Bulk recombination

Lifetimes of free atoms and radicals account for the degree of interaction of these particles with an ambient medium and with each other. Due to high reaction capability of active particles in gaseous and, especially, in liquid media, their lifetimes are rather small. In gaseous phase, at small pressures these lifetimes are determined by heterogeneous recombination of these particles on vessel walls and by interaction of these particles with an adsorbed layer. At high gas pressures, the lifetimes are determined by bulk recombination and chemical interaction with ambient molecules. 

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...

Fig. 16.3 Quantum yield (QY) for electron and hole transfer to solution redox acceptors/donors as a function of the reduced variables y (related to the surface properties of the catalyst, i.e., ratio between interfacial electron transfer rate and surface recombination rate) and w (related to the ratio between surface migration currents of hole and electrons to the rate of bulk recombination), according to the proposed kinetic model [23],...

Semiconductor structures that develop space charge layers and contact potentials, like films of proper thickness, films with applied external bias, homo- and hetero-(nano)junctions, permit significant suppression of bulk recombination processes and, potentially, allow high quantum yields. Spatial separation of electron and holes also allows the separation of cathodic and anodic processes in a photoelec-trochemical cell (eventually at the micro and nano level), minimizing surface re-... 

The dependence of photocurrent on bulk recombination rate allows us to realize an analytical tool for the characterization of silicon, as discussed in Section 10.3. 

Electron-Ion Recombination in Condensed Matter Geminate and Bulk Recombination Processes... 

A survey is given of the theoretical and experimental studies of electron-ion recombination in condensed matter as classified into geminate and bulk recombination processes. Because the recombination processes are closely related with the magnitudes of the electron drift mobility, which is largely dependent on molecular media of condensed matter, each recombination process is discussed by further classifying it to the recombination in low- and high-mobility media. 

The course of the recombination processes in a particular system depends on several factors. One of the most important ones is the polarity of the system. Both geminate and bulk recombination processes are strongly influenced by the Coulomb attraction between electrons and cations, and the range of this interaction in condensed matter is determined by the dielectric constant e. The range of the Coulomb interaction in a particular system is usually represented by the Onsager radius, r, which is defined as the distance at which the electrostatic energy of a pair of elementary charges falls down to the thermal level kj,T. 

When the motion of electrons and positive ions in a particular system may be described as ideal diffusion, the process of bulk recombination of these particles is described by the diffusion equation. The mathematical formalism of the bulk recombination theory is very similar to that used in the theory of geminate electron-ion recombination, which was described in Sec. 10.1.2 ( Diffusion-Controlled Geminate Ion Recombination ). Geminate recombination is described by the Smoluchowski equation for the probability density w(r,i) [cf. Eq. (2)], while the bulk recombination is described by the diffusion equation for the space and time-dependent concentration of electrons around a cation (or vice versa), c(r,i). 

The two equations have the same mathematical form, although they deal with different physical quantities. The initial and boundary conditions are also somewhat different. In the bulk recombination, the initial electron concentration is assumed to be uniform in the space and equal to the average concentration Cq... 

Bulk recombination is a many-body problem. It is not so obvious whether the approach based on Eqs. (29-34) correctly describes the many-body character of bulk recombination. Tachiya [29] formulated the rate of bulk recombination in terms of the pair survival probability of geminate recombination and showed that the approach described above is exact only when the minority reactants are fixed and the majority reactants are... 

EXPERIMENTAL STUDIES OF ELECTRON-ION BULK RECOMBINATION IN CONDENSED MATTER... 

Complementary studies of neutral [20] and charged [16] intrinsic trapped centers, comparison of cathodoluminescence [21] and thermoluminescence data [12] with results of analysis of photoelectron scattering [13] and pump-probe experiments [14] allow us to extend the energy relaxation scheme (Fig.2d, dotted arrows) including electron-hole recombination channels. The formation of H-band emitting centers (R2+) occurs through the excitation of STH by an exciton. The bulk recombination of trapped holes with electrons populates the (R2 ) states with subsequent M-band emission [22], After surface recombination of STH with electrons the excited dimers escape from the surface of the crystal with subsequent IF-band emission. 

This is in fact the yield of fluorescence from only the initial geminate part of quenching. If the transfer is reversible, the stationary detection of fluorescence also includes, besides this part, the contribution from the bulk recombination of transfer products back to the excited state (see Sections VIII and XI). However,... 

Figure 3.53. The quenching kinetics at long times with and without bulk recombination of ions (solid and long dashed lines, respectively). The false IET asymptote p- 5 2) is indicated by a dotted line, while the true asymptotic behavior of delayed fluorescence (t 2) is shown by a short dashed line. All the parameters are the same as for Figure 3.52. (From Ref. 189.)...

At the same time we do not have to assume that A -C c as we did previously. Under this condition the acceptor concentration A = [A] remained almost constant, approximately equal to its initial value c. In what follows we will eliminate this restriction and account for the expendable neutral acceptors whose concentration A(t) decreases in the course of ionization. When there is a shortage of acceptors, the theory becomes nonlinear in the concentration, even in absence of bulk recombination. Under such conditions only general encounter theories are appropriate for a full timescale (non-Markovian) description of the system relaxation. We will compare them against each other and with the properly generalized Markovian and model theories of the same phenomena. 

Only E3 is new and rather unusual. It describes the overpopulation of ion pairs [D+ A-], produced by electron transfer in closely situated products of ion recombination in the bulk, excited before their separation. Since the density of the correlated pairs is enhanced through bulk recombination, the ionization becomes faster than at the entirely homogeneous distribution of the reactants. The terms involving S3 account for this effect. However, unlike other kernels, E3 vanishes in the lowest-order approximation with respect to 7o- Therefore,... 

A completely different type of situation occurs when the singlet excitations are the products of not only geminate but the bulk recombination as well. The efficiency of the excitation in the bulk is given by Eq. (3.623). By substitution there Eqs. (3.625) and (3.627) as well as (3.626) and (3.628), the general expression for w can be put into the following form... 

In the absence of bulk recombination, N = P remains finite as t — oo. Coming to the limit No —> 0, one can exclude the bulk recombination and define the free-ion quantum yield as the ratio of ions that escaped geminate recombination 2P(oo) to the total initial concentration of excitations generated by pulse Nq ... 

Figure 3.100. The kinetics of charge accumulation without bulk recombination (dashed lines) and taking into account the bulk recombination (solid lines) calculated with the unified theory (UT) and its Markovian version (M). (a) fast ionization (to = 10 ns) (h) slow ionization (tp = 106ns) at No = 0.01 M, D = D = 10-6 cm2/s, rc = 0. (From Ref. 275.)...

It is generally accepted that three major processes limit the photoelectrochemical current in semiconductors after a bandgap excitation [76]. These processes are schematically illustrated in the band diagram shown in Fig. 3.2. The bold arrows show the desired processes for efficient water splitting PEC cell after a bandgap excitation the transport of electrons to the back contact, the transfer of the hole to the semiconductor surface and the oxidation of water at the semiconductor/electrolyte interface. The three major limiting processes are a) bulk recombination via bandgap states, or b) directly electron loss to holes in the... 

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