Majority carrier transfer

The forward current at a semiconductor-metal junction is mainly determined by a majority carrier transfer i.e. electrons for n-type, as illustrated in Fig. 1 d. In this majority carrier device the socalled thermionic emission model is applied according to which all electrons reaching the surface are transferred to the metal. In this case we have ... 

This relation is identical to that derived for a pn-junction (see e.g. [89]) (solid curve in Fig. 14). It also looks similar to the current-voltage relation derived for a majority carrier transfer, as given by Eq. (42), both relations differ only by the pre-exponential factor. The first case, i.e. limitation by surface kinetics (Eq. (44)), is difficult to realize, because the majority carrier transfer becomes dominant for redox systems, the standard potential of which is located in the middle of the gap. 

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-... 

Dark current-potential curves representing a majority carrier transfer to a redox system have been measured by many research groups. Mostly cathodic currents at n-type electrodes have been studied rather than anodic currents at p-type semiconductors. This is because anodic hole consumption from p-type electrodes usually results in corrosion of the material. At least it is difficult to find a redox system where the oxidation of the redox couple competes sufficiently quickly with the corrosion. 

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]. 

Current-voltage characteristics. I/U-characteristics at semiconductor electrodes are usually dominated by majority carriers transfer, i.e. the exchange of electrons via the conduction band in n-type semiconductors and the exchange of holes via the valence band in p-type semiconductors to or from a red/ox species in the electrolyte. 

Since under normal depletion conditions, conductivity changes are dominated by majority carriers, and interfacial electron transfer can be neglected in the dark, the carrier profile can be found by solving Poisson s equation ... 

Since the reorientationnergy X varies in the range of 0.5-2 eV the half width can be in the order of the bandgap of the semiconductor. Assuming that in the dark the electron transfer occurs entirely via the conduction band (majority carrier device) the current-potential dependence can be derived as follows ... 

However, this additional interaction is largely masked by interaction with the nuclei, generating bremsstrahlung, which is the major carrier of the energy transfer at highly relativistic speeds. 

The existence of two types of mobile charge carriers in semiconductors enables us to distinguish between a majority charge carrier transferred from the electrode into the electrolyte and a minority charge carrier injected from the electrolyte into the electrode. Minority carrier injection causes significant reverse currents, but may also contribute to the total current under forward conditions. 

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. 

Recombination in the depletion layer can become important when the concentration of minority carriers at the interface exceeds the majority carrier concentration. Under illumination minority carrier buildup at the semiconductor-electrolyte interface can occur due to slow charge transfer. Thus surface inversion may occur and recombination in the depletion region can become the dominant mechanism accounting for loss in photocurrent. 

In a PEIS experiment, the flux of minority carriers generated by illumination is constant to a good approximation, and if the condition 1/a < dSc + L is fulfilled, then g 7(0). The ac potential perturbs the density of majority carriers at the surface and therefore modulates knc about a mean (dc) value, giving rise to an ac photocurrent. The photoelec-trochemical admittance, (VVeis = 1/ZPE1S), is the ratio of the ac component of the total photocurrent to the ac voltage. For competition between recombination and electron transfer, the photoelectrochemical admittance is given by [29]... 

Let us consider the electrode kinetics associated with charge transfer from an n-type semiconductor particle to an electrode. As indicated by Albery et al. [164], the crucial difference between the electrochemistry of a colloidal particle and an ordinary electrochemically active solution phase species is the number of electrons transferred from the particle to the electrode may be large and will depend upon the potential of the electrode. Fig. 9.5 shows the model for an encounter of a particle with an electrode used by Albery and co-workers. kD is the mass-transfer coefficient for the transport of the particles to the electrode surface. In the simplest case, wherein it is assumed that the lifetime of the transferable electrons (majority carriers of thermal or photonic origin) is greater than the time taken by a particle to traverse the ORDE diffusion layer, this is given by... 

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