Carrier generation and 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 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, 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.
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 Boltzmann 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 an electron 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 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.
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., ), 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).
Radiative versus non-radiativeEdit
One common way to classify recombination events is based on whether the process produces light.
During radiative recombination, a form of spontaneous emission, a photon is emitted with the wavelength corresponding to the energy released. This effect is how LEDs create light. Because the photon carries relatively little momentum, radiative recombination is significant only in direct bandgap materials.
When photons are present in the material, they can either be absorbed, generating a pair of free carriers, or they can stimulate a recombination event, resulting in a generated photon with 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 responsible for laser action in laser diodes.
In thermal equilibrium the radiative recombination and thermal generation rate equal each other
where is called the radiative capture probability and the intrinsic carrier density.
Under steady-state conditions the radiative recombination rate and resulting net recombination rate are
where the carrier densities are made up of equilibrium and excess densities
The radiative lifetime is given by
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Non-radiative recombination is a process in phosphors and semiconductors, whereby charge carriers recombine without releasing photons. A phonon is released instead. 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 non-radiatively. 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, then a carrier is more likely to recombine non-radiatively. This results in low internal quantum efficiency.
When light with sufficient energy hits a semiconductor, it can excite electrons across the band gap. This generates additional holes and carriers, temporarily lowering the electrical resistance of the material. This higher conductivity in the presence of light is known as photoconductivity. This property of turning light into electricity is used in devices called photodiodes.
Generation and recombination can happen for many reasons. The main three are band-to-band recombination, trap-assisted recombination, and Auger recombination.
Band-to-band recombination is the name for the process of electrons jumping down from the conduction band to the valence band. If the material is a direct bandgap, it is usually a radiative recombination, if the material is an indirect bandgap, it usually is non-radiative recombination.
Shockley–Read–Hall (SRH) processEdit
In Shockley-Read-Hall recombination, 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 an impurity in the crystal lattice; such energy states are called deep-level traps. The localized impurity state can absorb differences in momentum between the carriers, and so this process is the dominant generation and recombination process in silicon and other indirect bandgap materials. It can also dominate in direct bandgap materials under conditions of very low carrier densities (very low level injection). The energy is exchanged in the form of lattice vibration, a phonon exchanging thermal energy with the material. The process is named after William Shockley, William Thornton Read and Robert N. Hall.
Various impurities and dislocations create energy levels within the band gap corresponding to neither donor nor acceptor levels, forming deep-level traps. Non-radiative recombination occurs primarily at such sites.
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 and thermal generation rate equal each other
where are the Auger capture probabilities.
The non-equilibrium Auger recombination rate and resulting net recombination rate under steady-state conditions are
The Auger lifetime is given by
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 opposite to that found for the drop.
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