Electron-hole pair annihilation

Electron hole pairs generated by photon absorption enable oxygen to desorb from the surface (bottom of Fig. 3). The oxygen desorption annihilates some of the holes, thereby decreasing the surface, so that electrons are now able to move from one ZnO grain to another. Thus, photoconductivity of the layer is produced. In the dark period which follows, the photoconductivity of the layer is preserved for some time due to the large number of shallow electron traps. 

Fig. 7. Energy spectrum of 662 keV photons detected in Csl at 77 K from the 137Cs (3 emitter (left) showing the photo peak and the Compton plateau. The low energy peak is due to photons back-scattered from the container. A similar spectrum is obtained for 1275 keV photons from the 22Na 0+ emitter (middle). In this case one also observes the 511 keV line from positron annihilation and its corresponding Compton plateau. The resolution is better than 6 % at 511 keV. The right spectrum shows the response of the photodiode to 22 and 88 keV X-rays from 109Cd. A Csl light yield of 26,000 photons/MeV at 511 keV is derived from this spectrum, assuming about 6000 electron-hole pairs for 22 keV X-rays. This is however a lower limit, as it assumes 100 % quantum efficiency for the photodiode...

The difference between the Fermi energies /xeh == f2 — fi is the free energy per electron-hole pair of the ensemble, also called the chemical potential of electron-hole pairs. It is free of entropy and we may therefore hope to transfer it into electrical energy without losses. If electron-hole pairs are not allowed to leave the 2-level system, i.e., under open-circuit conditions, they have to recombine and emit one photon per pair annihilation. These photons carry the free energy of the electron-hole pairs, and /n7 = /ieh = f2 — fi is recognised as their chemical potential. 

Step 2 This virtual electron-hole pair generates or annihilates a phonon and a second virtual electron-hole pair is formed. 

The role of illumination consists in creating electron-hole pairs, which are necessary for the partial reactions. During the reduction of OBr" ions, Br radicals are formed as intermediates (cfr. reaction (55)), which appear to initiate an autocatalytic reaction mechanism surface states are formed, through which holes are injected into the valence band (at least at not too high OBr concentrations). These surface states, which are experimentally detected as a peak in the capacitance-potential plot [24, 81], are believed to be associated with adsorbed OBr. Furthermore, voltammetric experiments demonstrate that these surface states can be annihilated by a sufficiently large concentration of holes at the surface. The latter explains why this induced electroless etching effect is not observed at p-GaP, since in this case the holes are present at the surface in a quasi-equilibrium cloud of majority carriers, in contrast to the case of n-GaP. 

Ax 1 cm, the uncertainty of the momentum, Ap, is small. Thus, the momentum is a good quantum number and its conservation has to be obeyed in electronic transitions. In silicon, which has an indirect band gap, the recombination of electrons and holes requires a creation or annihilation of phonons and is therefore predominantly of non-radiative nature.If, however, the size of an Si nanocrystal approches 1 nm. Ax 1 nm and Ap spans a significant part of the Brillouin zone. The momentum conservation is relaxed and electronic transitions (absorption of a photon with the formation of an electron-hole pair or their radiative recombination) become efficient. 

With the intensities obtained in Eqs. (84)-(86) we evaluate the probability of hole annihilation due to the second-order process. The probability of the ionization of the atom by an incident electron is determined by the corresponding integral intensity of the first-order process. An estimate of this probability has been made already. Then the probability of the radiationless annihilation of the electron-hole pair created in the atom upon interaction with the incident electron is determined by the ratio between the integral intensities of the first- and second-order processes, Ja /Ja This probability is determined as /Ja 0( rianpC, up to a constant that depends only slightly on the type of the wave function of the core electron. With the expressions obtained, we have determined the value of the constant of proportionality 0.6,0.4, and 0.5 for... 

Next, and this is the most important, from the viewpoint of physics, in copying the chemical concept of dismutation reaction to which this law corresponds, the classical approach gives credence to the existence of quantities of electron-hole pairs predicted by this reaction. However, their amount must be immediately neglected for keeping the system of equations amenable to a solution (i.e., ideal system) In addition, to consider a third species in equilibrium with the two others is contrary to the definition of a hole, which is the exact opposite of an electron, and therefore contrary to the fact that both annihilate. This is the kind of long-lasting paradox in physics (However, it mnst be acknowledged that the concept of separability is still not very well mastered in physics, even in quantum physics.)... 

The key point is the conservation of the total number of entities for a pair of objects. It translates Pauli s exclusion principle in the following manner The constancy of the total number of objects can be viewed as a fixed number of available sites or allowed energy states. A site (or energy state) can contain one electron or one hole but not both (no electron-hole pairs and no annihilation), because, if we could put more than one electron or hole on one site, the conservation would not be respected. This relies on the assumption that the conservation must... 

Similarly, due to the creation/annihilation reaction of electron-hole pairs, Equations (7.2) and (7.5) can be combined to yield the total electronic current density,7 ... 

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