Majority carrier transfer processes

As already mentioned above, it is assumed that the energy of the electrons in the conduction band is entirely kinetic energy. We have then 

Since the electrons can move everywhere, Eq. (2.10) describes the density of electrons having velocities between v and dv distributed over all directions. Considering the speeds in the three main directions we have 

This is the effective Richardson constant for thermionic emission. In the case of isotropic effective mass one can rewrite Eq. (2.15) as 

At equilibrium U = 0), the total current must be zero. Accordingly, there is a reverse current, from the metal to the semiconductor. Since the externally applied voltage occurs only across the space charge layer of the semiconductor, the barrier height also remains constant for reverse bias so that is independent of the voltage U. Therefore, must be equal to the y j -value at equilibrium, 

It is important to realize that this derivation is based on the assumption that all electrons reaching the surface with a speed are transferred. This is of interest especially in comparison with processes at the semiconductor-liquid interface. As a consequence of this assumption, the forward currents attain large values at relatively low voltages. Taking for instance a relative effective mass of one, then 

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In several cases it has been found that the oxidation of the redox system occurs entirely via hole transfer directly from the valence band to the reduced form of the couple. Then both processes, oxidation of the redox system and corrosion, proceed independently. This is usually not visible from measurements with an n-type electrode, because the photocurrent is entirely determined by the light intensity. As already mentioned above, p-type electrodes are more suitable, because the current is determined by majority carrier transfer (reaction rate Vf, in Fig. 21). From the thermodynamic point of view, the oxidation of Cu at GaAs is an interesting case. The corresponding current-potential curves are given in Fig. 22 [93]. The corrosion current is not changed upon addition of Cu, i.e. corrosion and redox process are completely independent. In this case, the kinetics of the direct hole transfer is obviously very fast, i.e. the redox current is considerably larger than the corrosion current. Both processes occur indepen-... 

More recently time-resolved techniques have been applied for studying photocarrier dynamics at the semiconductor-liquid interface. One of the main motivations is that such studies can lead to an estimation of the rate at which photo-induced charge carriers can be transferred from the semiconductor to a redox acceptor in the solution. This method is of great interest because rate constants for the transfer of photocarriers cannot be obtained from current-potential curves as in the case of majority carrier transfer (Section 7.3.5). The main aim is a detailed understanding of the carrier dynamics in the presence of surface states. The different recombination and transfer processes can be quantitatively analyzed by time-resolved photoluminescence emitted from the semiconductor following excitation by picosecond laser pulse. Two examples are shown in Fig. 7.60 [82, 83]. 

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. 

Oxidative phosphorylation occurs in the mitochondria of all animal and plant tissues, and is a coupled process between the oxidation of substrates and production of ATP. As the TCA cycle runs, hydrogen ions (or electrons) are carried by the two carrier molecules NAD or FAD to the electron transport pumps. Energy released by the electron transfer processes pumps the protons to the intermembrane region, where they accumulate in a high enough concentration to phosphorylate the ADP to ATP. The overall process is called oxidative phosphorylation. The cristae have the major coupling factors F, (a hydrophilic protein) and F0 (a hydrophobic lipoprotein complex). F, and F0 together comprise the ATPase (also called ATP synthase) complex activated by Mg2+. F0 forms a proton translocation pathway and Fj... 

In the previous section, we considered electron transfer processes involving only the majority carrier band. For semiconductors with lower band-gaps, either doped or intrinsic, both bands may be involved and we consider two current contributions arising from the two bands as shown in Fig. 41. In practice, it is found that the dominant contribution usually arises from only one of the two bands if the majority carrier band is involved, the treatment will reduce to that given above, but if the minority carrier band is the more significant, then the current may be limited by the rate of thermal generation and transport of the majority carriers to the surface. 

At n-type electrodes, the complete reaction already occurs in the dark because sufficient electrons are available in the conduction band. In the latter case the participation of the valence band has been proved by luminescence measurements. Since in the second reaction step electrons are transferred from the valence band to the OH radicals, hole are injected into the valence band of the n-type electrode which finally recombine with the electrons (majority carriers). In the case of n-GaP, this recombination is a light-emitting process, as has been found experimentally. The same result has been obtained with 820 [68] and for quinones [69]. Since the reduction of H2O2 consists of two consecutive steps, it is reasonable to describe its redox properties by two standard potentials, given by... 

Interestingly, the anodic dark current at n-Ge electrodes increases considerably upon addition of the oxidized species of a redox system, for instance Ce" ", to the electrolyte, as shown in Fig. 8.4 [7]. The cathodic current is due to the reduction of Ce. The latter process occurs also via the valence band (see Chapter 7), i.e. since electrons are transferred from the valence band to Ce", holes are injected into the Ge electrode. Under cathodic polarization these holes drift into the bulk of the semiconductor where they recombine with the electrons (majority carriers) and the latter finally carry the cathodic current. In the case of anodic polarization, however, the injected holes remain at the interface and are consumed for the anodic decomposition of germanium, as illustrated in the insert of Fig. 8.4. Accordingly, the cathodic and anodic current should be compensated to zero. Since, however, the anodic current is increased upon addition of the redox system there is obviously a current multiplication involved, similarly to the case of two-step redox processes (see Section 7.6). Thus, in step (e) (Fig. 8.1) electrons are injected into the conduction band. This experimental result is a very nice proof of the analytical result presented by Brattain and Garrett [3]. 

As already shown by the spectrum in Fig. 10.8, a cathodic photocurrent was also observed with n-GaP, its potential dependence being shown in Fig. 10.12b. Since the UfY, of n-GaP was found at a rather negative electrode potential, the energy bands are bent upwards at potentials positive of Ufh. Accordingly, the hole injected from the excited dye, cannot move into the bulk of the n-electrode (see insert of Fig. 10.12b) and are transferred back to the reduced dye molecule. The cathodic photocurrent shows a maximum, i.e. it decreases again at high cathodic polarization. This decrease is due to a reduction of the dye in the dark. The sensitization of the n-GaP electrode is, of course, a minority carrier process. The injected holes recombine with the electrons in the bulk and the current is carried by electrons. Many investigations have shown, however, that more reliable results could be obtained with majority carrier systems. 

The dominant role of organic substrates in the binding of metals such as Cd and Cu is of particular relevance for the transfer of these elements into biological systems. It can be expected that even at relatively small percentages of organic substrates these materials are primarily involved in metabolic processes and thus may constitute the major carriers by which metals are transferred within the food chain. 

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