business: The Ministry of Silly Walks, on the northern end of Whitehall. In the hallway, he passes other employees all exhibiting their own silly walks before arriving at his office (the Hollywood Bowl performance omits this preamble). Once there, he finds Mr Putey (Michael Palin) waiting for him and apologizes for the delay, explaining that his walk has become particularly silly of late and it takes longer for him to reach his destination.

Putey explains that he has a silly walk he wishes to develop with grant money. He demonstrates his walk which, to Teabag, isn't particularly silly ("The right leg isn't silly at all, and the left leg merely does a forward aerial half-turn every alternate step."). He tells Putey that he does not believe the ministry can help him, as Putey's walk is not silly enough and funding is short. The government, he explains (whilst walking around his office in increasingly silly ways), is supposed to give equally to Defence, Social Security, Health, Housing, Education, and Silly Walks, but recently spent less on Silly Walks than on national defence. After a visit by his secretary Mrs. Two-Lumps, Mr. Teabag shows Mr Putey a film on silly walks. (The segment is a parody of early 20th-century cinema, with Michael Palin dressed up as Little Tich; this film is also shown as part of the Hollywood Bowl performance of the sketch.) After tossing the projector offstage, Teabag offers Putey a grant that will allow him to work on the Anglo-French Silly Walk, La Marche Futile (a parody of Concorde's Anglo-French development), which is then demonstrated by a man (Terry Jones) dressed in a mixture of stereotypical English and French outfits, with a sped-up version of "La Marseillaise" playing.

Mrs. Two-Lumps, presumably the minister's secretary, makes a brief appearance, bringing in coffee with full silly walk. As she enters, the cups fall all over the tray, completely spilling their contents. The minister looks at the tray, says "Thank you, lovely" and she exits again, taking the tray with her, complete with upended cups. In the Hollywood Bowl version, Carol Cleveland plays Mrs. Two-Lumps, and spills some of the coffee on Cleese during the sketch.

As the years went by amid repeated requests to do the sketch, Cleese found it increasingly difficult to perform these walks. He would say, when told about a new Python tour, "I'm not doing silly walks." Accordingly, the sketch was not performed during Monty Python Live (Mostly), the troupe's 2014 reunion show. It was replaced by "The Silly Walks Song", which was performed by a group of (younger) dancers who mimicked Cleese's original walks while wearing bowler hats and carrying briefcases.

Reception

In 2005, the sketch was chosen in a poll taken by Channel 4 in Britain as the 15th greatest comedy sketch of all time (and one of five Monty Python sketches in the top 50).

Mobile game

Main article: Monty Python's The Ministry of Silly Walks

In 2014, an official video game adaption of the sketch was released for Android and iOS. It features Cleese, as the minister of silly walks, leaving his office and walking through London. It takes the form of an endless runner game, except with an appropriately absurd walking animation. The game includes voice acting from John Cleese.

References in popular culture

• In the 1988 Warhammer Fantasy Battle rulebook, Realm of Chaos: Slaves to Darkness, one of the possible mutations a creature might get is a "silly walk", which is considered widely by many to be a reference to this sketch, as early Warhammer products were considerably more comedic in tone, and contained many references to then-contemporary British culture.
• In the 1994 Beastie Boys "Sure Shot" music video, Adam Yauch demonstrates a Silly Walk step for Adam Horovitz. John Berry later reminisced of a teenage Yauch, "He was really into Monty Python, especially the Silly Walk skit."
• In 2000, an episode of Mission Hill, "Andy and Kevin Make a Friend (or One Bang for Two Brothers)", referenced the sketch when one of the characters attempts to impress a girl by showing how he does a "great silly walk" from the Ministry of Silly Walks.
• A reference is made to the Silly Walk in an episode of the WB's Gilmore Girls when Rory says "Please, don't walk away like that", and Dean responds with "Sorry, I'd do a silly walk, but I'm not feeling very John Cleese right now."
• In the video game Goldeneye 007, an image of a man doing John Cleese's silly walk can be seen on one of the computer monitors in the game.
• In an issue of The Simpsons Bongo Comic, when the British invade Springfield, it shows John Cleese doing the goosestep and labels him as "the Minister of Silly Walks".
• On an episode of The Chaser's War On Everything, Andrew Hansen and Chris Taylor do a sketch called "The Chaser's British Comedy Sketch", filled with various Monty Python cliches, which climaxes with Andrew screaming "I'm going to do something so totally bizarre it will be imitated verbatim by comedy nerds for decades to come!" He then does a silly walk, doing imitations of Pepperpots, until a 16-ton weight falls on his head.
• In November 2007, as the Eurostar duration between Brussels and London was reduced to 1 hour and 51 minutes, the "Ministry of Silly Walks" appeared in an ad campaign in Belgium. The adverts were all on building corners, showing two workers carrying a large glass pane walking towards the corner on one side. Walking towards them on the other side, a John Cleese look-alike performs a Silly Walk. The tagline read "Warning! London is just around the corner!".
• In the Season 6 episode of Futurama entitled "All the Presidents Heads", Dr. Zoidberg performs a silly walk.
• In the 25th anniversary reunion episode of I'm Sorry, I'll Read That Again, John Cleese consents to appear on the show on condition that he be allowed to do the Silly Walk; the other cast members are dubious about the comedic impact of doing the Walk on radio, but they ultimately give in after Cleese puts on a show of hurt feelings. Near the end of the show, Cleese presents the Silly Walk, rendered on radio as a series of loud, slow footsteps.
• In the video game Destroy All Humans! 2, if you read a hippie's mind in the Albion level, one of the thoughts is, "I hope I can get a job at the Ministry of Silly Walks" (This video game is known for spoofing popular culture of the decade in which it is set).
• In a standup comedy routine in Blue Collar Comedy Tour: One For the Road, Larry the Cable Guy, referring to strange people who go to Wal-Mart in the middle of the night, says that it "turns into Monty Python's Ministry of Silly Walks."
• In Improv Everywhere's 2010 MP3 experiment, participants were asked to walk in a silly manner. After the silly walk session was finished, 'Mark (the omnipotent voice from above)' stated: "Excellent silly walks. Those belong in the Ministry hall of fame".
• A segment in The Beano comic book featured Minnie the Minx as the "Minnie-ster of Silly Walks".
• In the Fawlty Towers episode "The Germans", Basil (John Cleese), after grandly announcing, "I'll do the funny walk", performs a goose step, reminiscent of a silly walk.
• In the second issue of Alan Moore and Kevin O'Neill's comic book The League of Extraordinary Gentlemen, Volume III: Century, the "Minister" can be seen performing the silly walk in the background in London, passing the League of Extraordinary Gentlemen.
• In the Czech city of Brno, a Silly Walk City March is held annually since 2012.
• The small town of Ørje, Norway found a way to spice up one of its crosswalks—pedestrians wishing to cross must do so using a silly walk. The town's mayor didn't seem to mind the silliness. "Clearly, one should listen to the authorities, but this kind of fun should be allowed", the mayor said. "You cannot just be square, right?"
• The 4 July 2016 issue of The New Yorker features a parody of the silly walk on its cover, a reference to Brexit, in which several men in the likeness of John Cleese's character do the silly walk off the edge of a cliff.
• The 22 January 2017 episode of Zondag met Lubach mentions Minister Jetta Klijnsma being a disabled politician from the Ministry of Silly Walks, so U.S. President Donald Trump can make fun of her.
• In the video game West of Loathing, there is an option for "stupid walking", which allows the player to "walk in silly ways". The entire game can be completed this way.
• In the video game Payday 2, the safe house butler Aldstone, voiced by John Cleese, has a rare chance of walking this way for a few seconds.
• On 28 October 2019, while celebrating the Ohi Day, a group of participants to the national military parade performed a silly walk as an anti-military demonstration in Nea Filadelfeia, Greece.
• The LaTeX package Sillypage was developed by Phelype H. Oleinik and Paulo R. M. Cereda to use the Cleese walk silhouettes as page numbers in a document.
• The 2017 video game Destiny 2 has an emote featuring the silly walk, titled "Bureaucratic Walk".

COVID-19 pandemic

Unofficial signs stating that certain sidewalks are under the jurisdiction of The Ministry of Silly Walks have been placed along sidewalks worldwide, including the United States, Canada, and England as a way to allow pedestrians to laugh in a stressful time.

Ministry (government department)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Ministry_(government_department)

 

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Ministry or department (also less commonly used secretariat, office, or directorate) are designations used by first-level executive bodies in the machinery of governments that manage a specific sector of public administration.

These types of organizations are usually led by a politician who is a member of a cabinet—a body of high-ranking government officials—who may use a title such as minister, secretary, or commissioner, and are typically staffed with members of a non-political civil service, who manage its operations; they may also oversee other government agencies and organizations as part of a political portfolio. Governments may have differing numbers and types of ministries and departments. In some countries, these terms may be used with specific meanings: for example, an office may be a subdivision of a department or ministry.

Usage

Canada

Further information: Structure of the Canadian federal government

The federal Government of Canada uses the term department to refer to its first-level executive bodies.

Subdivisions

In Canada, first-level subdivisions are known as provinces and territories. Five of the ten provincial governments use the term ministry to describe their departments (Ontario, Quebec, Saskatchewan, British Columbia, and Alberta) but the other five, as well as the three territorial governments, use the term department. Despite the difference in nomenclature, both the provincial and federal governments use the term "minister" to describe the head of a ministry or department. The specific task assigned to a minister is referred to as his or her "portfolio".

United Kingdom

Main article: British government departments

In the United Kingdom, all government organisations that consist of civil servants, and which may or may not be headed by a government minister or secretary of state, are considered to be departments. Until 2018, the term "ministry" had been retained only for the Ministry of Defence and the Ministry of Justice. On 8 January 2018, Prime Minister Theresa May announced that the Department of Communities and Local Government would be renamed to the Ministry of Housing, Communities and Local Government to emphasise her government's prioritising of housing policy. In September 2021, Prime Minister Boris Johnson reverted the ministry to a department, renaming it the Department for Levelling Up, Housing and Communities and giving it the responsibility of overseeing his government's levelling up policy.

Other countries

Some countries, such as Switzerland, the Philippines and the United States, do not use or no longer use the term "ministry" and instead call their main government bodies "departments". However, in other countries such as Luxembourg a department is a subdivision of a ministry, usually led by a government member called a secretary of state who is subordinate to the minister.

In Australia at the federal level, and also at the state level, the term ministry refers to the ministerial office held by a member of Cabinet, the executive, which is then responsible for one or more departments, the top division of the public service. The collection of departments responsible to a ministerial office and hence the minister, is referred to as the minister's "portfolio".

New Zealand's state agencies include many ministries and a smaller number of departments. Increasingly, state agencies are styled neither as ministries nor as departments. All New Zealand agencies are under the direction of one or more ministers or associate ministers, whether they are styled ministries or not. Each body also has an apolitical chief executive, and in ministries and departments these chief executives often have the title of Secretary.

In Indonesia, the term ministry (Indonesian: Kementerian) is used. From the New Order to 2009, the office was known as department (Indonesian: Departemen).

In Malaysia, the term ministry is used for all but one government cabinet portfolio. The Prime Minister Department is the only portfolio that uses department instead. All government portfolios in the Peninsular Malaysia states use committee, while Sabah and Sarawak state governments following the federal government's style in naming certain portfolios.

In Hong Kong, the term bureau is used, and departments are subordinate to the bureaus.

In Mexico, ministries are referred to as secretariats.

In 1999, the ministries of the federal government of Belgium became known as federal public service, the exception being the Ministry of Defense which kept the original designation.

In the Republic of China, ministry is used.

In the People's Republic of China, ministry is used.

In Portugal, the organization adopted by the XXI (2015–2019) and the XXII (2019-2024) governments ceased to expressly foresee the existence of ministries, with the portfolios of the ministers being instead referred as "government areas" and having, in theory, a more flexible organization. Although the term "ministry" has been eliminated from the Government communication and from most of the new published laws, it continues to be used in some legislation, especially those referring to some government areas that existed for a long time as ministries (Finance, National Defense, Foreign Affairs, Health, etc.). The term "ministry" also continues to be used as the vernacular to refer to a government area.

In Nigeria each ministry is led by a minister who is not a member of the Nigerian legislature (due to the separation of powers) and is responsible to the popularly elected president.

In Lebanon, there are 21 ministries. Each ministry is led by a minister, and the prime minister is the 23rd minister of the Lebanese government.

In the European Union, the equivalent organisation to a national government department is termed directorate-general with the civil servant in charge called a director-general (in the European Commission, the political head of the department is one of the European Commissioners).

The government departments of the Soviet Union were termed people's commissariats between 1917 and 1946. Ministry was used, thereafter.

In popular culture

The term ministry has also been widely used in fiction, notably in satires and parodies.

Books and films

Portrayals of various fictional government ministries include:

• The Ministry of Magic is the governing body of the wizarding world of the United Kingdom and Ireland in the Harry Potter series (not a department of the British Government responsible for magical affairs). It is led by a Minister for Magic.
• In the novel Nineteen Eighty-Four there are four Ministries in charge of Oceania: the Ministry of Truth (education, culture and propaganda), the Ministry of Love (the interior, security and policing), the Ministry of Plenty (economic affairs) and the Ministry of Peace (war and foreign affairs).
• The Ministry of Information Retrieval features in the film Brazil.
• The Ministry of Social Coherence appears in an Estonian comedy series Riigimehed (Statesmen).

Television

• In Yes Minister the Department of Administrative Affairs (DAA) is responsible for the administration of other government departments and the British Civil Service. This ministry had a number of other responsibilities, including National Health Service administration, local government, organising state visits by foreign leaders, enforcing European regulations, the arts and telecommunications.
• The Thick of It is set at the fictional Department of Social Affairs, later called the Department of Social Affairs and Citizenship, or "DoSAC" for short.
• The Ministry of Silly Walks is the subject of a sketch in Monty Python's Flying Circus.
• The Spanish television show El ministerio del tiempo follows the exploits of an investigative team in the fictional Ministry of Time, which deals with incidents caused by time travel that can cause changes to the present day

Carrier generation and recombination

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Carrier_generation_and_recombination

In 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 fundamental to the operation of many optoelectronic semiconductor devices, such as photodiodes, light-emitting diodes and laser diodes. They are also critical to a full analysis of p-n junction devices such as bipolar junction transistors 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 an electron is a transition from the valence band to the conduction band and recombination leads to a reverse transition.

Overview

See also: Electronic band structure

Electronic band structure of a semiconductor material.

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 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 between two allowed bands called the valence band 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 electrons, 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 like a physicaly 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 quantized energy crystal momentum, and the vibrating lattice which 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

The following image shows change in excess carriers being generated (green:electrons and purple:holes) with increasing light intensity (generation rate /cm³) at the center of an intrinsic semiconductor bar. Electrons have higher diffusion constant than holes leading to fewer excess electrons at the center as compared to holes.

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 (${\displaystyle n}$ and ${\displaystyle p}$) is a constant ${\displaystyle (n_o{p}_o=n_i^2)}$ at equilibrium, maintained by recombination and generation occurring at equal rates. When there is a surplus of carriers (i.e., ${\displaystyle np>n_i^2}$), 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., ${\displaystyle np<n_i^2}$), 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. photons, electron, or the system of vibrating lattice atoms).

Carrier generation

See also: Absorption (electromagnetic radiation)

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 photodiodes, solar cells and other semiconductor photodetectors, while stimulated emission is the principle of operation in laser diodes.

Besides light excitation, carriers in semiconductors can also be generated by an external electric field, for example in light-emitting diodes and transistors.

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. This conversion of light into electricity is widely used in photodiodes.

Recombination mechanisms

Main article: Carrier lifetime

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 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 emission after the mean lifetime ${\displaystyle {\tau }_{nr}}$, whereas in the former at least part of the energy is released by light emission or luminescence after a radiative lifetime ${\displaystyle {\tau }_r}$. The carrier lifetime ${\displaystyle \tau }$is then obtained from the rate of both type of events according to:

$${\displaystyle \frac{1}{\tau }=\frac{1}{{\tau }_r}+\frac{1}{{\tau }_{nr}}}$$

From which we can also define the internal quantum efficiency or quantum yield, ${\displaystyle \eta }$ as:

$${\displaystyle \eta =\frac{1/{\tau }_r}{1/{\tau }_r+1/{\tau }_{nr}}=\frac{\text{radiative recombination}}{\text{total recombination}}\le 1.}$$

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 energy than those initially absorbed. This effect is how LEDs create light. Because the photon carries relatively little momentum, radiative recombination is significant only in direct bandgap 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 ${\displaystyle n(t)}$ and ${\displaystyle p(t)}$ respectively. Let us represent the radiative recombination as ${\displaystyle R_r}$ 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 G_L:

$${\displaystyle G=G_0+G_L}$$

Here we will consider the case in which there is no illumination on the semiconductor. Therefore ${\displaystyle G_L=0}$ and ${\displaystyle G=G_0}$, and we can express the change in carrier density as a function of time as

$${\displaystyle \frac{dn}{dt}=G-R_r=G_0-R_r}$$

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 R_r should be proportional to np:

$${\displaystyle R_r\propto np}$$

and we add a proportionality constant B_r to eliminate the ${\displaystyle \propto }$ sign:

$${\displaystyle R_r=B_{r}np}$$

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 ${\displaystyle R_0}$ must be exactly balanced by the thermal generation rate ${\displaystyle G_0}$.

Therefore：

$${\displaystyle R_0=G_0=B_r{n}_0{p}_0}$$

where ${\displaystyle n_0}$ and ${\displaystyle p_0}$ are the equilibrium carrier densities. Using the mass action law ${\displaystyle np=n_i^2}$，with ${\displaystyle n_i}$ being the intrinsic carrier density, we can rewrite it as

$${\displaystyle R_0=G_0=B_r{n}_0{p}_0=B_r{n}_i^2}$$

The non-equilibrium carrier densities are given by 

$${\displaystyle n=n_0+\mathrm{\Delta }n,}$$

$${\displaystyle p=p_0+\mathrm{\Delta }p}$$

Then the new recombination rate ${\displaystyle R_{\text{net}}}$ becomes,

$${\displaystyle R_{\text{net}}=R_r-G_0=B_{r}np-G_0=B_r(n_0+\mathrm{\Delta }n)(p_0+\mathrm{\Delta }p)-G_0}$$

Because ${\displaystyle n_0\gg \mathrm{\Delta }n}$ and ${\displaystyle p_0\gg \mathrm{\Delta }p}$, we can say that ${\displaystyle \mathrm{\Delta }n\mathrm{\Delta }p\approx 0}$

${\displaystyle R_{\text{net}}=B_r(n_0+\mathrm{\Delta }n)(p_0+\mathrm{\Delta }p)-G_0=B_r(n_0{p}_0+\mathrm{\Delta }n{p}_0+\mathrm{\Delta }p{n}_0)-B_r{n}_i^2}$

${\displaystyle R_{\text{net}}=B_r(n_i^2+\mathrm{\Delta }n{p}_0+\mathrm{\Delta }p{n}_0-n_i^2)}$

${\displaystyle R_{\text{net}}=B_r(\mathrm{\Delta }n{p}_0+\mathrm{\Delta }p{n}_0)}$

In an n-type semiconductor,

${\displaystyle p_0\ll n_0}$ and ${\displaystyle \mathrm{\Delta }p\ll n_0}$

thus

${\displaystyle R_{net}\approx B_r\mathrm{\Delta }p{n}_0}$

Net recombination is the rate at which excess holes ${\displaystyle \mathrm{\Delta }p}$ disappear

${\displaystyle \frac{d\mathrm{\Delta }p}{dt}=-R_{\text{net}}\approx -B_r\mathrm{\Delta }p{n}_0}$

Solve this differential equation to get a standard exponential decay

${\displaystyle \mathrm{\Delta }p=p_{max}{e}^{-B_r{n}_{0}t}}$

where p_max is the maximum excess hole concentration when t = 0. (It can be proved that ${\displaystyle p_{max}=\frac{G_L}{B{n}_0}}$, but here we will not discuss that).

When ${\displaystyle t=\frac{1}{B{n}_0}}$, all of the excess holes will have disappeared. Therefore, we can define the lifetime of the excess holes in the material ${\displaystyle {\tau }_p=\frac{1}{B{n}_0}}$

So the lifetime of the minority carrier is dependent upon the majority carrier concentration.

Stimulated emission

See also: Stimulated emission and Laser

Stimulated emission is a process where an incident photon interacts with an excited electron causing it to recombine and emit a photon with the same properties as the incident photon , in terms of phase, frequency, polarization, and direction of travel. Stimulated emission together with the principle of population inversion are at the heart of operation of lasers and masers. It has been shown by Einstein at the beginning of the twentieth century that if the excited and the ground level are non degenerate then the absorption rate ${\displaystyle W_{12}}$and the stimulated emission rate ${\displaystyle W_{21}}$are the same. Else if level 1 and level 2 are ${\displaystyle g_1}$-fold and ${\displaystyle g_2}$-fold degenerate respectively, the new relation is:

$${\displaystyle g_1{W}_{12}=g_2{W}_{21}.}$$

Trap emission

Trap emission is a multistep process wherein a carrier falls into defect-related wave states 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.on-radiative recombination

Non-radiative recombination is a process in phosphors and semiconductors, whereby charge carriers recombine releasing phonons 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 in the conduction band of a semiconductor recombines with a hole. It is an important parameter in optoelectronics where radiative recombination 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 by a dopant or a defect in the crystal lattice; 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 between the carriers, SRH is the dominant recombination process in silicon and other indirect bandgap materials. However, trap-assisted recombination can also dominate in direct bandgap materials under conditions of very low carrier densities (very low level injection) or in materials with high density of traps such as perovskites. The process is named after William Shockley, William Thornton Read 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 they become hole traps.

Shallow traps vs. deep traps

See also: Deep-level trap and Deathnium

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 k_BT 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. 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

Electron and hole trapping in the Shockley-Read-Hall 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 by that of the intragap state. The term ${\displaystyle p(n)}$is replaced by the density of trapped electrons/holes ${\displaystyle N_t(1-f_t)}$.

$${\displaystyle R_{nt}=B_{n}n{N}_t(1-f_t)}$$

Where ${\displaystyle N_t}$ is the density of trap states and ${\displaystyle f_t}$ is the probability of that occupied state. Considering a material containing both types of traps, we can define two trapping coefficients ${\displaystyle B_n,B_p}$ and two de-trapping coefficients ${\displaystyle G_n,G_p}$. In equilibrium, both trapping and de-trapping should be balanced (${\displaystyle R_{nt}=G_n}$ and ${\displaystyle R_{pt}=G_p}$). Then, the four rates as a function of ${\displaystyle f_t}$become:

$${\displaystyle \begin{array}{ll}{R}_{nt}=B_{n}n{N}_t(1-f_t)& G_n=B_n{n}_t{N}_t{f}_t\\ R_{pt}=B_{p}p{N}_t{f}_t& G_p=B_p{p}_t{N}_t(1-f_t)\end{array}}$$

Where ${\displaystyle n_t}$ and ${\displaystyle p_t}$ are the electron and hole densities when the quasi Fermi level 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: ${\displaystyle R_{nt}-G_n=R_{pt}-G_p}$. This eliminates the occupation probability ${\displaystyle f_t}$ and leads to the Shockley-Read-Hall expression for the trap-assisted recombination:

$${\displaystyle R=\frac{np}{{\tau }_n(p+p_t)+{\tau }_p(n+n_t)}}$$

Where the average lifetime for electrons and holes are defined as:

$${\displaystyle {\tau }_n=\frac{1}{B_n{N}_t},{\tau }_p=\frac{1}{B_p{N}_t}.}$$

Auger recombination

Main article: Auger effect

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 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 ${\displaystyle R_A}$ and thermal generation rate ${\displaystyle G_0}$ equal each other

$${\displaystyle R_{A0}=G_0=C_n{n}_0^2{p}_0+C_p{n}_0{p}_0^2}$$

where ${\displaystyle C_n,C_p}$ are the Auger capture probabilities. The non-equilibrium Auger recombination rate ${\displaystyle r_A}$ and resulting net recombination rate ${\displaystyle U_A}$ under steady-state conditions are

$${\displaystyle r_A=C_n{n}^{2}p+C_{p}n{p}^2,R_A=r_A-G_0=C_n\left(n^{2}p-n_0^2{p}_0\right)+C_p\left(n{p}^2-n_0{p}_0^2\right).}$$

The Auger lifetime ${\displaystyle {\tau }_A}$ is given by

$${\displaystyle {\tau }_A=\frac{\mathrm{\Delta }n}{R_A}=\frac{1}{n^2{C}_n+2n_i^2(C_n+C_p)+p^2{C}_p}.}$$

The mechanism causing LED efficiency droop was identified in 2007 as Auger recombination, which met with a mixed reaction. 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 droop.

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 cells) and other such systems. The Langevin recombination strength is defined as ${\displaystyle \gamma =\frac{q}{\epsilon }\mu }$.