Charge-carrier recombination

In a given liquid electron, holes, positive ions, and negative ions may be present at the same time. Recombination of electrons or negative ions with holes or positive ions takes place. 

The recombination process can be treated as a chemical reaction, the rate of which depends on the spatial distribution of the reactants. Two cases can be distinguished (1) electrons (or negative ions) and positive ions are distributed homogeneously throughout the volume (volume recombination) and (2) electrons (or negative ions) and positive ions are distributed in close spatial correlation (geminate recombination see Section 3.10). 

The volume recombination of excess electrons or negative ions and positive ions is described by the rate equation 

The recombination process can be treated as a bimolecular chemical reaction. The rate constant is then related to the diffusion coefficients, D , of the participating species via the Smoluchowski equation. 

Ri are the reaction radii of the ions. Since the diffusion coefficient is related to the mobility by the Nemst-Einstein equation. 

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A device model to describe two-carrier structures is basically similar to that used for one carrier structures except that continuity equations for both earner types are solved. The additional process that must be considered is charge carrier recombination. The recombination is bimolecular, R=y(np), where the recombination coefficient is given by 43)... 

Choi W, Termin A, Hoffmann MR (1994) The role of metal ion dopants in quantum-sized Ti02 Correlation between photoreactivity and charge carrier recombination dynamics. J Phys Chem 98 13669-13679... 

The photocurrent-voltage curve of a cell made with the I /I2 redox couple (Fig. 8) shows behavior typical of the standard DSSC. The substantial photovoltaic effect is expected from the fact that the dark current (Fig. 4) is negligible positive of about -0.5 V. On the other hand, a cell made with the FcCp2 70 redox couple shows no measurable photoeffect Its current under illumination (Fig. 8) is essentially equal to its dark current (Fig. 4). The photovoltaic effect is negligible because practically all photogenerated charge carriers recombine before they can be collected in the external circuit. In general, fast rates of reactions (4) and (5) tend to eliminate the photovoltaic effect in DSSCs. 

These reactions would produce a net e /h recombination and, conse-quendy, net null cycles, decreasing the rate of degradation [37]. As for salicylic acid cited earlier, the formation of surface-adsorbed cation radicals was invoked to increase the charge-carrier recombination rate and thus lower the quantum yields for degradation [27]. Added redox reagents can also act as recombination sites, so that the overall photocatalytic rate could increase, decrease, or remain unchanged [40]. 

The primary steps in photoelectrochemical mechanism are as follows (1) formation of charge carriers by a photon (2) charge-carrier recombination to liberate heat (3) initiation of an oxidative pathway by a valence-band hole (4) initiation of a reductive pathway by a conduction-band electron (5) further... 

In electrochemical light-emitting cells, the semiconductive polymer can be surrounded asymmetrically with a hole-injecting material on one side and a low work function electron injecting metal (such as magnesium, calcium, or aluminum) on the other side. The emission of light may occur when a charge carrier recombines in the polymer as electrons from one side and holes from the other meet. 

From the analysis of their experimental results of the investigation of the charge carrier recombination kinetics in titanium dioxide colloidal solutions and in dispersions Serpone et al. and Bowman and co-workers have also assumed the existence of two different traps [5,6]. 

It is assumed that deeply trapped holes, h+ff, are chemically equivalent to surface-bound hydroxyl radicals. Weakly trapped holes, on the other hand, that are readily detrapped apparently posses an electrochemical potential close to that of free holes and can therefore be considered to be chemically similar to the latter. Their shallow traps are probably created by surface imperfections of the semiconductor nanocrystals. From these traps the charge carriers recombine or they are transferred by interfacial charge transfer to suitable electron acceptors or donors adsorbed at the surface of the semiconductor. 

Colombo, D. P. J. Bowman, R. M. Does interfacial charge transfer compete with charge carrier recombination Femtosecond diffuse reflectance investigation of Ti02 nanoparticles, J. Phys. Chem. 1996, 100, 18445. 

The lifetime of separated charges increases after electron and hole trapping in certain states, eg in the case of titanium dioxide, electrons are trapped as Tim centres [30,31] with the holes as [>rHIVOFI ]+ [30], Trapping of holes proceeds in 10-100ns, whereas this process is faster for electrons and requires a few hundred picoseconds. Charge-carrier recombination from the trapped states also proceeds in 10-100 ns. 

This review will proceed as follows. After a description of the primary processes common to all colloidal semiconductor applications, the thermodynamic requirements of those processes will be discussed, with special emphasis on those relevant to photocatalysis. This will be followed by a short section on how the colloidal state affects the semiconductor band structure and photogenerated charge carrier recombination dynamics, leading into a longer section on the dynamics of interfacial charge transfer... 

Femtosecond flash photolysis studies on Q-state CdS [107] indicate that reaction (4a) proceeds via two recombination processes a 50 ps decay at low excitation intensities, postulated to correspond to geminate e h+ recombination, and a faster 2 ps decay at higher flash fluences, corresponding to non-geminate or possibly three body Auger charge carrier recombination. Other studies by Nosaka and Fox [118] indicate that the second order rate coefficient for electron-hole recombination within CdS particles is of the order 9 x 10 t7 m3 s l. 

Fig. 9.31. Dlustration of the potential modulation of the bands of a doping superlattice. The dashed line illustrates the screening of the potential by photoexcited charge carriers. Recombination of electrons and holes is by tunneling between layers.

Charge Carrier Recombination and Interfacial Electron Transfer... 

FIGURE 2.3. A schematic representation of the elementary processes for charge carrier recombination, production of molecular excitons, emission, and external emission. 

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