Semiconductors electron annihilation

Here d ,dl and airaj are annihilation and creation operators for the QD electrons and phonons, respectively. As in case (1), Mq is a semiconductor electron-phonon constant and a>fD is a phonon frequency. A-D is the energy of noninteracting electrons and 3 is a Coulomb integral. 

When a semiconductor is illuminated with the band-gap radiation, excess electrons and holes are photo-created. They can form free excitons or be trapped by ionized impurities, but their ultimate fate is their annihilation by thermal or radiative recombination. The formation of free excitons will be discussed in Sect. 3.3.2, but in direct band-gap semiconductors, electron-hole radiative recombination can also occur at an energy close to Eg if the pumping beam is kept at a low level. This can provide an accurate determination of Eg [87],... 

When a semiconductor electrode is at the flat band potential, photoexdted electrons and holes are soon annihilated by their recombination. In the presence of a space charge layer, however, the photoexdted electrons and holes are separated, vrith each moving in the opposite direction under an electric field in the space charge layer as shown in Fig. 10-4. 

As can be verified, Ep equals Therefore it has been shown that eqn (1.133) is identical to eqn (1.135). From this, the creation and annihilation of electrons and holes in semiconductors may be written as the following chemical equation... 

At low light flux, the semiconductor sensitization is constrained to one electron routes, since the valence band hole is annihilated by a single electron transfer. Presumably after decarboxylation the resulting alkyl radical can be reduced to the observed monodecarboxylate more rapidly than it can transfer a second electron to form the alkene. In a conventional electrochemical cell, in contrast, the initially formed radical is held at an electrode poised at the potential of the first oxidation so that two-electron products cannot be avoided and alkene is isolated in fair chemical yield. Other contrasting reactivity can be expected for systems in which the usual electrochemistry follows multiple electron paths. 

Apart from fundamental transitions in direct-gap semiconductors, other processes may be responsible for radiative decay of the semiconductor excited states. The most common are processes associated with electron-hole annihilation involving donor and acceptor sites (Figure 7.10) [33],... 

The enhanced surface selectivity of PAES stems from the fact that positrons implanted into a metal or semiconductor at low energies have a high probability of diffusing to the surface and becoming trapped in an image-correlation well before they annihilate [3, 9]. The positrons in this well are localized at the surface and annihilate almost exclusively with atoms at the surface. As a result almost all of the Auger electrons originate from the... 

In principle, an excited molecule can also be produced by an electron transfer from the conduction band of a semiconductor to the oxidized species of an organic molecule (e.g. Ru(bipy)3 ). Instead of the annihilation reaction given by Eq. (10.27) we have then for the Ru complex... 

Bard and co-workers have pointed out that it is frequently difficult to attribute the electrogenerated luminescence unambiguously to the process discussed above [62]. In several cases, instead of reaction (Eq. 10.29), the reduced species is also formed at a semiconductor electrode leading to the annihilation process (Eq. 10.27). This difficulty is caused by the fact that the reduction potential of a molecule in the dark ( Frejjox(M/ M )) is frequently rather close to the oxidation potential of the excited molecule ( predox(MVM)) (see e.g. Fig. 10.3). Luttmer and Bard found one system, rubrene, for which these two potentials are well separated. These authors observed a luminescence due to electron transfer from a ZnO electrode to the oxidized species of rubrene [62j. Another interesting example is the formation of an excited molecule by transfer of hot electrons, as already discussed in Section 7.8. 

The formation of photoactive films on metal electrodes is not restricted to inorganic materials. Copper, for example, can be anodised to form polymeric phenylacetylide [33] and acetylide [34] layers that appear to behave as p-type organic semiconductors. The photoconducting properties of the arylethynyl polymers have been known for some time, although the mechanism of photoconductivity is not well understood. It seems probable that charge carriers are created by the annihilation of mobile Frenkel excitons at electron traps such as adsorbed oxygen rather than by direct interband excitation. 

Photoluminescence could be due to the radiative annihilation (or recombination) of excitons to produce a free exciton peak or due to recombination of an exciton bound to a donor or acceptor impurity (neutral or charged) in the semiconductor. The free exciton spectrum generally represents the product of the polariton distribution function and the transmission coefficient of polaritons at the sample surface. Bound exciton emission involves interaction between bound charges and phonons, leading to the appearance of phonon side bands. The above-mentioned electronic properties exhibit quantum size effect in the nanometric size regime when the crystallite size becomes comparable to the Bohr radius, qb- The basic physics of this effect is contained in the equation for confinement energy,... 

A second consideration is vitally important. Ideally, LEDs must be highly efficient and give an adequate light output under a small voltage. To achieve this, the nature of the excitation of an electron from the valence band to the conduction band and the reverse process of annihilation must be efficient. This efficiency depends on the detailed band structure of the semiconductors, and the flat-band model used in Chapter 13 is no longer adequate. 

Another difference that may come into the semiconductor-solution interface is the importance of recombination at the surface of the semiconductor. The carrier prior exit to an ion in solution may be trapped and thereby annihilated with surface combination centers on the surface. Some surface states behave as traps. It may be that the final rate of a reaction to the semiconductor-solution interface depends upon recombination of holes and electrons within the semiconductor. Such a situation occurs under illumination condition. 

When a p-type and an n-type semiconductor are connected to each other, as shown in Figure 11.52, the result is a p-n junction. Almost every modem electronic device (from laptops to cell phones to mp3 players) contains a p-n junction as part of its integrated circuitry. In the absence of an applied potential, there is no net flow of charge carriers in the p-n junction. The surplus of electrons in the n-type semiconductor is attracted to the surplus of holes in the p-type semiconductor. When the electrons and holes meet in the center, they annihilate each other in a process known as recombination and a nonconductive depletion zone (or barrier) is formed. 

It is clear that presence of oxygen annihilates the accumulation of electrons. Instead, however, fiillerene Ceo can react with the electrons accumulated on the semiconductor surface as reported by Vinodgopal et al. ° As reported by these authors, the electronic transfer between the Ti02 particles and Ceo takes place with a quantum efficiency of 24%. The reduction of Ceo leads to the radical formation C eo, with a characteristic peak centered at 1060 nm, see lower ctrrve of the spectra. Fig. 23. Indicating that, in our experimental conditions, the reaction can proceed, after the scheme shown on the bottom left. 

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