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Non-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 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. 1 τ = 1 τ r + 1 τ n r {displaystyle {frac {1}{ au }}={frac {1}{ au _{r}}}+{frac {1}{ au _{nr}}}} η = 1 / τ r 1 / τ r + 1 / τ n r = r a d i a t i v e   r e c o m b i n a t i o n t o t a l   r e c o m b i n a t i o n ≤ 1. {displaystyle eta ={frac {1/ au _{r}}{1/ au _{r}+1/ au _{nr}}}={frac {radiative recombination}{total recombination}}leq 1.} d n d t = G − R r = G − B r n p {displaystyle {dn over dt}=G-R_{r}=G-B_{r}np} R 0 = G 0 = B r n 0 p 0 = B r n i 2 {displaystyle R_{0}=G_{0}=B_{r}n_{0}p_{0}=B_{r}n_{i}^{2}} n = n 0 + Δ n {displaystyle n=n_{0}+Delta n} p = p 0 + Δ p {displaystyle p=p_{0}+Delta p} R r = B r n p − G 0 = B r ( n p − n 0 p 0 ) = B r ( n p − n i 2 ) {displaystyle R_{r}=B_{r}np-G_{0}=B_{r}(np-n_{0}p_{0})=B_{r}(np-n_{i}^{2})} τ r = Δ n R r = 1 B r ( n 0 + p 0 + Δ n ) . {displaystyle au _{r}={frac {Delta n}{R_{r}}}={frac {1}{B_{r}left(n_{0}+p_{0}+Delta n ight)}},.} g 1 W 12 = g 2 W 21 . {displaystyle g_{1}W_{12}=g_{2}W_{21}.} R n t = B n n N t ( 1 − f t ) {displaystyle R_{nt}=B_{n}nN_{t}(1-f_{t})} R n t = B n n N t ( 1 − f t ) G n = B n n t N t f t R p t = B p p N t f t G p = B p p t N t ( 1 − f t ) { extstyle {egin{array}{l l}R_{nt}=B_{n}nN_{t}(1-f_{t})&G_{n}=B_{n}n_{t}N_{t}f_{t}\R_{pt}=B_{p}pN_{t}f_{t}&G_{p}=B_{p}p_{t}N_{t}(1-f_{t})end{array}}} R = n p τ n ( p + p t ) + τ p ( n + n t ) {displaystyle R={frac {np}{ au _{n}(p+p_{t})+ au _{p}(n+n_{t})}}} τ n = 1 B n N t , τ p = 1 B p N t . {displaystyle au _{n}={frac {1}{B_{n}N_{t}}},quad au _{p}={frac {1}{B_{p}N_{t}}}.} R A 0 = G 0 = C n n 0 2 p 0 + C p n 0 p 0 2 {displaystyle R_{A0}=G_{0}=C_{n}n_{0}^{2}p_{0}+C_{p}n_{0}p_{0}^{2}} r A = C n n 2 p + C p n p 2 , R A = r A − G 0 = C n ( n 2 p − n 0 2 p 0 ) + C p ( n p 2 − n 0 p 0 2 ) . {displaystyle r_{A}=C_{n}n^{2}p+C_{p}np^{2},,quad R_{A}=r_{A}-G_{0}=C_{n}left(n^{2}p-n_{0}^{2}p_{0} ight)+C_{p}left(np^{2}-n_{0}p_{0}^{2} ight),.} τ A = Δ n R A = 1 n 2 C n + 2 n i 2 ( C n + C p ) + p 2 C p . {displaystyle au _{A}={frac {Delta n}{R_{A}}}={frac {1}{n^{2}C_{n}+2n_{i}^{2}(C_{n}+C_{p})+p^{2}C_{p}}},.} 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 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. 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 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 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 ( n {displaystyle n} and p {displaystyle p} ) is a constant ( n o p o = n i 2 ) {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., n p > n i 2 {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., n p < n i 2 {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).

[ "Spontaneous emission", "semiconductor materials", "Photoluminescence", "Recombination" ]
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