Radiative recombination

Light is generated in semiconductors in the process of radiative recombination. In a direct semiconductor, minority carrier population created by injection in a forward biased p-n junction can recombine radiatively, generating photons with energy about equal to E. The recombination process is spontaneous, individual electron-hole recombination events are random and not related to each other. This process is the basis of LEDs [36]. 

The enormous progress in the field of electroluminescent conjugated polymers has led to performances of oiganic light-emitting devices (LEDs) that are comparable and in some aspects superior to their inorganic counterparts 11). Quantum efficiencies in excess of 5% have been demonstrated [2] and show that a high fraction of the injected carriers in a polymeric electroluminescence (EL) device form electronic excitations which recombine radiatively. 

Fig. 3 Cartoon of exciton formation, migration, and recombination (radiative and nonradiative)...

Changes in intensity of semiconductor PL or EL can be used to detect molecular adsorption onto semiconductor surfaces [1,3]. PL occurs most efficiently when ultra-band-gap radiation excites electrons from the valence band to the conduction band of a direct-band-gap semiconductor and the electrons recombine radiatively with the holes left behind in the valence band. 

When an electron neutralizes a positive ion, the energy released can be dissipated either in photon emission (radiative recombination), or by a third body encounter with the transient excited atom or molecule (three-body recombination) or by the fragmentation of the transient excited molecule (dissociative recombination). Radiative recombination only occurs with a very small probability and three-body recombination only occurs at high pressures or high charge densities, neither of these being appropriate to the atmospheric plasma. It is the dissociative process, exemplified by reactions (5a) and (5b), which is dominant in the ionosphere. In fact, reactions (5a) and (5b) are almost entirely responsible for the loss of ionization in the ionosphere above 85 km altitude (with N2 recombination contributing somewhat) as is readily shown by simple calculations based on laboratory determinations of dissociative recombination coefficients, are, for the dominant molecular ions 02 and NO+. 

Various processes contribute to emission of the visible Ha light. Excitation of ground state atoms, dissociation of FF into an excited state of one of the Franck Condon atoms, likewise for EFj", and recombination (radiative or three-body) of H+ into an excited state of the atom. In this example, but more generally for all current limiter tokamak experiments one finds that the first contribution is dominant globally, the second and third are important in a narrow layer near the limiter and, usually, the last one is irrelevant. In order to extract the various contributions from the simulation model, collision radiative models [9,12,13] are been employed. 

Ej is a demarcation energy, similar to that defined in the analysis of dispersive transport (see Section 3.2.1). It is assumed that all carriers which are thermally excited recombine non-radiatively, but the same result is obtained if some fraction are subsequently retrapped and recombine radiatively. The luminescence efficiency is given by the fraction of carriers deeper than E, . An exponential band tail density of states proportional to exp (E/kf,) results in a quantum efficiency of... 

The effective masses of electrons and holes are estimated by parabolic approximation a large curvature corresponds to a small effective mass and a small curvature corresponds to a large mass. With this band concept, light absorption and luminescence are interpreted as follows Light is absorbed by the transition from valence band to conduction band. Therefore, the broadening of the absorption spectrum originates basically from the one dimensionality of the joint density of states, which is described by (E - g) . Excited electrons and holes relax to the bottom of the bands and then recombine radiatively. Therefore, the photoluminescence of the spectrum is very sharp. The energy difference between two peaks is called the Stokes shift. 

Another factor which determines the efficiency of LEDs is the photoluminescence (PL) efficiency, i.e. the fraction of photoexcited states which recombine radiatively. Since the radiative lifetime of most conjugated polymers is less than 1 ns and there are relatively few non-radiative channels for relaxation, the PL efficiency can be quite high. Many conjugated polymers have photoluminescence efficiencies higher than 60%. A subject of substantial debate is whether or not the electroluminescence (EL) efficiency can be as high as the photoluminescence (PL) efficiency. As summarized in Section IVB, EL efficiency as high as 50% of the PL efficiency has been demonstrated [158]. 

Until recently, photoionization cross sections and recombination (radiative and di-electronic) coefficient sets used in photoionization computations were not obtained self-consistently. Photoionization and recombination calculations are presently being carried out using the same set of eigenfunctions as in the IRON project (Nahar Pradhan 1997, Nahar et al. 2000). The expected overall uncertainty is 10 - 20%. Experimental checks on a few species (see e.g. Savin 1999) can provide benchmarks for confrontation with numerical computations. 

The probability that electrons and holes recombine radiatively is proportional to the electron and hole concentrations, that is, R . n p. The recombination rate per unit time per unit volume can be written as... 

Once electrons and holes have been injected into the polymer, they must encounter each other and recombine radiatively to give off light. In this context, the low mobility of the charge carriers (polarons) in semiconducting polymers is helpful since the slow drift of the charge carriers across the thickness of the semiconducting polymer will allow enough time for the carriers to meet and recombine radiatively. 

In the DAP recombination mechanism electrons bound at neutral donors recombine radiatively with holes bound at neutral acceptors. If an isolated neutral donor and acceptor are separated by a reasonably small distance r, the electron and hole can recombine with emission of a photon of energy E(r) given by [75] ... 

Only singlet excitons, S, are created by photon absorption (direct triplet generation is forbidden from the spin selection) and recombine radiatively with a certain probability, expressed by the PL quantum efficiency, (the ratio between the number of photons emitted and the number of photons absorbed). When the exciton is created by the coalescence of two polarons, the probability of forming a singlet exciton is 1/4 while... 

Back to the case of a single trap (N) and a single luminescence center (M) we assume that the N electrons will be released during the warming and recombine radiatively with holes at M centers. The TL intensity (7) will go up with die concentration of electrons in the CB (/tc) and holes at M (nt). If the probability of a radiative transition is A we obtain... 

FIGURE 16 Formation of excitons (electron-hole pairs) by the addition of isoelectronic dopants N and ZnO to an indirect semiconductor. The excitons have a high probability to recombine radiatively. [From Flaitz, R. FI., Craford, M. G., and Weissman, R. FI. (1995). In Flandbook of Optics, 2nd ed., Vol. 1, McGraw-Flill, New York. With permission.]... 

A more difficult problem to address is that of the thermal quenching of luminescence. Rathei than recombining radiatively across the band gap, free excitons within a quantum dot are readily bounc to lattice phonons at temperatures exceeding lOO C. " An example of this phonon-driven effect car be found in a Sandia National Lab study on the thermal stability of CdS and CdSe quantum dots encapsulated in both epoxy and silicon as is routinely done for plication to a LED device. " In that study, the luminescence from CdS quantum dots decreased by 50% at 75C. Similar thermal quenching... 

When a diode is forward biased with f/bias > E /e, holes from the p-region are injected into the n-region, and electrons from the n-region are injected into the p-region. If electrons and holes are present in the same region, then they may recombine radiatively, emitting a photon in the process with energy of flie order of the band gap. 

FIGURE 13.1 Orbital scenario of the PIET process. The charge-separated state may recombine radiatively or nonradiatively. 

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