Generation of Electron-Hole Pairs

Photons of energy hio from the sun and the 300 K surroundings are regularly absorbed in band-to-band transitions, and (4.41) is the generation rate for electrons (in the conduction band) and holes (in the valence band). 

Since some of the photons may be absorbed in transitions which do not generate electron-hole pairs, a quantum efficiency (3 is defined such that the generation rate of electron hole pairs (number per unit volume and unit time) is 

The generation dG per unit area is obtained by integrating over the thickness of a body. According to (4.45), 

The total generation by photons incident on an area A is found by integrating over the contributions from all photon energies and equals the absorbed photon current 

In some simple cases re is independent of the generation rate, because the density of holes with which the electrons recombine is so large that it is little affected by the additional photogeneration of electron-hole pairs. One example is the recombination of electrons with holes in impurity states, if the material is not sufficiently pure, so that the concentration of holes in impurities is large. Another example is electron recombination with free holes in the valence band, if the density of free holes is large due to p-type doping. 

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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. 

The primary photochemical act, subsequent to near-uv light (wavelengths <400 nm) absorption by Ti02 particles, is generation of electron—hole pairs where the separation (eq. 3) into conduction band electrons (e g ) and valence band holes (/lyB ) faciUtated by the electric field gradient in the space charge region. Chemically, the hole associated with valence band levels is constrained at... 

The generation of electron-hole pairs under the action of the light is the initiating step in photocatalysis ... 

Heterogeneous photocatalysis is based on the photonie exeitation of a solid, which renders it more complex. The term photocatalysis may designate several phenomena that involve photons and catalyst, while this part of the ehapter will consider only semiconductor photocatalysis. Photocatalytic activity of Ti02 is based on its semiconductor properties. Radiation by photons, whieh have higher transfer energy, of such semiconductor leads to generation of electron-hole pairs [94] ... 

There are also other mechanism which can lead to desorption. For example, the generation of electron hole pairs by either photons or electrons can produce desorption from some insulators and semiconductors. The holes are believed to reach the surface where they neutralize adsorbed negative ions which are subsequently desorbed into the gas phase. It is also possible that other defects (such as migrating H centers in the alkali halides) may cause desorption when they reach the surface . Moreover, interstitial atoms generated within the solid may diffuse to the surface where they are desorbed . 

In addition to the dark oxidation of S(IV) on surfaces, there may be photochemically induced processes as well. For example, irradiation of aqueous suspensions of solid a-Fe203 (hematite) containing S(IV) with light of A > 295 nm resulted in the production of Fe(II) in solution (Faust and Hoffmann, 1986 Faust et al., 1989 Hoffmann et al., 1995). This reductive dissolution of the hematite has been attributed to the absorption of light by surface Fe(III)-S(IV) complexes, which leads to the generation of electron-hole pairs, followed by an electron transfer in which the adsorbed S(IV) is oxidized to the SO-p radical anion. This initiates the free radical chemistry described earlier. 

In conclusion it must be stressed that, for applications of the semiconductor properties of organic dyes and other compounds, the important factors besides the energy gap AE and the primary quantum efficiency r of the generation of electron-hole pairs are the characteristic parameters mobility and lifetime of electrons and holes. 

The maximum value of the minority-carrier current, which may flow under steady state conditions from the semiconductor bulk to the surface, is called the limiting current. It is determined by bulk generation of electron-hole pairs. As simple calculation shows (see, for example, Myamlin and Pleskov, 1967), the absolute value of the limiting current of minority carriers, holes for illustration, is... 

Indeed, irradiation of Ti02 particles with light of energy higher than the band gap (A. < 390 nm) results in generation of electron-hole pairs ... 

The electronic structure of semiconductors is usually comprised of a filled valence band and an empty conduction band which are energetically separated by an inter-band gap, Es. All of the reactions described above involve the initial absorption of photons by the semiconductor and, for ultra-band gap photon energies, the subsequent generation of electron-hole pairs within the material lattice (ec B> J vb). as shown in Fig. 9.1a and equation (9.1). The entire process is thought to occur in <1 fs [96]. 

Figure 5. Generation of electron hole pairs and their motion to the respective electrodes.

Fano factors have been calculated and also measured. For semiconductor detectors, F values as low as 0.06 have been reported. For gas-filled counters, reported F values lie between 0.2 and 0.5. Values of f < 1 mean that the generation of electron-hole pairs does not exactly follow Poisson statistics. Since Poisson statistics applies to outcomes that are independent, it seems that the ionization events in a counter are interdependent. 

Heterogeneous photocatalysis steps were reviewed by Cunningham and Hodnett, (1981), Jacoby etal., (1996) and Yue( 1993) among others. These steps include the mass transfer of substrate from the bulk of the fluid to the catalyst surface, the transport of the reactants within the catalyst particle and the adsorption of substrates on the active catalytic surface. Once the Ti02 is irradiated, photon energy is absorbed, followed by the generation of electron-hole pairs, the formation of radicals, the surface reaction, radical recombination and finally the desoiption and mass transfer of products from the particle surface into the bulk of the fluid. 

The basis of the processes is the absorption of incident solar photons leading to the generation of electron-hole pairs in a semiconductor in contact with an aqueous electrolyte. It is energetically favorable for the minority carriers (holes) to difEuse to the semiconductor/electrolyte interface, where recombination with electrons from the valence band of water can take place. The hydrogen ions migrate to the metal cathode and are reduced to hydrogen molecules. 

Illumination under open-circuit conditions produces electron-hole pairs, which are separated by the potential gradient (see Fig. 3). The concentration of holes increases near the interface, and the concentration of electrons increases near the current collector (curve b in Fig. 4). Under steady-state conditions, the rate of generation of electron-hole pairs is balanced by the rate of homogeneous and interfacial recombination. As the system without kinetic limitations approaches short circuit (curve c in Fig. 4), the concentrations of holes and electrons approach the equilibrium distributions. 

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