217:
5365:
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.
36:
4228:
5364:
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
4624:
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
5355:
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
530:), 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.
319:
The following image shows change in excess carriers being generated (green:electrons and purple:holes) with increasing light intensity (generation rate /cm) at the center of an intrinsic semiconductor bar. Electrons have higher diffusion constant than holes leading to fewer excess electrons at the
5155:
271:. 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.
940:
3308:
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.
2350:
1392:
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
5347:
3972:
316:
2031:
4908:
3503:
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
202:, 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.
4605:
835:
2470:
2821:
802:
5838:
Kandada, Ajay Ram
Srimath; D'Innocenzo, Valerio; Lanzani, Guglielmo; Petrozza, Annamaria (2016), Da Como, Enrico; De Angelis, Filippo; Snaith, Henry; Walker, Alison (eds.), "Chapter 4. Photophysics of Hybrid Perovskites",
5537:
Stranks, Samuel D.; Burlakov, Victor M.; Leijtens, Tomas; Ball, James M.; Goriely, Alain; Snaith, Henry J. (2014-09-11). "Recombination
Kinetics in Organic-Inorganic Perovskites: Excitons, Free Charge, and Subgap States".
4493:
4805:
2554:
2147:
1749:
5191:
5356:
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.
5425:
2896:
2962:
2704:
1276:
3062:
606:
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
3713:
3464:
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
1875:
1521:
4360:
2140:
3292:
446:
3010:
3360:
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
3087:
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
53:
4502:
2636:
2105:
2069:
1798:
1839:
3412:. 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.
3333:
instead of photons. Non-radiative recombination in optoelectronics and phosphors is an unwanted process, lowering the light generation efficiency and increasing heat losses.
1318:
528:
487:
3633:
2600:
1868:
489:), 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.,
1388:
1126:
3938:
3894:
1619:
4847:
3849:
3809:
3529:
286:, 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.
676:
5184:
707:
2730:
1342:
957:
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
737:
1194:
1161:
4223:{\displaystyle {\begin{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}}}
3175:
3148:
4901:
4874:
4684:
4657:
4387:
4284:
4257:
3965:
3769:
3742:
3229:
3202:
1646:
1575:
1548:
1445:
1418:
1069:
828:
730:
3584:
1280:
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
1042:
1013:
3520:. 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.
4290:
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:
385:
365:
4394:
2358:
5150:{\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}\right)+C_{p}\left(np^{2}-n_{0}p_{0}^{2}\right)\,.}
4691:
2738:
100:
935:{\displaystyle \eta ={\frac {1/\tau _{r}}{1/\tau _{r}+1/\tau _{nr}}}={\frac {\text{radiative recombination}}{\text{total recombination}}}\leq 1.}
72:
1653:
557:
551:
296:
describes processes by which a conduction band electron loses energy and re-occupies the energy state of an electron hole in the valence band.
292:
describes processes by which electrons gain energy and move from the valence band to the conduction band, producing two mobile carriers; while
5460:
Elhami
Khorasani, Arash; Schroder, Dieter K.; Alford, T. L. (2014). "Optically Excited MOS-Capacitor for Recombination Lifetime Measurement".
5993:
5928:
5893:
5595:
568:
a recombination event. The generated photon has similar properties to the one responsible for the event. Absorption is the active process in
6058:
79:
240:
temperature, all of the electrons have energy below the Fermi level; but at non-zero temperatures the energy levels are filled following a
3771:
is the probability of that occupied state. Considering a material containing both types of traps, we can define two trapping coefficients
307:
which plays a large role in conserving momentum as in collisions, photons can transfer very little momentum in relation to their energy.
6145:
2478:
2345:{\displaystyle R_{\text{net}}=B_{r}(n_{0}+\Delta n)(p_{0}+\Delta p)-G_{0}=B_{r}(n_{0}p_{0}+\Delta np_{0}+\Delta pn_{0})-B_{r}n_{i}^{2}}
1199:
5811:
5623:
3546:
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.
274:
However, if an electron in the valence band acquires enough energy to reach the conduction band as a result of interaction with other
86:
5945:"The LED's Dark Secret: Solid-state lighting won't supplant the lightbulb until it can overcome the mysterious malady known as droop"
5856:
5522:
119:
6150:
3640:
1453:
448:
at equilibrium, maintained by recombination and generation occurring at equal rates. When there is a surplus of carriers (i.e.,
68:
4629:
process is not easily produced, because the third particle would have to begin the process in the unstable high-energy state.
3234:
3120:
57:
5392:
3528:
3012:, all of the excess holes will have disappeared. Therefore, we can define the lifetime of the excess holes in the material
3428:
3424:
1578:
591:
Besides light excitation, carriers in semiconductors can also be generated by an external electric field, for example in
5462:
2832:
2908:
2647:
1758:
1802:
184:
160:) are created and eliminated. Carrier generation and recombination processes are fundamental to the operation of many
3549:
A captured hole can be released into the valence band. Analogous to the capture of an electron from the valence band.
1287:
628:
Carrier recombination can happen through multiple relaxation channels. The main ones are band-to-band recombination,
337:
6155:
961:, the energy absorbed by a material is released in the form of photons. Generally these photons contain the same or
3015:
1347:
1085:
336:
density remains constant. The resulting probability of occupation of energy states in each energy band is given by
324:
Recombination and generation are always happening in semiconductors, both optically and thermally. As predicted by
93:
46:
5342:{\displaystyle \tau _{A}={\frac {\Delta n}{R_{A}}}={\frac {1}{n^{2}C_{n}+2n_{i}^{2}(C_{n}+C_{p})+p^{2}C_{p}}}\,.}
3385:
225:
211:
5711:"The Kinetics of the Radiative and Nonradiative Processes in Nanocrystalline ZnO Particles upon Photoexcitation"
6180:
6175:
4293:
3304:
is a multistep process wherein a carrier falls into defect-related wave states in the middle of the bandgap. A
2110:
241:
629:
228:
determined by the crystal properties of the material. Energy distribution among electrons is described by the
6170:
5366:
3357:
390:
3444:
2970:
3432:
986:
This type of recombination depends on the density of electrons and holes in the excited state, denoted by
344:
5748:
Shockley, W.; Read, W. T. (1 September 1952). "Statistics of the
Recombinations of Holes and Electrons".
3436:
3116:
2605:
2074:
2038:
5381:. The model is often used for disordered systems such as organic materials (and is hence relevant for
6085:
6022:
5757:
5683:
5547:
5471:
3104:
3100:
3096:
966:
958:
592:
492:
451:
172:
164:
3589:
2565:
2026:{\displaystyle R_{\text{net}}=R_{r}-G_{0}=B_{r}np-G_{0}=B_{r}(n_{0}+\Delta n)(p_{0}+\Delta p)-G_{0}}
1846:
3075:
633:
603:
581:
329:
133:
5514:
3900:
3856:
1583:
5958:
5671:
5487:
5382:
4812:
3814:
3774:
3361:
1130:
Here we will consider the case in which there is no illumination on the semiconductor. Therefore
807:
5709:
van Dijken, Addy; Meulenkamp, Eric A.; Vanmaekelbergh, Daniël; Meijerink, Andries (2000-03-01).
651:
5162:
685:
6111:
6103:
6040:
5989:
5924:
5889:
5852:
5817:
5807:
5730:
5652:
5629:
5619:
5591:
5518:
5377:
For free carriers in low-mobility systems, the recombination rate is often described with the
4287:
3554:
3066:
So the lifetime of the minority carrier is dependent upon the majority carrier concentration.
2712:
1327:
607:
1166:
1133:
6093:
6030:
5916:
5881:
5844:
5765:
5722:
5691:
5583:
5555:
5510:
5479:
3440:
3153:
3126:
710:
623:
300:
6098:
6073:
4879:
4852:
4662:
4635:
4365:
4262:
4235:
3943:
3747:
3720:
3207:
3180:
1624:
1553:
1526:
1423:
1396:
1047:
813:
715:
4600:{\displaystyle \tau _{n}={\frac {1}{B_{n}N_{t}}},\quad \tau _{p}={\frac {1}{B_{p}N_{t}}}.}
3560:
3517:
3494:
3469:
3405:
3353:
3341:
1018:
989:
267:
161:
6011:"Calculation of surface generation and recombination velocities at the Si-SiO2 interface"
6089:
6026:
5761:
5687:
5551:
5475:
216:
3448:
3401:
3326:
3119:
at the beginning of the twentieth century that if the excited and the ground level are
974:
370:
350:
333:
325:
149:
5505:
Pelant, Ivan; Valenta, Jan (2012-02-09), "Luminescence of disordered semiconductors",
6164:
3516:. Alternatively, if the difference is larger than the thermal energy, it is called a
3349:
3345:
3322:
3088:
2465:{\displaystyle R_{\text{net}}=B_{r}(n_{i}^{2}+\Delta np_{0}+\Delta pn_{0}-n_{i}^{2})}
678:, whereas in the former at least part of the energy is released by light emission or
577:
279:
237:
199:
157:
137:
5957:
Justin
Iveland; Lucio Martinelli; Jacques Peretti; James S. Speck; Claude Weisbuch.
5559:
5491:
4389:
and leads to the
Shockley-Read-Hall expression for the trap-assisted recombination:
5436:
4626:
4615:
3477:
3389:
962:
679:
261:
180:
17:
5695:
4849:
are the Auger capture probabilities. The non-equilibrium Auger recombination rate
2816:{\displaystyle {\frac {d\Delta p}{dt}}=-R_{\text{net}}\approx -B_{r}\Delta pn_{0}}
5944:
797:{\displaystyle {\frac {1}{\tau }}={\frac {1}{\tau _{r}}}+{\frac {1}{\tau _{nr}}}}
5848:
5441:
3505:
3472:, they can temporarily immobilize excited electrons or in other words, they are
585:
233:
229:
176:
35:
332:
will have generation and recombination rates that are balanced so that the net
315:
3977:
3435:(very low level injection) or in materials with high density of traps such as
611:
596:
573:
569:
168:
6107:
6044:
5821:
5734:
5710:
5656:
5633:
5483:
5352:
3553:
When carrier recombination occurs through traps, we can replace the valence
3498:
3092:
2905:
is the maximum excess hole concentration when t = 0. (It can be proved that
1196:, and we can express the change in carrier density as a function of time as
6115:
5769:
5920:
5885:
5587:
4625:
in non-equilibrium conditions when the carrier density is very high. The
3416:
3393:
3337:
3318:
970:
535:
275:
252:
153:
3540:
An electron in the conduction band can be trapped in an intragap state.
3420:
561:
5726:
3543:
An electron can be emitted into the conduction band from a trap level.
636:
and surface recombination. These decay channels can be separated into
6035:
6010:
5910:
5875:
5577:
4488:{\displaystyle R={\frac {np}{\tau _{n}(p+p_{t})+\tau _{p}(n+n_{t})}}}
3427:
materials. However, trap-assisted recombination can also dominate in
3397:
3330:
2826:
Solve this differential equation to get a standard exponential decay
645:
539:
531:
304:
283:
4800:{\displaystyle R_{A0}=G_{0}=C_{n}n_{0}^{2}p_{0}+C_{p}n_{0}p_{0}^{2}}
3468:
they leave behind. In this context, if trap levels are close to the
732:
is then obtained from the rate of both type of events according to:
4497:
Where the average lifetime for electrons and holes are defined as:
3851:. In equilibrium, both trapping and de-trapping should be balanced
3419:
between the carriers, SRH is the dominant recombination process in
644:
The latter occurs when the excess energy is converted into heat by
3527:
3112:
3108:
3079:
314:
247:
In undoped semiconductors the Fermi level lies in the middle of a
215:
188:
2549:{\displaystyle R_{\text{net}}=B_{r}(\Delta np_{0}+\Delta pn_{0})}
5369:
techniques are also employed to minimize surface recombination.
3536:
In the SRH model, four things can happen involving trap levels:
6059:"Recombination in low mobility semiconductors: Langevin theory"
602:
When light with sufficient energy hits a semiconductor, it can
3103:
of travel. Stimulated emission together with the principle of
1044:
respectively. Let us represent the radiative recombination as
610:. This conversion of light into electricity is widely used in
29:
969:
create light. Because the photon carries relatively little
198:
is the fundamental unit of generation and recombination in
6072:
Lakhwani, Girish; Rao, Akshay; Friend, Richard H. (2014).
5783:
Hall, R.N. (1951). "Germanium rectifier characteristics".
3532:
Electron and hole trapping in the
Shockley-Read-Hall model
1744:{\displaystyle R_{0}=G_{0}=B_{r}n_{0}p_{0}=B_{r}n_{i}^{2}}
1648:
being the intrinsic carrier density, we can rewrite it as
1078:
and generation due to light shining on the semiconductor G
1420:
must be exactly balanced by the thermal generation rate
965:
energy than those initially absorbed. This effect is how
3476:. On the other hand, if their energy lies close to the
556:
When light interacts with a material, it can either be
5420:{\displaystyle \gamma ={\tfrac {q}{\varepsilon }}\mu }
5403:
3586:
is replaced by the density of trapped electrons/holes
3336:
Non-radiative life time is the average time before an
220:
Electronic band structure of a semiconductor material.
5395:
5194:
5165:
4911:
4882:
4855:
4815:
4694:
4665:
4638:
4505:
4397:
4368:
4296:
4265:
4238:
3975:
3946:
3903:
3859:
3817:
3777:
3750:
3723:
3643:
3592:
3563:
3237:
3210:
3183:
3156:
3129:
3018:
2973:
2911:
2835:
2741:
2715:
2650:
2608:
2568:
2481:
2361:
2150:
2113:
2077:
2041:
1878:
1849:
1805:
1761:
1656:
1627:
1586:
1556:
1529:
1456:
1426:
1399:
1350:
1330:
1290:
1202:
1169:
1136:
1088:
1050:
1021:
992:
838:
816:
740:
718:
688:
654:
495:
454:
393:
373:
353:
6074:"Bimolecular Recombination in Organic Photovoltaics"
2709:
Net recombination is the rate at which excess holes
1753:The non-equilibrium carrier densities are given by
3231:-fold degenerate respectively, the new relation is:
1074:
Total generation is the sum of thermal generation G
224:Like other solids, semiconductor materials have an
60:. Unsourced material may be challenged and removed.
27:
Phenomenon in solid-state physics of semiconductors
5672:"Dislocation Related Photoluminescence in Silicon"
5419:
5341:
5178:
5149:
4895:
4868:
4841:
4799:
4678:
4651:
4599:
4487:
4381:
4354:
4278:
4251:
4222:
3959:
3932:
3888:
3843:
3803:
3763:
3736:
3707:
3627:
3578:
3286:
3223:
3196:
3169:
3142:
3056:
3004:
2956:
2891:{\displaystyle \Delta p=p_{\max }e^{-B_{r}n_{0}t}}
2890:
2815:
2724:
2698:
2630:
2594:
2548:
2464:
2344:
2134:
2099:
2063:
2025:
1862:
1833:
1792:
1743:
1640:
1613:
1577:are the equilibrium carrier densities. Using the
1569:
1542:
1515:
1439:
1412:
1382:
1336:
1312:
1270:
1188:
1155:
1120:
1063:
1036:
1007:
934:
822:
796:
724:
701:
670:
522:
481:
440:
379:
359:
2957:{\displaystyle p_{\max }={\frac {G_{L}}{Bn_{0}}}}
2699:{\displaystyle R_{net}\approx B_{r}\Delta pn_{0}}
1271:{\displaystyle {dn \over dt}=G-R_{r}=G_{0}-R_{r}}
973:, radiative recombination is significant only in
5959:"Cause of LED Efficiency Droop Finally Revealed"
5843:, Royal Society of Chemistry, pp. 107–140,
2917:
2850:
5988:. London: Imperial College Press. p. 116.
4632:In thermal equilibrium the Auger recombination
299:These processes must conserve quantized energy
179:. They are also critical to a full analysis of
3177:are the same. Else if level 1 and level 2 are
5869:
5867:
5571:
5569:
5509:, Oxford University Press, pp. 242–262,
4362:. This eliminates the occupation probability
4286:are the electron and hole densities when the
3057:{\displaystyle \tau _{p}={\frac {1}{Bn_{0}}}}
311:Relation between generation and recombination
8:
3317:Non-radiative recombination is a process in
5507:Luminescence Spectroscopy of Semiconductors
3708:{\displaystyle R_{nt}=B_{n}nN_{t}(1-f_{t})}
1516:{\displaystyle R_{0}=G_{0}=B_{r}n_{0}p_{0}}
806:From which we can also define the internal
560:(generating a pair of free carriers or an
6097:
6034:
5515:10.1093/acprof:oso/9780199588336.003.0009
5402:
5394:
5335:
5326:
5316:
5300:
5287:
5274:
5269:
5253:
5243:
5233:
5222:
5208:
5199:
5193:
5170:
5164:
5143:
5132:
5127:
5117:
5104:
5086:
5068:
5058:
5053:
5037:
5022:
5009:
4996:
4983:
4974:
4968:
4955:
4939:
4929:
4916:
4910:
4887:
4881:
4860:
4854:
4833:
4820:
4814:
4791:
4786:
4776:
4766:
4753:
4743:
4738:
4728:
4715:
4699:
4693:
4670:
4664:
4643:
4637:
4585:
4575:
4565:
4556:
4539:
4529:
4519:
4510:
4504:
4473:
4454:
4438:
4419:
4404:
4396:
4373:
4367:
4355:{\displaystyle R_{nt}-G_{n}=R_{pt}-G_{p}}
4346:
4330:
4317:
4301:
4295:
4270:
4264:
4243:
4237:
4207:
4188:
4178:
4168:
4155:
4143:
4133:
4120:
4104:
4090:
4080:
4070:
4060:
4047:
4032:
4013:
4000:
3984:
3976:
3974:
3951:
3945:
3940:). Then, the four rates as a function of
3924:
3908:
3902:
3880:
3864:
3858:
3835:
3822:
3816:
3795:
3782:
3776:
3755:
3749:
3728:
3722:
3696:
3677:
3664:
3648:
3642:
3616:
3597:
3591:
3562:
3275:
3265:
3252:
3242:
3236:
3215:
3209:
3188:
3182:
3161:
3155:
3134:
3128:
3045:
3032:
3023:
3017:
2993:
2980:
2972:
2945:
2931:
2925:
2916:
2910:
2877:
2867:
2859:
2849:
2834:
2807:
2791:
2775:
2742:
2740:
2714:
2690:
2674:
2655:
2649:
2622:
2607:
2586:
2573:
2567:
2537:
2518:
2499:
2486:
2480:
2453:
2448:
2435:
2416:
2397:
2392:
2379:
2366:
2360:
2336:
2331:
2321:
2305:
2286:
2267:
2257:
2244:
2231:
2206:
2181:
2168:
2155:
2149:
2135:{\displaystyle \Delta n\Delta p\approx 0}
2112:
2082:
2076:
2046:
2040:
2017:
1992:
1967:
1954:
1941:
1922:
1909:
1896:
1883:
1877:
1854:
1848:
1816:
1804:
1772:
1760:
1735:
1730:
1720:
1707:
1697:
1687:
1674:
1661:
1655:
1632:
1626:
1605:
1600:
1585:
1561:
1555:
1534:
1528:
1507:
1497:
1487:
1474:
1461:
1455:
1431:
1425:
1404:
1398:
1368:
1355:
1349:
1329:
1295:
1289:
1262:
1249:
1236:
1203:
1201:
1180:
1168:
1141:
1135:
1112:
1099:
1087:
1055:
1049:
1020:
991:
977:materials. This process is also known as
916:
901:
892:
880:
871:
860:
851:
845:
837:
815:
783:
774:
763:
754:
741:
739:
717:
693:
687:
659:
653:
514:
509:
494:
473:
468:
453:
429:
424:
411:
401:
392:
372:
352:
120:Learn how and when to remove this message
3557:by that of the intragap state. The term
3287:{\displaystyle g_{1}W_{12}=g_{2}W_{21}.}
5452:
3431:materials under conditions of very low
1320:and we add a proportionality constant B
6146:PV Lighthouse Recombination Calculator
6099:10.1146/annurev-physchem-040513-103615
5841:Unconventional Thin Film Photovoltaics
3415:Since traps can absorb differences in
2964:, but here we will not discuss that).
1071:and the carrier generation rate as G.
552:Absorption (electromagnetic radiation)
441:{\displaystyle (n_{o}p_{o}=n_{i}^{2})}
69:"Carrier generation and recombination"
5833:
5831:
4876:and resulting net recombination rate
3392:(localized state) created within the
3384:, the electron in transition between
3005:{\displaystyle t={\frac {1}{Bn_{0}}}}
7:
5609:
5607:
950:Band-to-band radiative recombination
58:adding citations to reliable sources
6078:Annual Review of Physical Chemistry
6009:Eades, W.D.; Swanson, R.M. (1985).
5715:The Journal of Physical Chemistry B
5912:Semiconductor Physical Electronics
5877:Semiconductor Physical Electronics
5579:Semiconductor Physical Electronics
5211:
4903:under steady-state conditions are
3744:is the density of trap states and
3352:. It is an important parameter in
2836:
2797:
2748:
2716:
2680:
2609:
2527:
2508:
2425:
2406:
2295:
2276:
2215:
2190:
2120:
2114:
2091:
2055:
2001:
1976:
1825:
1781:
25:
6151:PV Lighthouse Band Gap Calculator
5943:Stevenson, Richard (August 2009)
3811:and two de-trapping coefficients
3150:and the stimulated emission rate
3107:are at the heart of operation of
2631:{\displaystyle \Delta p\ll n_{0}}
2100:{\displaystyle p_{0}\gg \Delta p}
2064:{\displaystyle n_{0}\gg \Delta n}
1793:{\displaystyle n=n_{0}+\Delta n,}
648:emission after the mean lifetime
584:is the principle of operation in
540:system of vibrating lattice atoms
3408:; such energy states are called
3374:Shockley-Read-Hall recombination
1843:Then the new recombination rate
1834:{\displaystyle p=p_{0}+\Delta p}
284:vibrating crystal lattice itself
34:
6131:N.W. Ashcroft and N.D. Mermin,
5560:10.1103/PhysRevApplied.2.034007
5387:Langevin recombination strength
4978:
4551:
1313:{\displaystyle R_{r}\propto np}
523:{\displaystyle np<n_{i}^{2}}
482:{\displaystyle np>n_{i}^{2}}
45:needs additional citations for
5806:. SOCIETA EDITRICE ESCULAPIO.
5618:. SOCIETA EDITRICE ESCULAPIO.
5385:) and other such systems. The
5306:
5280:
4479:
4460:
4444:
4425:
4213:
4194:
4038:
4019:
3702:
3683:
3628:{\displaystyle N_{t}(1-f_{t})}
3622:
3603:
3573:
3567:
3512:it is often said that it is a
2595:{\displaystyle p_{0}\ll n_{0}}
2543:
2505:
2459:
2385:
2311:
2250:
2221:
2199:
2196:
2174:
2007:
1985:
1982:
1960:
1863:{\displaystyle R_{\text{net}}}
1284:should be proportional to np:
1031:
1025:
1002:
996:
435:
394:
148:are processes by which mobile
1:
5963:Physical Review Letters, 2013
5696:10.1103/PhysRevLett.87.187404
3460:Electron traps vs. hole traps
3439:. The process is named after
2559:In an n-type semiconductor,
1383:{\displaystyle R_{r}=B_{r}np}
1121:{\displaystyle G=G_{0}+G_{L}}
632:trap-assisted recombination,
5463:IEEE Electron Device Letters
4659:and thermal generation rate
3933:{\displaystyle R_{pt}=G_{p}}
3889:{\displaystyle R_{nt}=G_{n}}
3488:Shallow traps vs. deep traps
3451:, who published it in 1952.
1614:{\displaystyle np=n_{i}^{2}}
320:center as compared to holes.
185:bipolar junction transistors
5849:10.1039/9781782624066-00107
5379:Langevin recombination rate
4842:{\displaystyle C_{n},C_{p}}
3844:{\displaystyle G_{n},G_{p}}
3804:{\displaystyle B_{n},B_{p}}
3382:trap-assisted recombination
3313:Non-radiative recombination
682:after a radiative lifetime
345:electron and hole densities
6197:
6015:Journal of Applied Physics
5986:The Physics of Solar Cells
5909:Li, Sheng S., ed. (2006).
5874:Li, Sheng S., ed. (2006).
5576:Li, Sheng S., ed. (2006).
4613:
3492:
3073:
955:Band-to-band recombination
671:{\displaystyle \tau _{nr}}
621:
549:
209:
5179:{\displaystyle \tau _{A}}
3123:then the absorption rate
979:bimolecular recombination
702:{\displaystyle \tau _{r}}
226:electronic band structure
212:Electronic band structure
5484:10.1109/LED.2014.2345058
3368:Shockley–Read–Hall (SRH)
2725:{\displaystyle \Delta p}
1337:{\displaystyle \propto }
630:Shockley–Read–Hall (SRH)
618:Recombination mechanisms
576:and other semiconductor
242:Fermi-Dirac distribution
200:inorganic semiconductors
5804:SEMICONDUCTOR PHOTONICS
5802:NISOLI, MAURO. (2016).
5676:Physical Review Letters
5649:Principles of Lasers ..
5616:SEMICONDUCTOR PHOTONICS
5614:NISOLI, MAURO. (2016).
5540:Physical Review Applied
3358:radiative recombination
3115:. It has been shown by
1189:{\displaystyle G=G_{0}}
1156:{\displaystyle G_{L}=0}
945:Radiative recombination
919:radiative recombination
5984:Nelson, Jenny (2003).
5770:10.1103/PhysRev.87.835
5421:
5373:Langevin recombination
5351:The mechanism causing
5343:
5180:
5151:
4897:
4870:
4843:
4801:
4680:
4653:
4601:
4489:
4383:
4356:
4280:
4253:
4224:
3961:
3934:
3890:
3845:
3805:
3765:
3738:
3709:
3629:
3580:
3533:
3288:
3225:
3198:
3171:
3170:{\displaystyle W_{21}}
3144:
3143:{\displaystyle W_{12}}
3058:
3006:
2958:
2892:
2817:
2726:
2700:
2632:
2596:
2550:
2466:
2346:
2136:
2101:
2065:
2027:
1864:
1835:
1794:
1745:
1642:
1615:
1571:
1544:
1517:
1441:
1414:
1384:
1338:
1314:
1272:
1190:
1157:
1122:
1065:
1038:
1009:
936:
824:
798:
726:
703:
672:
524:
483:
442:
381:
361:
338:Fermi–Dirac statistics
321:
221:
5921:10.1007/0-387-37766-2
5886:10.1007/0-387-37766-2
5588:10.1007/0-387-37766-2
5422:
5360:Surface recombination
5344:
5181:
5152:
4898:
4896:{\displaystyle U_{A}}
4871:
4869:{\displaystyle r_{A}}
4844:
4802:
4681:
4679:{\displaystyle G_{0}}
4654:
4652:{\displaystyle R_{A}}
4602:
4490:
4384:
4382:{\displaystyle f_{t}}
4357:
4281:
4279:{\displaystyle p_{t}}
4254:
4252:{\displaystyle n_{t}}
4225:
3962:
3960:{\displaystyle f_{t}}
3935:
3891:
3846:
3806:
3766:
3764:{\displaystyle f_{t}}
3739:
3737:{\displaystyle N_{t}}
3710:
3630:
3581:
3531:
3445:William Thornton Read
3388:passes through a new
3289:
3226:
3224:{\displaystyle g_{2}}
3199:
3197:{\displaystyle g_{1}}
3172:
3145:
3059:
3007:
2959:
2893:
2818:
2727:
2701:
2633:
2597:
2551:
2467:
2347:
2137:
2102:
2066:
2028:
1865:
1836:
1795:
1746:
1643:
1641:{\displaystyle n_{i}}
1616:
1572:
1570:{\displaystyle p_{0}}
1545:
1543:{\displaystyle n_{0}}
1518:
1442:
1440:{\displaystyle G_{0}}
1415:
1413:{\displaystyle R_{0}}
1385:
1339:
1315:
1273:
1191:
1158:
1123:
1066:
1064:{\displaystyle R_{r}}
1039:
1010:
937:
825:
823:{\displaystyle \eta }
799:
727:
725:{\displaystyle \tau }
704:
673:
593:light-emitting diodes
525:
484:
443:
382:
362:
318:
236:of the electrons. At
219:
173:light-emitting diodes
165:semiconductor devices
146:carrier recombination
5393:
5353:LED efficiency droop
5192:
5163:
4909:
4880:
4853:
4813:
4692:
4663:
4636:
4503:
4395:
4366:
4294:
4263:
4236:
3973:
3944:
3901:
3857:
3815:
3775:
3748:
3721:
3641:
3590:
3579:{\displaystyle p(n)}
3561:
3329:recombine releasing
3235:
3208:
3181:
3154:
3127:
3105:population inversion
3016:
2971:
2909:
2833:
2739:
2713:
2648:
2606:
2566:
2479:
2359:
2148:
2111:
2075:
2039:
1876:
1847:
1803:
1759:
1654:
1625:
1584:
1554:
1527:
1454:
1424:
1397:
1348:
1328:
1288:
1200:
1167:
1134:
1086:
1048:
1037:{\displaystyle p(t)}
1019:
1008:{\displaystyle n(t)}
990:
959:spontaneous emission
836:
814:
738:
716:
686:
652:
493:
452:
391:
371:
351:
54:improve this article
6135:, Brooks Cole, 1976
6133:Solid State Physics
6090:2014ARPC...65..557L
6027:1985JAP....58.4267E
5762:1952PhRv...87..835S
5688:2001PhRvL..87r7404B
5552:2014PhRvP...2c4007S
5476:2014IEDL...35..986K
5383:organic solar cells
5279:
5159:The Auger lifetime
5137:
5063:
4796:
4748:
4622:Auger recombination
4610:Auger recombination
3085:Stimulated emission
3076:Stimulated emission
3070:Stimulated emission
2458:
2402:
2341:
1740:
1610:
922:total recombination
634:Auger recombination
582:stimulated emission
519:
478:
434:
343:The product of the
330:thermal equilibrium
134:solid-state physics
18:Auger recombination
5417:
5412:
5339:
5265:
5176:
5147:
5123:
5049:
4893:
4866:
4839:
4797:
4782:
4734:
4676:
4649:
4597:
4485:
4379:
4352:
4276:
4249:
4220:
4218:
3957:
3930:
3886:
3841:
3801:
3761:
3734:
3705:
3625:
3576:
3534:
3362:quantum efficiency
3348:recombines with a
3284:
3221:
3194:
3167:
3140:
3054:
3002:
2954:
2888:
2813:
2722:
2696:
2628:
2592:
2546:
2462:
2444:
2388:
2342:
2327:
2132:
2107:, we can say that
2097:
2061:
2023:
1860:
1831:
1790:
1741:
1726:
1638:
1611:
1596:
1567:
1540:
1513:
1437:
1410:
1380:
1334:
1310:
1268:
1186:
1153:
1118:
1061:
1034:
1005:
932:
820:
810:or quantum yield,
808:quantum efficiency
794:
722:
699:
668:
546:Carrier generation
520:
505:
479:
464:
438:
420:
377:
357:
322:
290:Carrier generation
282:, photons, or the
222:
196:electron–hole pair
142:carrier generation
6021:(11): 4267–4276.
5995:978-1-86094-340-9
5930:978-0-387-28893-2
5895:978-0-387-28893-2
5727:10.1021/jp993327z
5670:Blumenau (2001).
5597:978-0-387-28893-2
5411:
5333:
5228:
4686:equal each other
4592:
4546:
4483:
4288:quasi Fermi level
3555:density of states
3433:carrier densities
3052:
3000:
2952:
2778:
2763:
2489:
2369:
2158:
1886:
1857:
1324:to eliminate the
1221:
924:
923:
920:
911:
792:
769:
749:
608:photoconductivity
380:{\displaystyle p}
360:{\displaystyle n}
305:vibrating lattice
187:and p-n junction
130:
129:
122:
104:
16:(Redirected from
6188:
6120:
6119:
6101:
6069:
6063:
6062:
6055:
6049:
6048:
6038:
6036:10.1063/1.335562
6006:
6000:
5999:
5981:
5975:
5974:
5972:
5970:
5954:
5948:
5941:
5935:
5934:
5906:
5900:
5899:
5871:
5862:
5861:
5835:
5826:
5825:
5799:
5793:
5792:
5780:
5774:
5773:
5745:
5739:
5738:
5721:(8): 1715–1723.
5706:
5700:
5699:
5667:
5661:
5660:
5647:Svelto. (1989).
5644:
5638:
5637:
5611:
5602:
5601:
5573:
5564:
5563:
5534:
5528:
5527:
5502:
5496:
5495:
5457:
5426:
5424:
5423:
5418:
5413:
5404:
5348:
5346:
5345:
5340:
5334:
5332:
5331:
5330:
5321:
5320:
5305:
5304:
5292:
5291:
5278:
5273:
5258:
5257:
5248:
5247:
5234:
5229:
5227:
5226:
5217:
5209:
5204:
5203:
5185:
5183:
5182:
5177:
5175:
5174:
5156:
5154:
5153:
5148:
5142:
5138:
5136:
5131:
5122:
5121:
5109:
5108:
5091:
5090:
5078:
5074:
5073:
5072:
5062:
5057:
5042:
5041:
5027:
5026:
5014:
5013:
5001:
5000:
4988:
4987:
4973:
4972:
4960:
4959:
4944:
4943:
4934:
4933:
4921:
4920:
4902:
4900:
4899:
4894:
4892:
4891:
4875:
4873:
4872:
4867:
4865:
4864:
4848:
4846:
4845:
4840:
4838:
4837:
4825:
4824:
4806:
4804:
4803:
4798:
4795:
4790:
4781:
4780:
4771:
4770:
4758:
4757:
4747:
4742:
4733:
4732:
4720:
4719:
4707:
4706:
4685:
4683:
4682:
4677:
4675:
4674:
4658:
4656:
4655:
4650:
4648:
4647:
4606:
4604:
4603:
4598:
4593:
4591:
4590:
4589:
4580:
4579:
4566:
4561:
4560:
4547:
4545:
4544:
4543:
4534:
4533:
4520:
4515:
4514:
4494:
4492:
4491:
4486:
4484:
4482:
4478:
4477:
4459:
4458:
4443:
4442:
4424:
4423:
4413:
4405:
4388:
4386:
4385:
4380:
4378:
4377:
4361:
4359:
4358:
4353:
4351:
4350:
4338:
4337:
4322:
4321:
4309:
4308:
4285:
4283:
4282:
4277:
4275:
4274:
4258:
4256:
4255:
4250:
4248:
4247:
4229:
4227:
4226:
4221:
4219:
4212:
4211:
4193:
4192:
4183:
4182:
4173:
4172:
4160:
4159:
4148:
4147:
4138:
4137:
4125:
4124:
4112:
4111:
4095:
4094:
4085:
4084:
4075:
4074:
4065:
4064:
4052:
4051:
4037:
4036:
4018:
4017:
4005:
4004:
3992:
3991:
3966:
3964:
3963:
3958:
3956:
3955:
3939:
3937:
3936:
3931:
3929:
3928:
3916:
3915:
3896:
3895:
3893:
3892:
3887:
3885:
3884:
3872:
3871:
3850:
3848:
3847:
3842:
3840:
3839:
3827:
3826:
3810:
3808:
3807:
3802:
3800:
3799:
3787:
3786:
3770:
3768:
3767:
3762:
3760:
3759:
3743:
3741:
3740:
3735:
3733:
3732:
3714:
3712:
3711:
3706:
3701:
3700:
3682:
3681:
3669:
3668:
3656:
3655:
3634:
3632:
3631:
3626:
3621:
3620:
3602:
3601:
3585:
3583:
3582:
3577:
3506:thermal energy k
3441:William Shockley
3425:indirect bandgap
3293:
3291:
3290:
3285:
3280:
3279:
3270:
3269:
3257:
3256:
3247:
3246:
3230:
3228:
3227:
3222:
3220:
3219:
3203:
3201:
3200:
3195:
3193:
3192:
3176:
3174:
3173:
3168:
3166:
3165:
3149:
3147:
3146:
3141:
3139:
3138:
3063:
3061:
3060:
3055:
3053:
3051:
3050:
3049:
3033:
3028:
3027:
3011:
3009:
3008:
3003:
3001:
2999:
2998:
2997:
2981:
2963:
2961:
2960:
2955:
2953:
2951:
2950:
2949:
2936:
2935:
2926:
2921:
2920:
2897:
2895:
2894:
2889:
2887:
2886:
2882:
2881:
2872:
2871:
2854:
2853:
2822:
2820:
2819:
2814:
2812:
2811:
2796:
2795:
2780:
2779:
2776:
2764:
2762:
2754:
2743:
2731:
2729:
2728:
2723:
2705:
2703:
2702:
2697:
2695:
2694:
2679:
2678:
2666:
2665:
2637:
2635:
2634:
2629:
2627:
2626:
2601:
2599:
2598:
2593:
2591:
2590:
2578:
2577:
2555:
2553:
2552:
2547:
2542:
2541:
2523:
2522:
2504:
2503:
2491:
2490:
2487:
2471:
2469:
2468:
2463:
2457:
2452:
2440:
2439:
2421:
2420:
2401:
2396:
2384:
2383:
2371:
2370:
2367:
2351:
2349:
2348:
2343:
2340:
2335:
2326:
2325:
2310:
2309:
2291:
2290:
2272:
2271:
2262:
2261:
2249:
2248:
2236:
2235:
2211:
2210:
2186:
2185:
2173:
2172:
2160:
2159:
2156:
2141:
2139:
2138:
2133:
2106:
2104:
2103:
2098:
2087:
2086:
2070:
2068:
2067:
2062:
2051:
2050:
2032:
2030:
2029:
2024:
2022:
2021:
1997:
1996:
1972:
1971:
1959:
1958:
1946:
1945:
1927:
1926:
1914:
1913:
1901:
1900:
1888:
1887:
1884:
1869:
1867:
1866:
1861:
1859:
1858:
1855:
1840:
1838:
1837:
1832:
1821:
1820:
1799:
1797:
1796:
1791:
1777:
1776:
1750:
1748:
1747:
1742:
1739:
1734:
1725:
1724:
1712:
1711:
1702:
1701:
1692:
1691:
1679:
1678:
1666:
1665:
1647:
1645:
1644:
1639:
1637:
1636:
1620:
1618:
1617:
1612:
1609:
1604:
1576:
1574:
1573:
1568:
1566:
1565:
1549:
1547:
1546:
1541:
1539:
1538:
1522:
1520:
1519:
1514:
1512:
1511:
1502:
1501:
1492:
1491:
1479:
1478:
1466:
1465:
1446:
1444:
1443:
1438:
1436:
1435:
1419:
1417:
1416:
1411:
1409:
1408:
1389:
1387:
1386:
1381:
1373:
1372:
1360:
1359:
1343:
1341:
1340:
1335:
1319:
1317:
1316:
1311:
1300:
1299:
1277:
1275:
1274:
1269:
1267:
1266:
1254:
1253:
1241:
1240:
1222:
1220:
1212:
1204:
1195:
1193:
1192:
1187:
1185:
1184:
1162:
1160:
1159:
1154:
1146:
1145:
1127:
1125:
1124:
1119:
1117:
1116:
1104:
1103:
1070:
1068:
1067:
1062:
1060:
1059:
1043:
1041:
1040:
1035:
1014:
1012:
1011:
1006:
941:
939:
938:
933:
925:
921:
918:
917:
912:
910:
909:
908:
896:
885:
884:
875:
866:
865:
864:
855:
846:
829:
827:
826:
821:
803:
801:
800:
795:
793:
791:
790:
775:
770:
768:
767:
755:
750:
742:
731:
729:
728:
723:
711:carrier lifetime
708:
706:
705:
700:
698:
697:
677:
675:
674:
669:
667:
666:
624:Carrier lifetime
604:excite electrons
529:
527:
526:
521:
518:
513:
488:
486:
485:
480:
477:
472:
447:
445:
444:
439:
433:
428:
416:
415:
406:
405:
387:) is a constant
386:
384:
383:
378:
366:
364:
363:
358:
328:, a material at
301:crystal momentum
183:devices such as
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
6196:
6195:
6191:
6190:
6189:
6187:
6186:
6185:
6181:Charge carriers
6176:Optoelectronics
6161:
6160:
6142:
6128:
6126:Further reading
6123:
6071:
6070:
6066:
6061:. 4 April 2008.
6057:
6056:
6052:
6008:
6007:
6003:
5996:
5983:
5982:
5978:
5968:
5966:
5965:. Science Daily
5956:
5955:
5951:
5947:. IEEE Spectrum
5942:
5938:
5931:
5915:. p. 144.
5908:
5907:
5903:
5896:
5880:. p. 143.
5873:
5872:
5865:
5859:
5837:
5836:
5829:
5814:
5801:
5800:
5796:
5785:Physical Review
5782:
5781:
5777:
5750:Physical Review
5747:
5746:
5742:
5708:
5707:
5703:
5669:
5668:
5664:
5646:
5645:
5641:
5626:
5613:
5612:
5605:
5598:
5582:. p. 140.
5575:
5574:
5567:
5536:
5535:
5531:
5525:
5504:
5503:
5499:
5470:(10): 986–988.
5459:
5458:
5454:
5450:
5433:
5391:
5390:
5375:
5362:
5322:
5312:
5296:
5283:
5249:
5239:
5238:
5218:
5210:
5195:
5190:
5189:
5166:
5161:
5160:
5113:
5100:
5096:
5092:
5082:
5064:
5033:
5032:
5028:
5018:
5005:
4992:
4979:
4964:
4951:
4935:
4925:
4912:
4907:
4906:
4883:
4878:
4877:
4856:
4851:
4850:
4829:
4816:
4811:
4810:
4772:
4762:
4749:
4724:
4711:
4695:
4690:
4689:
4666:
4661:
4660:
4639:
4634:
4633:
4618:
4612:
4581:
4571:
4570:
4552:
4535:
4525:
4524:
4506:
4501:
4500:
4469:
4450:
4434:
4415:
4414:
4406:
4393:
4392:
4369:
4364:
4363:
4342:
4326:
4313:
4297:
4292:
4291:
4266:
4261:
4260:
4239:
4234:
4233:
4217:
4216:
4203:
4184:
4174:
4164:
4151:
4149:
4139:
4129:
4116:
4100:
4097:
4096:
4086:
4076:
4066:
4056:
4043:
4041:
4028:
4009:
3996:
3980:
3971:
3970:
3947:
3942:
3941:
3920:
3904:
3899:
3898:
3876:
3860:
3855:
3854:
3852:
3831:
3818:
3813:
3812:
3791:
3778:
3773:
3772:
3751:
3746:
3745:
3724:
3719:
3718:
3692:
3673:
3660:
3644:
3639:
3638:
3612:
3593:
3588:
3587:
3559:
3558:
3526:
3509:
3501:
3495:Deep-level trap
3491:
3470:conduction band
3462:
3457:
3406:crystal lattice
3380:), also called
3370:
3354:optoelectronics
3342:conduction band
3327:charge carriers
3315:
3299:
3271:
3261:
3248:
3238:
3233:
3232:
3211:
3206:
3205:
3184:
3179:
3178:
3157:
3152:
3151:
3130:
3125:
3124:
3082:
3072:
3041:
3037:
3019:
3014:
3013:
2989:
2985:
2969:
2968:
2941:
2937:
2927:
2912:
2907:
2906:
2904:
2873:
2863:
2855:
2845:
2831:
2830:
2803:
2787:
2771:
2755:
2744:
2737:
2736:
2711:
2710:
2686:
2670:
2651:
2646:
2645:
2618:
2604:
2603:
2582:
2569:
2564:
2563:
2533:
2514:
2495:
2482:
2477:
2476:
2431:
2412:
2375:
2362:
2357:
2356:
2317:
2301:
2282:
2263:
2253:
2240:
2227:
2202:
2177:
2164:
2151:
2146:
2145:
2109:
2108:
2078:
2073:
2072:
2042:
2037:
2036:
2013:
1988:
1963:
1950:
1937:
1918:
1905:
1892:
1879:
1874:
1873:
1850:
1845:
1844:
1812:
1801:
1800:
1768:
1757:
1756:
1716:
1703:
1693:
1683:
1670:
1657:
1652:
1651:
1628:
1623:
1622:
1582:
1581:
1579:mass action law
1557:
1552:
1551:
1530:
1525:
1524:
1503:
1493:
1483:
1470:
1457:
1452:
1451:
1427:
1422:
1421:
1400:
1395:
1394:
1364:
1351:
1346:
1345:
1326:
1325:
1323:
1291:
1286:
1285:
1283:
1258:
1245:
1232:
1213:
1205:
1198:
1197:
1176:
1165:
1164:
1137:
1132:
1131:
1108:
1095:
1084:
1083:
1081:
1077:
1051:
1046:
1045:
1017:
1016:
988:
987:
952:
947:
897:
876:
867:
856:
847:
834:
833:
812:
811:
779:
759:
736:
735:
714:
713:
689:
684:
683:
655:
650:
649:
626:
620:
554:
548:
491:
490:
450:
449:
407:
397:
389:
388:
369:
368:
349:
348:
313:
268:conduction band
214:
208:
150:charge carriers
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
6194:
6192:
6184:
6183:
6178:
6173:
6171:Semiconductors
6163:
6162:
6159:
6158:
6153:
6148:
6141:
6140:External links
6138:
6137:
6136:
6127:
6124:
6122:
6121:
6084:(1): 557–581.
6064:
6050:
6001:
5994:
5976:
5949:
5936:
5929:
5901:
5894:
5863:
5857:
5827:
5813:978-8893850025
5812:
5794:
5775:
5756:(5): 835–842.
5740:
5701:
5682:(18): 187404.
5662:
5639:
5625:978-8893850025
5624:
5603:
5596:
5565:
5529:
5523:
5497:
5451:
5449:
5446:
5445:
5444:
5439:
5432:
5429:
5416:
5410:
5407:
5401:
5398:
5389:is defined as
5374:
5371:
5361:
5358:
5338:
5329:
5325:
5319:
5315:
5311:
5308:
5303:
5299:
5295:
5290:
5286:
5282:
5277:
5272:
5268:
5264:
5261:
5256:
5252:
5246:
5242:
5237:
5232:
5225:
5221:
5216:
5213:
5207:
5202:
5198:
5173:
5169:
5146:
5141:
5135:
5130:
5126:
5120:
5116:
5112:
5107:
5103:
5099:
5095:
5089:
5085:
5081:
5077:
5071:
5067:
5061:
5056:
5052:
5048:
5045:
5040:
5036:
5031:
5025:
5021:
5017:
5012:
5008:
5004:
4999:
4995:
4991:
4986:
4982:
4977:
4971:
4967:
4963:
4958:
4954:
4950:
4947:
4942:
4938:
4932:
4928:
4924:
4919:
4915:
4890:
4886:
4863:
4859:
4836:
4832:
4828:
4823:
4819:
4794:
4789:
4785:
4779:
4775:
4769:
4765:
4761:
4756:
4752:
4746:
4741:
4737:
4731:
4727:
4723:
4718:
4714:
4710:
4705:
4702:
4698:
4673:
4669:
4646:
4642:
4614:Main article:
4611:
4608:
4596:
4588:
4584:
4578:
4574:
4569:
4564:
4559:
4555:
4550:
4542:
4538:
4532:
4528:
4523:
4518:
4513:
4509:
4481:
4476:
4472:
4468:
4465:
4462:
4457:
4453:
4449:
4446:
4441:
4437:
4433:
4430:
4427:
4422:
4418:
4412:
4409:
4403:
4400:
4376:
4372:
4349:
4345:
4341:
4336:
4333:
4329:
4325:
4320:
4316:
4312:
4307:
4304:
4300:
4273:
4269:
4246:
4242:
4215:
4210:
4206:
4202:
4199:
4196:
4191:
4187:
4181:
4177:
4171:
4167:
4163:
4158:
4154:
4150:
4146:
4142:
4136:
4132:
4128:
4123:
4119:
4115:
4110:
4107:
4103:
4099:
4098:
4093:
4089:
4083:
4079:
4073:
4069:
4063:
4059:
4055:
4050:
4046:
4042:
4040:
4035:
4031:
4027:
4024:
4021:
4016:
4012:
4008:
4003:
3999:
3995:
3990:
3987:
3983:
3979:
3978:
3954:
3950:
3927:
3923:
3919:
3914:
3911:
3907:
3883:
3879:
3875:
3870:
3867:
3863:
3838:
3834:
3830:
3825:
3821:
3798:
3794:
3790:
3785:
3781:
3758:
3754:
3731:
3727:
3704:
3699:
3695:
3691:
3688:
3685:
3680:
3676:
3672:
3667:
3663:
3659:
3654:
3651:
3647:
3624:
3619:
3615:
3611:
3608:
3605:
3600:
3596:
3575:
3572:
3569:
3566:
3551:
3550:
3547:
3544:
3541:
3525:
3522:
3507:
3490:
3485:
3474:electron traps
3461:
3458:
3456:
3455:Types of traps
3453:
3449:Robert N. Hall
3429:direct bandgap
3369:
3366:
3323:semiconductors
3314:
3311:
3298:
3295:
3283:
3278:
3274:
3268:
3264:
3260:
3255:
3251:
3245:
3241:
3218:
3214:
3191:
3187:
3164:
3160:
3137:
3133:
3121:non degenerate
3071:
3068:
3048:
3044:
3040:
3036:
3031:
3026:
3022:
2996:
2992:
2988:
2984:
2979:
2976:
2948:
2944:
2940:
2934:
2930:
2924:
2919:
2915:
2902:
2899:
2898:
2885:
2880:
2876:
2870:
2866:
2862:
2858:
2852:
2848:
2844:
2841:
2838:
2824:
2823:
2810:
2806:
2802:
2799:
2794:
2790:
2786:
2783:
2774:
2770:
2767:
2761:
2758:
2753:
2750:
2747:
2721:
2718:
2707:
2706:
2693:
2689:
2685:
2682:
2677:
2673:
2669:
2664:
2661:
2658:
2654:
2639:
2638:
2625:
2621:
2617:
2614:
2611:
2589:
2585:
2581:
2576:
2572:
2557:
2556:
2545:
2540:
2536:
2532:
2529:
2526:
2521:
2517:
2513:
2510:
2507:
2502:
2498:
2494:
2485:
2473:
2472:
2461:
2456:
2451:
2447:
2443:
2438:
2434:
2430:
2427:
2424:
2419:
2415:
2411:
2408:
2405:
2400:
2395:
2391:
2387:
2382:
2378:
2374:
2365:
2353:
2352:
2339:
2334:
2330:
2324:
2320:
2316:
2313:
2308:
2304:
2300:
2297:
2294:
2289:
2285:
2281:
2278:
2275:
2270:
2266:
2260:
2256:
2252:
2247:
2243:
2239:
2234:
2230:
2226:
2223:
2220:
2217:
2214:
2209:
2205:
2201:
2198:
2195:
2192:
2189:
2184:
2180:
2176:
2171:
2167:
2163:
2154:
2131:
2128:
2125:
2122:
2119:
2116:
2096:
2093:
2090:
2085:
2081:
2060:
2057:
2054:
2049:
2045:
2020:
2016:
2012:
2009:
2006:
2003:
2000:
1995:
1991:
1987:
1984:
1981:
1978:
1975:
1970:
1966:
1962:
1957:
1953:
1949:
1944:
1940:
1936:
1933:
1930:
1925:
1921:
1917:
1912:
1908:
1904:
1899:
1895:
1891:
1882:
1853:
1830:
1827:
1824:
1819:
1815:
1811:
1808:
1789:
1786:
1783:
1780:
1775:
1771:
1767:
1764:
1738:
1733:
1729:
1723:
1719:
1715:
1710:
1706:
1700:
1696:
1690:
1686:
1682:
1677:
1673:
1669:
1664:
1660:
1635:
1631:
1608:
1603:
1599:
1595:
1592:
1589:
1564:
1560:
1537:
1533:
1510:
1506:
1500:
1496:
1490:
1486:
1482:
1477:
1473:
1469:
1464:
1460:
1434:
1430:
1407:
1403:
1379:
1376:
1371:
1367:
1363:
1358:
1354:
1333:
1321:
1309:
1306:
1303:
1298:
1294:
1281:
1265:
1261:
1257:
1252:
1248:
1244:
1239:
1235:
1231:
1228:
1225:
1219:
1216:
1211:
1208:
1183:
1179:
1175:
1172:
1152:
1149:
1144:
1140:
1115:
1111:
1107:
1102:
1098:
1094:
1091:
1079:
1075:
1058:
1054:
1033:
1030:
1027:
1024:
1004:
1001:
998:
995:
975:direct bandgap
951:
948:
946:
943:
931:
928:
915:
907:
904:
900:
895:
891:
888:
883:
879:
874:
870:
863:
859:
854:
850:
844:
841:
819:
789:
786:
782:
778:
773:
766:
762:
758:
753:
748:
745:
721:
696:
692:
665:
662:
658:
642:non-radiative.
622:Main article:
619:
616:
578:photodetectors
547:
544:
517:
512:
508:
504:
501:
498:
476:
471:
467:
463:
460:
457:
437:
432:
427:
423:
419:
414:
410:
404:
400:
396:
376:
356:
334:charge carrier
326:thermodynamics
312:
309:
249:forbidden band
207:
204:
162:optoelectronic
158:electron holes
138:semiconductors
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6193:
6182:
6179:
6177:
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5651:. p. 3.
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3346:semiconductor
3343:
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3302:Trap emission
3297:Trap emission
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2018:
2014:
2010:
2004:
1998:
1993:
1989:
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374:
354:
346:
341:
339:
335:
331:
327:
317:
310:
308:
306:
302:
297:
295:
294:recombination
291:
287:
285:
281:
277:
272:
270:
269:
264:
263:
258:
257:allowed bands
254:
250:
245:
243:
239:
238:absolute zero
235:
231:
227:
218:
213:
205:
203:
201:
197:
192:
190:
186:
182:
178:
174:
170:
166:
163:
159:
155:
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147:
143:
139:
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124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
6156:PV Education
6132:
6081:
6077:
6067:
6053:
6018:
6014:
6004:
5985:
5979:
5967:. Retrieved
5962:
5952:
5939:
5911:
5904:
5876:
5840:
5803:
5797:
5788:
5784:
5778:
5753:
5749:
5743:
5718:
5714:
5704:
5679:
5675:
5665:
5648:
5642:
5615:
5578:
5543:
5539:
5532:
5506:
5500:
5467:
5461:
5455:
5437:Auger effect
5386:
5378:
5376:
5363:
5350:
5188:
5186:is given by
5158:
4905:
4808:
4688:
4631:
4627:Auger effect
4621:
4619:
4616:Auger effect
4499:
4496:
4391:
4231:
3969:
3716:
3637:
3552:
3535:
3514:shallow trap
3513:
3502:
3487:
3481:
3480:they become
3478:valence band
3473:
3465:
3463:
3414:
3409:
3390:energy state
3381:
3377:
3373:
3371:
3335:
3316:
3305:
3301:
3300:
3097:polarization
3084:
3083:
3065:
2966:
2900:
2825:
2708:
2640:
2558:
2034:
1872:
1842:
1755:
1752:
1650:
1449:
1391:
1279:
1129:
1073:
985:
981:
978:
954:
953:
832:
805:
734:
680:luminescence
641:
637:
627:
601:
590:
586:laser diodes
565:
564:) or it can
555:
342:
323:
298:
293:
289:
288:
273:
266:
262:valence band
260:
256:
255:between two
248:
246:
223:
195:
193:
181:p-n junction
177:laser diodes
145:
141:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
5442:Cage effect
5367:Passivation
3482:hole traps.
3437:perovskites
1450:Therefore：
612:photodiodes
597:transistors
574:solar cells
570:photodiodes
259:called the
234:temperature
230:Fermi level
169:photodiodes
110:August 2021
6165:Categories
5448:References
3493:See also:
3423:and other
3325:, whereby
3204:-fold and
3074:See also:
2732:disappear
550:See also:
303:, and the
210:See also:
167:, such as
80:newspapers
6108:0066-426X
6045:0021-8979
5822:964380194
5791:(1): 228.
5735:1520-6106
5657:249201544
5634:964380194
5415:μ
5409:ε
5397:γ
5212:Δ
5197:τ
5168:τ
5111:−
5047:−
5003:−
4554:τ
4508:τ
4452:τ
4417:τ
4340:−
4311:−
4201:−
4026:−
3690:−
3610:−
3524:SRH model
3518:deep trap
3499:Deathnium
3319:phosphors
3101:direction
3093:frequency
3021:τ
2861:−
2837:Δ
2798:Δ
2785:−
2782:≈
2769:−
2749:Δ
2717:Δ
2681:Δ
2668:≈
2616:≪
2610:Δ
2580:≪
2528:Δ
2509:Δ
2442:−
2426:Δ
2407:Δ
2315:−
2296:Δ
2277:Δ
2225:−
2216:Δ
2191:Δ
2127:≈
2121:Δ
2115:Δ
2092:Δ
2089:≫
2056:Δ
2053:≫
2011:−
2002:Δ
1977:Δ
1935:−
1903:−
1870:becomes,
1826:Δ
1782:Δ
1332:∝
1302:∝
1256:−
1230:−
927:≤
899:τ
878:τ
858:τ
840:η
818:η
781:τ
761:τ
747:τ
720:τ
691:τ
657:τ
638:radiative
566:stimulate
538:, or the
276:electrons
154:electrons
6116:24423376
5969:23 April
5492:19785166
5431:See also
3967:become:
3417:momentum
3394:band gap
3338:electron
3117:Einstein
2035:Because
971:momentum
580:, while
558:absorbed
536:electron
265:and the
253:band gap
232:and the
206:Overview
6086:Bibcode
6023:Bibcode
5758:Bibcode
5684:Bibcode
5548:Bibcode
5472:Bibcode
3421:silicon
3404:in the
3340:in the
3331:phonons
2901:where p
562:exciton
532:photons
94:scholar
6114:
6106:
6043:
5992:
5927:
5892:
5855:
5820:
5810:
5733:
5655:
5632:
5622:
5594:
5521:
5490:
4809:where
4232:Where
3717:Where
3402:defect
3398:dopant
3356:where
3113:masers
3109:lasers
3099:, and
1621:，with
1523:where
1344:sign:
709:. The
646:phonon
189:diodes
96:
89:
82:
75:
67:
5488:S2CID
3466:holes
3410:traps
3400:or a
3396:by a
3386:bands
3344:of a
3089:phase
3080:Laser
2967:When
2641:thus
280:holes
101:JSTOR
87:books
6112:PMID
6104:ISSN
6041:ISSN
5990:ISBN
5971:2013
5925:ISBN
5890:ISBN
5853:ISBN
5818:OCLC
5808:ISBN
5731:ISSN
5653:OCLC
5630:OCLC
5620:ISBN
5592:ISBN
5519:ISBN
4259:and
3897:and
3497:and
3447:and
3350:hole
3321:and
3306:trap
3111:and
3078:and
2602:and
2071:and
1550:and
1163:and
1015:and
967:LEDs
963:less
830:as:
640:and
595:and
503:<
462:>
367:and
194:The
175:and
156:and
144:and
73:news
6094:doi
6031:doi
5917:doi
5882:doi
5845:doi
5766:doi
5723:doi
5719:104
5692:doi
5584:doi
5556:doi
5511:doi
5480:doi
4620:In
3378:SRH
3372:In
2918:max
2903:max
2851:max
2777:net
2488:net
2368:net
2157:net
1885:net
1856:net
542:).
251:or
136:of
132:In
56:by
6167::
6110:.
6102:.
6092:.
6082:65
6080:.
6076:.
6039:.
6029:.
6019:58
6017:.
6013:.
5961:.
5923:.
5888:.
5866:^
5851:,
5830:^
5816:.
5789:83
5787:.
5764:.
5754:87
5752:.
5729:.
5717:.
5713:.
5690:.
5680:87
5678:.
5674:.
5628:.
5606:^
5590:.
5568:^
5554:.
5542:.
5517:,
5486:.
5478:.
5468:35
5466:.
5427:.
3635:.
3443:,
3364:.
3277:21
3254:12
3163:21
3136:12
3095:,
3091:,
1447:.
1082::
930:1.
614:.
599:.
588:.
572:,
534:,
340:.
278:,
244:.
191:.
171:,
140:,
6118:.
6096::
6088::
6047:.
6033::
6025::
5998:.
5973:.
5933:.
5919::
5898:.
5884::
5847::
5824:.
5772:.
5768::
5760::
5737:.
5725::
5698:.
5694::
5686::
5659:.
5636:.
5600:.
5586::
5562:.
5558::
5550::
5544:2
5513::
5494:.
5482::
5474::
5406:q
5400:=
5337:.
5328:p
5324:C
5318:2
5314:p
5310:+
5307:)
5302:p
5298:C
5294:+
5289:n
5285:C
5281:(
5276:2
5271:i
5267:n
5263:2
5260:+
5255:n
5251:C
5245:2
5241:n
5236:1
5231:=
5224:A
5220:R
5215:n
5206:=
5201:A
5172:A
5145:.
5140:)
5134:2
5129:0
5125:p
5119:0
5115:n
5106:2
5102:p
5098:n
5094:(
5088:p
5084:C
5080:+
5076:)
5070:0
5066:p
5060:2
5055:0
5051:n
5044:p
5039:2
5035:n
5030:(
5024:n
5020:C
5016:=
5011:0
5007:G
4998:A
4994:r
4990:=
4985:A
4981:R
4976:,
4970:2
4966:p
4962:n
4957:p
4953:C
4949:+
4946:p
4941:2
4937:n
4931:n
4927:C
4923:=
4918:A
4914:r
4889:A
4885:U
4862:A
4858:r
4835:p
4831:C
4827:,
4822:n
4818:C
4793:2
4788:0
4784:p
4778:0
4774:n
4768:p
4764:C
4760:+
4755:0
4751:p
4745:2
4740:0
4736:n
4730:n
4726:C
4722:=
4717:0
4713:G
4709:=
4704:0
4701:A
4697:R
4672:0
4668:G
4645:A
4641:R
4595:.
4587:t
4583:N
4577:p
4573:B
4568:1
4563:=
4558:p
4549:,
4541:t
4537:N
4531:n
4527:B
4522:1
4517:=
4512:n
4480:)
4475:t
4471:n
4467:+
4464:n
4461:(
4456:p
4448:+
4445:)
4440:t
4436:p
4432:+
4429:p
4426:(
4421:n
4411:p
4408:n
4402:=
4399:R
4375:t
4371:f
4348:p
4344:G
4335:t
4332:p
4328:R
4324:=
4319:n
4315:G
4306:t
4303:n
4299:R
4272:t
4268:p
4245:t
4241:n
4214:)
4209:t
4205:f
4198:1
4195:(
4190:t
4186:N
4180:t
4176:p
4170:p
4166:B
4162:=
4157:p
4153:G
4145:t
4141:f
4135:t
4131:N
4127:p
4122:p
4118:B
4114:=
4109:t
4106:p
4102:R
4092:t
4088:f
4082:t
4078:N
4072:t
4068:n
4062:n
4058:B
4054:=
4049:n
4045:G
4039:)
4034:t
4030:f
4023:1
4020:(
4015:t
4011:N
4007:n
4002:n
3998:B
3994:=
3989:t
3986:n
3982:R
3953:t
3949:f
3926:p
3922:G
3918:=
3913:t
3910:p
3906:R
3882:n
3878:G
3874:=
3869:t
3866:n
3862:R
3853:(
3837:p
3833:G
3829:,
3824:n
3820:G
3797:p
3793:B
3789:,
3784:n
3780:B
3757:t
3753:f
3730:t
3726:N
3703:)
3698:t
3694:f
3687:1
3684:(
3679:t
3675:N
3671:n
3666:n
3662:B
3658:=
3653:t
3650:n
3646:R
3623:)
3618:t
3614:f
3607:1
3604:(
3599:t
3595:N
3574:)
3571:n
3568:(
3565:p
3510:T
3508:B
3376:(
3282:.
3273:W
3267:2
3263:g
3259:=
3250:W
3244:1
3240:g
3217:2
3213:g
3190:1
3186:g
3159:W
3132:W
3047:0
3043:n
3039:B
3035:1
3030:=
3025:p
2995:0
2991:n
2987:B
2983:1
2978:=
2975:t
2947:0
2943:n
2939:B
2933:L
2929:G
2923:=
2914:p
2884:t
2879:0
2875:n
2869:r
2865:B
2857:e
2847:p
2843:=
2840:p
2809:0
2805:n
2801:p
2793:r
2789:B
2773:R
2766:=
2760:t
2757:d
2752:p
2746:d
2720:p
2692:0
2688:n
2684:p
2676:r
2672:B
2663:t
2660:e
2657:n
2653:R
2624:0
2620:n
2613:p
2588:0
2584:n
2575:0
2571:p
2544:)
2539:0
2535:n
2531:p
2525:+
2520:0
2516:p
2512:n
2506:(
2501:r
2497:B
2493:=
2484:R
2460:)
2455:2
2450:i
2446:n
2437:0
2433:n
2429:p
2423:+
2418:0
2414:p
2410:n
2404:+
2399:2
2394:i
2390:n
2386:(
2381:r
2377:B
2373:=
2364:R
2338:2
2333:i
2329:n
2323:r
2319:B
2312:)
2307:0
2303:n
2299:p
2293:+
2288:0
2284:p
2280:n
2274:+
2269:0
2265:p
2259:0
2255:n
2251:(
2246:r
2242:B
2238:=
2233:0
2229:G
2222:)
2219:p
2213:+
2208:0
2204:p
2200:(
2197:)
2194:n
2188:+
2183:0
2179:n
2175:(
2170:r
2166:B
2162:=
2153:R
2130:0
2124:p
2118:n
2095:p
2084:0
2080:p
2059:n
2048:0
2044:n
2019:0
2015:G
2008:)
2005:p
1999:+
1994:0
1990:p
1986:(
1983:)
1980:n
1974:+
1969:0
1965:n
1961:(
1956:r
1952:B
1948:=
1943:0
1939:G
1932:p
1929:n
1924:r
1920:B
1916:=
1911:0
1907:G
1898:r
1894:R
1890:=
1881:R
1852:R
1829:p
1823:+
1818:0
1814:p
1810:=
1807:p
1788:,
1785:n
1779:+
1774:0
1770:n
1766:=
1763:n
1737:2
1732:i
1728:n
1722:r
1718:B
1714:=
1709:0
1705:p
1699:0
1695:n
1689:r
1685:B
1681:=
1676:0
1672:G
1668:=
1663:0
1659:R
1634:i
1630:n
1607:2
1602:i
1598:n
1594:=
1591:p
1588:n
1563:0
1559:p
1536:0
1532:n
1509:0
1505:p
1499:0
1495:n
1489:r
1485:B
1481:=
1476:0
1472:G
1468:=
1463:0
1459:R
1433:0
1429:G
1406:0
1402:R
1378:p
1375:n
1370:r
1366:B
1362:=
1357:r
1353:R
1322:r
1308:p
1305:n
1297:r
1293:R
1282:r
1264:r
1260:R
1251:0
1247:G
1243:=
1238:r
1234:R
1227:G
1224:=
1218:t
1215:d
1210:n
1207:d
1182:0
1178:G
1174:=
1171:G
1151:0
1148:=
1143:L
1139:G
1114:L
1110:G
1106:+
1101:0
1097:G
1093:=
1090:G
1080:L
1076:0
1057:r
1053:R
1032:)
1029:t
1026:(
1023:p
1003:)
1000:t
997:(
994:n
982:.
914:=
906:r
903:n
894:/
890:1
887:+
882:r
873:/
869:1
862:r
853:/
849:1
843:=
788:r
785:n
777:1
772:+
765:r
757:1
752:=
744:1
695:r
664:r
661:n
516:2
511:i
507:n
500:p
497:n
475:2
470:i
466:n
459:p
456:n
436:)
431:2
426:i
422:n
418:=
413:o
409:p
403:o
399:n
395:(
375:p
355:n
347:(
152:(
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
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