Transition recombination

In Ref. [68], the character of the electronic decay dynamics in a multiply charged system was investigated by constructing a simple but realistic model based on the Li-L2/3M CK decay in Ar (see Ref. [69] and references therein). Due to the relatively low energy of the recombination transition within a single shell, CK processes are characterized by the emission of relatively slow electrons with kinetic energies of the order of several tens of electron volt. This circumstance makes CK decay processes in general and the Ar decay in particular very well suited for the study of the effect... 

A solid state Si(Li) detector is used to maximise the flux of helium-like vanadium transitions, to minimise contamination from undesirable charge states and to monitor dielectronic recombination transitions. A small amount of pure nitrogen gas is leaked into the trap (injection pressure 5x 10 7Torr) to increase the proportion of lower charge states via evaporative cooling. 

Electron-hole correlations are an important aspect of the recombination. The recombination transition necessarily involves two particles, the electron and the hole, and so the recombination rate depends on whether they are spatially correlated or distributed randomly. The electron-hole pairing in a crystal is manifested in excitonic effects, but these are not detectable in the absorption spectra... 

Recombination is evidently controlled by trapping into defect states, consistent with the other recombination measurements. The recombination transitions through defects with two gap states are illustrated in Fig. 8.24, with electrons and holes captured into either of the two states. This type of recombination is analyzed by the Shockley-Read-Hall approach which distinguishes between shallow traps, for which the carrier is usually thermally excited back to the band edge, and deep traps, at which the carriers recombine. A demarcation energy, which is usually close to the quasi-Fermi energy, separates the two types of states. The occupancy of the shallow states is determined by the quasi-equilibrium and that of the deep states by the recombination processes. No attempt is made here at a comprehensive analysis of the photoconductivity, which rapidly becomes complicated. Instead some approximate solutions are derived which illustrate the processes. 

Figure 4.16 Band structure model for semiconductor diode laser, with and without bias voltage. Lower part relative band population distributions and recombination transition. Eg is the band-gap energy E and are the valence- and conduction-band energies fv and Eh are the Fermi energies for the valence and conduction bands...

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

Although the transition to difhision control is satisfactorily described in such an approach, even for these apparently simple elementary reactions the situation in reality appears to be more complex due to the participation of weakly bonding or repulsive electronic states which may become increasingly coupled as the bath gas density increases. These processes manifest tliemselves in iodine atom and bromine atom recombination in some bath gases at high densities where marked deviations from TronnaF behaviour are observed [3, 4]. In particular, it is found that the transition from Lto is significantly broader than... 

Keck J 1960 Variational theory of chemical reaction rates applied to three-body recombinations J. Chem. Phys. 32 1035 Anderson J B 1973 Statistical theories of chemical reactions. Distributions in the transition region J. Chem. Phys. 58 4684... 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

The light emitted in the spontaneous recombination process can leave tire semiconductor, be absorbed or cause additional transitions by stimulating electrons in tire CB to make a transition to tire VB. In tliis stimulated recombination process anotlier photon is emitted. The rate of stimulated emission is governed by a detailed balance between absorjDtion, and spontaneous and stimulated emission rates. Stimulated emission occurs when tire probability of a photon causing a transition of an electron from tire CB to VB witli tire emission of anotlier photon is greater tlian that for tire upward transition of an electron from tire VB to tire CB upon absorjDtion of tire photon. These rates are commonly described in tenns of Einstein s H and 5 coefficients [8, 43]. For semiconductors, tliere is a simple condition describing tire carrier density necessary for stimulated emission, or lasing. This carrier density is known as... 

In discussing mechanism (5.F) in the last chapter we noted that the entrapment of two reactive species in the same solvent cage may be considered a transition state in the reaction of these species. Reactions such as the thermal homolysis of peroxides and azo compounds result in the formation of two radicals already trapped together in a cage that promotes direct recombination, as with the 2-cyanopropyl radicals from 2,2 -azobisisobutyronitrile (AIBN),... 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

The variations in D and D and the much larger value for In show the limitations of a simple hydrogen atom model. Other elements, particularly transition metals, tend to introduce several deep levels in the energy gap. For example, gold introduces a donor level 0.54 eV below D and an acceptor level 0.35 eV above D in siHcon. Because such impurities are effective aids to the recombination of electrons and holes, they limit carrier lifetime. 

The equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

A simplified schematic diagram of transitions that lead to luminescence in materials containing impurides is shown in Figure 1. In process 1 an electron that has been excited well above the conduction band et e dribbles down, reaching thermal equilibrium with the lattice. This may result in phonon-assisted photon emission or, more likely, the emission of phonons only. Process 2 produces intrinsic luminescence due to direct recombination between an electron in the conduction band... 

In contrast to the extensive body of work on the preparation of these zinc carbenoids, few investigations are on record concerning the mechanism of the Furu-kawa method for carbenoid formation. Two limiting mechanisms can be envisioned - a concerted metathesis via a four-centered transition structure or a stepwise radical cleavage-recombination (Scheme 3.11). 

Biisslcr et ai [110-113] treated charge recombination in organic LEDs in terms of chemical kinetics. The probability of recombination depends on the ratio of recombination rate ynp-np (where y represents a bimolecular rate constant) and the transition time (itr=dlpE) of the charge carriers through the device. 

Obviously, the recombination rate increases with decreasing transition time of the minority charge carriers. 

---