Electron-hole recombination rate constant

Nosaka and Fox determined the quantum yield for the reduction of methyl viologen adsorbed on colloidal CdS particles as a function of incident light intensity. Electron transfer from CdS to MV " competes with electron-hole recombination. They derived a bimolecular rate constant of 9 10 cm s for the latter process. 

Fig. 16.2 Simplified kinetic model of the photocatalytic process. ps represents the light absorbed per unit surface area of the photocatalyst, e b and h+b are the photogenerated electrons and holes, respectively, in the semiconductor bulk, kR is the bulk recombination rate constant and /R the related flux, whatever recombination mechanism is operating A is the heat resulting from the recombination kDe and kDh are the net first-order diffusion constants for fluxes Je and Jh to the surface of e b and h+b in the semiconductor lattice, respectively e s and h+s are the species resulting from...

The hypothesis that electron scavenging by oxygen or other oxidants is faster than electron-hole recombination is perhaps too restrictive, as it is now recognized that this reaction, in particular with oxygen, can be rather slow (see Ref. 19 and the values of estimated rate constants in Ref. 41). When 0x2 acts as a mere electron scavenger, reaction (Ig) could be neglected. The rate... 

Bowman and coworkers characterized the subpicosecond dynamics of titanium dioxide sols employing particle sizes of about 2 nm prepared by hydrolysis of titanium tetraisopropoxide [6]. From their spectral results the authors inferred that the average lifetime of an electron/hole pair is 23 5 ps, and substantial electron/hole recombination occurs within the first 30 ps. A second-order recombination rate constant of (1.8 0.7) x 1CT10 cm3 s 1 for trapped electrons with holes has been obtained [6a]. 

Here g is the Gartner flux of holes into the surface generated by illumination, [Red] is the bulk concentration of reduced species in solution and nxm.o is the electron density at x = 0. The rate constants, kET, for electron transfer involving free and trapped holes, and the recombination rate constant, kr, are shown in Fig. 8.5. They have units cm3 s-1 and can be converted to conventional heterogeneous rate constants (units cm4 s l) by multiplying by S. 

A similar model has been advanced by Brown and Rajapakse [186], again based on the work done by Albery et al. [84], They also suggest that electron-hole recombination can be effectively slowed by the presence of interband hole traps, some of which can be attributed to sulphur vacancies, in agreement with conclusions made by Ramsden and Gratzel [169]. Work must be done to refine this model and to identify the nature of the interband hole traps. Nonetheless, the pseudo-first order rate constant for electron loss to them is 0.168 0.052 s 1 a value which has far-reaching implications for the design of photocatalytic systems employing colloidal CdS in photoreduction reactions. 

In addition to the mobility values which can be derived from the magnitude of transients such as those shown in Fig. 4, information can be obtained from the temporal form on the kinetics of the reaction of the polymer with the primary hole (or electron) and the rate constant for the ultimate charge recombination reaction which controls the decay of the conductivity at long times.Recent studies have looked into the influence of broken conjugation and polymer chain length on the intra-chain mobility. 

For the influence of the specific surface area of the semiconductor powder on the rate of product formation, two opposite effects are of major importance [81]. One is concerned with the rate of electron-hole recombination which increases linearly with surface area, and accordingly the reaction rate should decrease. The other is a linear increase in the reaction rate of the reactive electron-hole pair with the adsorbed substrates, which should increase product formation. It is therefore expected that, depending on the nature of semiconductor and substrates, the reaction rate, or increasing surface area. This is nicely reflected by the CdS/Pt-catalyzed photoreduction of water by a mixture of sodium sulfide and sulfite. The highest p values are observed with small surface areas and are constant up to 2 m g". From there a linear decrease to almost zero at a specific surface area of 6 m g" takes place. Upon further increase to 100 m g" this low quantum yield stays constant [82]. 

The electron-hole recombination processes in the ion radical pairs P+B"H and P+BH across the A branch of the bacterial photosynthetic reaction center (RC) are taking place in the same molecular framework in which the primary charge separation occurs. Consequently, the rate constants for the recombinations are correlated to the rate constants of the primary processes, and their investigation can help in the elucidation of the primary charge separation mechanism. 

This case is shown in Fig. 10.6c and d where through absorption of light a photohole in the vb and a photoelectron in the cb are formed. The probability that interfacial electron transfer takes place, i.e. that a thermodynamically suitable electron donor is oxidized by the photohole of the vb depends (i) on the rate constant of the interfacial electron transfer, kET, (ii) on the concentration of the adsorbed electron donor, [Rads]. and (iii) on the rate constants of recombination of the electron-hole pair via radiative and radiationless transitions,Ykj. At steady-state of the electronically excited state, the quantum yield, Ox, ofinterfacial electron-transfer can be expressed in terms of rate constants ... 

Such a concept of quasi-Fermi level is valid under the condition that the time constant for the establishment of thermal equilibrium of electrons or holes in the conduction or valence band (the redprocal of the rate of establishing equilibrium between electrons and phonons) is much smaller than the time constant for the recombination of exdted electron-hole pairs (the redprocal d the recombination... 

Fig. 13 Recombination losses occurring under forward bias in a typical OPV device. Holes injected from the anode Fermi level into the HOMO level ( ) of the donor and electrons injected from the cathode Fermi level ( f,c) into the LUMO level ( J of the acceptor are transported to the D/A interface. Coulombic attraction between holes and electrons yields the (D A ) CT state with energy Ect- Charge recombination reaction (D A ) D + A occurs with rate constant...

The above relationship between 0 and the rate constants is derived based on the conventional formulation of the rate equations. The unit to measure the amount of electrons and holes in the particle is density, the same as in bulk semiconductors. When the particle size is extremely small or the photon density is very low, only a few pairs of electron and hole are photogenerated and recombine with each other in the particle. This means that photon density does not take continuous values as suitably used in the conventional rate equations, but takes some series of values whose unit is the inverse of the particle volume. Taking into account this deviation, we proposed a new model in which particles are assigned by two integers, n and m, which represent the numbers of... 

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