Energy bands at the surface

Fig. 9. Position of energy bands at the surface of various semiconductors at pH 0 (d) dark (/) illuminated...

If the density of holes Ps at the surface - or equivalently the quasi-Fermi level Ep p — are equal at the surface of an n- and p-semiconductor electrode, then the same reaction with identical rates, i.e. equal currents, takes place at both types of electrodes (Fig. 15). Since holes are majority carriers in a p-type semiconductor, the position of the quasi-Fermi level Ep,p is identical to the electrode potential (see right side of Fig. 15), and therefore-with respect to the reference electrode - directly measurable. The density of p can easily be calculated, provided that the positions of the energy bands at the surface are known. The measurements of a current-potential curve also yields automatically the relationship between current and quasi-Fermi level of holes. The basic concept implies that the position of the quasi-Fermi level Ep,p at the surface of an n-type semiconductor and the corresponding hole density Ps can be derived for a given photocurrent, since the same relationship between current and the quasi-Fermi level of holes holds. 

Fig. 28. Distribution of electron states of Eu /Eu with respect to energy bands at the surface of GaAs and InP [132]...

The position of energy bands at the surface of particles cannot be determined exactly, because capacity measurements are not possible. Their position can only be estimated by checking which reaction is possible. Frequently, methyl viologen (MV ) has been used as an electron acceptor which can accept an electron from the conduction bemd upon illumination, provided the conduction band is above the reduction potential of MV. The radical (MV formed in this reaction is usually spectroscopically [16] or electrochemically [180] analyzed. These methods, however, give a very rough estimate, because usually it is not known whether surface states are involved in the charge transfer process. 

It is further clear from Fig. 5.19 that the n-electrode has to be polarized cathodically with respect to the equilibrium potential, and the p-electrode anodically, in order to reach the corresponding flatband situation (see lower part of Fig. 5.19), provided that the positions of the energy bands at the surface are the same for the two types of electrodes. Keeping in mind that the electrode potential refers to the Fermi level of the electrode, then the difference of flatband potentials corresponds exactly to the difference of the two Fermi levels. Since the Fermi level in the bulk of a semiconductor with the usual doping (>1() cm ) is rather close to the corresponding band, the difference in the flatband potentials approximates the bandgap of the semiconductor as found with GaP. 

Electroluminescence was first observed with n-GaP electrodes using hole donors such as [Fe(CN)(,] in alkaline or S2O8 in acid solutions [112]. In these two cases the corresponding standard potentials occur at or even below the valence band edge (see Table in Appendix). In the case of [Fe(CN)(s] no luminescence was found in acid solutions although the current-potential curve indicates that the redox species is reduced. The differences between alkaline and acid solutions can be explained by the pH-dependence of the position of the energy bands at the surface, as shown in Fig. 7.62. Since is far below Ep.redox at pH 1 no charge transfer between the redox couple and the valence band is possible anymore, and the cathodic current is only due to an electron transfer via the conduction band. 

Fig. 8.20 a) Anodic photocurrent vs. electrode potential for an n-WSe2 electrode in the absence and in the presence of a redox. system, b) Position of energy bands at the surface of WSe2 in the dark and under illumination. (After ref. [64])... 

FIGURE 16. Relative position of energy bands at the surface of various semiconductor electrodes [values vs. NHE (vacuum scale)] (from Ref. 27). 

Since the potential across the Helmholtz layer is constant, also the relative position of energy states on both sides of the interface, and consequently the energy difference between the energy bands at the surface and the Fermi level in the redox system, remain unchanged. Accordingly, the exponential terms in the current equations (32) and (35) are independent of any applied voltage. The only potential-dependent quantities in these equations are the carrier densities ris and Ps. They depend exponentially on Use as given by Eqs. (2a) and (2b). Since n, and Ps occur only in two current equations (32b) and (34a), ic and C depend on Use and therefore on the applied potential, whereas the other two partial currents C and are always potentially independent, i.e.. 

Figure 3.54 Bending of energy bands at the surface of a semiconductor electrode.

Another important result is that the flatband potentials and therefore the position of the energy bands at the semiconductor surface contacting an aqueous electrolyte are usually independent of any redox system added to the solution. Hence, the interaction between semiconductor and H2O determines the Helmholtz layer and the position of the energy bands. Therefore, it is reasonable to characterize semiconductor electrodes by their positioning of energy bands at the surface for a given pH. A selection is shown in Figure 5.20. 

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