Current-potential curves at semiconductor electrodes

Qualitative Description of Current-Potential Curves at Semiconductor Electrodes 165... 

Fig. 8.11 Top theoretical current-potential curves at a p-type semiconductor electrode in the presence (solid curve) and absence (long-dashed curve) of a redox system with a very positive standard potential short-dashed curve, cathodic partial current for a redox system which is reduced by an electron transfer via the valence band of a semiconductor. Bottom energy diagrams for cathodic (left) and anodic (right) polarization...

Fig. 8.12 Theoretical current-potential curves at an n-type semiconductor electrode in the presence of a redox system of a high standard potential (similarly as in Fig. 8.11)...

Figure 8.11 (a) theoretical current-potential curves at a p-type semiconductor electrode in the presence (solid curve) and absence (long-dashed curve) of a redox system with a... 

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. 

Figure 2.23 Positions of quasi-Fermi levels at high positive overpotential (A and B) and low negative overpotential (C and D) in the dark and under illumination centre current-potential curve for an w-type semiconductor electrode (Memming, 2000).

In this technique, as first developed by Li and Peters [16], the photocurrent instead of the potential is modulated. Hence, it is only applicable for minority carrier processes. The modulation of current is achieved by modulating the exciting light intensity. The current modulation is illustrated by a current-potential curve of an n-type semiconductor electrode (Fig. 4.15). The quantum efficiency is defined as the ratio of the current and intensity modulation ( = AJ/AT). Since the intensity is not always known it is easier to use a relative quantum yield as defined by... 

A theoretical current-potential curve (/7/q vs. fj) is given in Fig. 7.3 for r] = 0.5. It should be emphasized here that Eq. (7.11) is only valid in this simple form if the current is really kinetically controlled, i.e. if diffusion of the redox species toward the electrode surface is sufficiently fast. According to the Butler-Volmer equation (Eq. 7.11) the current increases exponentially with potential in both directions. In this aspect charge transfer processes at metal electrodes differ completely from those at semiconductors. When the overpotential is sufficiently large, erj/kT 1. one of the exponential terms in Eq. (7.11) can be neglected compared to the other. In this case we have either... 

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. 

In the case of semiconductor electrodes, it is impossible to obtain the same information because the energy bands are fixed at the surface and any potential variation occurs only across the space charge layer. Here the maximum rate constant is expected if the peak of the distribution curve occurs at the lower edge of the conduction band of an n-type semiconductor. Therefore, the experimental results obtained with the modified metal electrodes, are of great importance for the quantitative analysis of rate constants from current-potential curves measured with semiconductor electrodes (see e.g. Section 7.3.4). 

Fig. 7.45 A, B, C,D, positions of quasi-Fermi levels at different potentials center, current-potential curve for an n-type semiconductor electrode...

Figure 18.2.7 Current-potential curves for a solution containing couple O/R. (a) n-type semiconductor in the dark (curve 1) and under irradiation (curve 2). (b) p-iypt semiconductor in the dark (curve 1) and under irradiation (curve 2). For both (a) and (b), curve 3 is the i-E curve at a platinum electrode.

In the dark (curve 1), essentially no current flows when the potential of the semiconductor electrode is made more and more positive, because, as discussed in the preceding section, there are few holes in the semiconductor to accept electrons from the reduced form of a redox couple located at potentials within the gap. ... 

The principles that govern electrochemistry at semiconductor electrodes can also be applied to redox processes in particle systems. In this case, one considers the rates of the oxidation and reduction half-reactions that occur on the particle, usually in terms of the current, as a function of particle potential. One can use current-potential curves to estimate the nature and rates of heterogeneous reactions on surfaces. This approach applies not only to semiconductor particles, but also to metal particles that behave as catalysts and to surfaces undergoing corrosion. 

Silicon. The snrface of silicon immersed in fluoride media is of interest for semiconductor processing and production of porous silicon (Section 5.7) [541, 542, 549, 550]. A typical current-potential curve of p-Si in a flnoride electrolyte (0.975 MNH4CI + 0.025 MNH4F + 0.025 MHF, pH 2.8) measured at a rotating disk electrode at rotation rate of 3000 rpm and potential scanning speed of 5 mV s is shown in Fig. 7.29. The steep rise of the current density near... 

This equation was derived at first by Heyrovsky and llkovic [10] and is usually called the Heyrovsky-llkovic equation. In most cases, the diffusion coefficients of the Ox and Red species are not very different, so that essentially the standard redox potential. A theoretical current-potential curve in terms of versus — Uy2 shown in Figure 7.7. A semilogarithmic plot would yield a straight line (see Section 7.1.3). It should be mentioned here that Eq. (7.32) can also be applied to majority carrier processes at semiconductor electrodes (see, e.g.. Section 7.3.4). 

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