Minority Carrier Reactions

If the charge carriers to be transferred across the interface are minority carriers, then the corresponding current is very low because the minority carriers are mainly produced by thermal generation. The current is given by Eq. (7.65), i.e. it is determined 

Concerning the potential dependence of the interfacial current under illumination, it is frequently useful to measure it in the presence of only one species of the redox couple, the reduced species for an anodic and the oxidized species for a cathodic reaction. Taking n-WSe2 as an example, then the current-potential curve under illumination, as measured in an aqueous solution free from any redox system, is presented in Fig. 7.26. The cathodic dark current which occurs cathodic of the flatband potential, is due to H2 formation (conduction band process). The anodic photocurrent which starts 

7 Charge Transfer Processes at the Semiconductor-Liquid Interface 

The shift of the Mott-Schottky curve was explained by a trapping of electrons in surface states which leads to a change of the potential across the Helmholtz double layer by A(A( ). We have then according to Eq. (5.49) 

The rate constants are also affected by the shift of bands. Instead of Eq. (7.55) we have 

Concerning the potential dependence of the interfacial current under illumination, it is frequently useful to measure it in the presence of only one species of the 

According to these experimental results, the primary effect here is an accumulation of holes on the surface because the anodic dissolution seems to be a very slow reaction. Working at a potential between f/ft,(dark) and f/f, (light), the bands become flattened due to their shift. Since then the majority carrier density is increased near and on the surface, the recombination rate increases (the recombination rate is proportional to n and p, see Section 1.6). Accordingly, the high recombination is a consequence of the band-edge shift on the surface. In the case 

OpVth correspond to and k, respectively. The Faraday fluxes via the conduction band and the surface states are given by 

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The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

In the theory of non-equilibrium processes at solid state junction and also semiconductor-liquid interfaces, as developed in the previous section, frequently quasi-Fermi levels have been used for the description of minority carrier reactions [90, 91], A concept for a quantitative analysis for reactions at n- and p-type electrodes has been derived [92, 93], using the usual definition of a quasi-Fermi level (Eqs. (3a) and (3b)). Taking a valence band process as an example, the quasi-Fermi level concept can be illustrated as follows ... 

Fig. 31. Concept of overpotential for minority carrier reactions at n-type electrode (left) and for majority carrier reactions at p-type electrode (right)...

Kinetics of Minority Carrier Reactions at Semiconductor Electrodes... 

Accordingly, the exchange current Jq should be small. In an electrochemical cell o depends on the charge transfer kinetics as derived in Chapter 7. Similarly as in pure solid-state devices (Chapter 2), also minority as well as majority processes are possible in electrochemical cells (Sections 7.3.4 and 7.3.5). The lowest Jq values were obtained with minority carrier reactions. Since most electrochemical photovoltaic systems, studied so far are governed by majority carrier processes, relatively low conversion efficiencies were found experimentally. 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

Depending on the nature of the electrode and reaction, the carriers involved in an electrochemical reaction at a semiconductor electrode can be electrons from the conduction band (in the following to be called simply electrons), electrons from the valence band (holes), or both. The concentration of the minority carriers in semiconductors (electrons in p-type, and holes in n-type semiconductors) is always much... 

A typical featnre of reactions involving the minority carriers are the limiting currents developing when the snrface concentration of these carriers has dropped to zero and they mnst be snpplied by slow dilfnsion from the bulk of the semiconductor. A reaction of this type, which has been stndied in detail, is the anodic dissolution of germanium. Holes are involved in the first step of this reaction Ge — Ge(II), and electrons in the second Ge(ll) —> Ge(IV). The overall reaction equation can be written as... 

This is the regime of cathodic currents. The silicon atoms of the electrode do not participate in the chemical reaction in this regime. An n-type electrode is under forward bias and the current is caused by majority carriers (electrons). The fact that photogenerated minority carriers (holes) are detectable at the collector indicates that the front is under flat band or accumulation. A decrease of IBC with cathodization time is observed. As Fig. 3.2 shows, the minority carrier current at the collector after switching to a cathodic potential is identical to that at VQcp in the first moment, but then it decreases within seconds to lower values, as indicated by arrows in Fig. 3.2. This can be interpreted as an increase of the surface recombination velocity with time under cathodic potential. It can be speculated that protons, which rapidly diffuse into the bulk of the electrode, are responsible for the change of the electronic properties of the surface layer [A17]. However, any other effect sufficient to produce a surface recombination velocity in excess of 100 cm s 1 would produce similar results. 

Little is known about the mechanisms that cause the three other current extrema ]2 to J4. The kinetic and diffusional contributions of the characteristic currents Ji to J4 show a different concentration dependence. While the diffusion current is found to be roughly proportional to Cp, the kinetic current shows an exponent of 2 < <2.5 [Ha3]. No dependence of the characteristic currents to ]4 on doping kind and density is observed. This indicates again that to ]4 depend on mass transport and reaction kinetics rather than on charge supply. For n-type electrodes, of course, strong illumination is necessary in order to generate a sufficient number of minority carriers to support the currents. 

Chapter 10 deals with photoelectrode reactions at semiconductor electrodes in which the concentration of minority carriers is increased by photoexcitation, thereby enabling the transfer of electrons to occur that can not proceed in the dark. The concept of quasi-Fermi level is introduced to account for photoenergy gain in semiconductor electrodes. Chapter 11 discusses the coupled electrode. mixed electrode) at which anodic and cathodic reactions occur at the same rate on a single electrode this concept is illustrated by corroding metal electrodes in aqueous solutions. 

Also of interest in connection with Fig. 16 is a process that has been labeled hot transfer (see, for example, Toyozawa, 1978 Kayanuma and Nasu, 1978 Jortner, 1979). Here it is suggested that in the case AE > A the transition to the ground state can take place during the lattice relaxation, i.e., before the excited state has reached its equilibrium position. This effect was first suggested by Dexter et al. (1955) and further analyzed by Bartram and Stoneham (1975) for F centers. A recent slight modification, in terms of fast capture of a majority carrier subsequent to that of a minority carrier, has been suggested by Sumi (1981) he points out that this process may be active in recombination-enhanced defect reactions. 

Note also that p8 and ns, appearing in Eqs. (23) and (24), generally do not coincide with those given by equilibrium distributions (13), even in the absence of illumination. The electrode reaction can disturb significantly the distribution of charge carriers in a semiconductor electrode. In particular, if minority carriers become involved in an electrode reaction, its rate may be limited by the rate at which these carriers are supplied from the bulk of the semiconductor to its surface. 

Let us note that secondary reactions, leading to the multiplication of the minority-carrier current, may also take place in darkness, which results, for example, in an increase of the maximum observed current, as compared to ipim. 

In the simplest case where the oxidation reaction of a semiconductor material (42a) proceeds exclusively through the valence band and the reaction of reduction of the Ox component of the solution exclusively through the conduction band (see Fig. 13a), corrosion kinetics is limited by minority carriers for either type of conductivity. In fact, it can be seen from Fig. 12 that icorr(p) = i"m(p) and 1 ( ) = ipim(n), where ijj are the limiting currents of minority carriers (symbols in parentheses denote the type of conductivity of a sample under corrosion). Since the corrosion rate is limited by the supply of minority carriers to the interface, it appears to be rather low in darkness. The values of [Pg.283]

Thus, nonequilibrium electrons and holes generated by light in a corroding semiconductor are consumed to accelerate the corresponding partial reactions. Simultaneous disappearance of these carriers in the course of photocorrosion is similar, from the formal point of view, to surface recombination. This gives every reason to speak about such processes as electrochemical recombination (Belyakov et ai, 1976). If the dark corrosion rate and equilibrium concentration of minority carriers are known, the rate of electrochemical recombination can be calculated. 

Consider now the processes caused by the formation of quasilevels. As was noted above, the shift of Fn relative to F is very small for majority carriers (electrons) and can usually be neglected precisely, this was done in constructing Fig. 16b. But for minority carriers (holes) the shift of Fp can be very large. The shifts of both Fnx F and Fp increase with the growing intensity of semiconductor illumination, so that for a certain illumination intensity Fp may reach the level of the electrochemical potential of anodic decomposition Fdec, p, and Fn—the level of a certain cathodic reaction (for example, reduction of water with hydrogen evolution FHljH20). These reactions start to proceed simultaneously, and their joint action constitutes the process of photocorrosion. 

Here corrosion occurs even in darkness. In the simplest case where the partial cathodic reaction proceeds exclusively through the conduction band and the anodic reaction through the valence band, the corrosion rate is limited, as was shown in Section 8, by the supply of minority carriers to the surface, irrespective of the type of sample conductivity. Therefore, in darkness the corrosion rate is low. Illumination accelerates corrosion. This case is similar to case (a), but with the difference that the role of anodic polarization is played by chemical polarization with the help of an oxidizer introduced into the solution (see Section 13 for examples). 

The occurrence and deactivation of excited states of the first type are schematically shown in Fig. 35. Let the minority carriers (holes) be injected into the semiconductor in the course of an electrode reaction (reduction of substance A). The holes recombine with the majority carriers (electrons). The energy, which is released in the direct band-to-band recombination, is equal to the energy gap, so that we have the relation ha> = Eg for the emitted light quantum (case I). More probable, however, is recombination through surface or bulk levels, lying in the forbidden band, which successively trap the electrons and holes. In this case the excess energy of recombined carriers is released in smaller amounts, so that hco < Eg (case II in Fig. 35). Both these types of recombination are revealed in luminescence spectra recorded with n-type semiconductor electrodes under electrochemical generation of holes (Fig. 

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