Semiconductors current-potential curve

Electrode reactions are heterogeneous chemical reactions in which stoichiometric transfer of electric charges takes place between the electrode and the electrolyte. The kinetics of such reactions depend not only on concentration and chemical structure, but also on the electrical conditions in and near the phase boundary. Semiconductor and metal electrodes present very different electrical conditions. Here we shall discuss current-potential curves which show the significance of these differences with respect to the mechanism of electrode reactions. 

The potentials of the capacity minima are strongly dependent on the pH of the electrolyte. The current potential curves show the same dependence. These potential differences are not caused by changes in the space charge. It must be assumed that the source of these potential differences lies between the semiconductor surface and the Helmholtz plane in the electrolyte. Adsorption of OH ions may be an explanation of this effect. 

Fig. 14. Theoretical current-potential curve for a n-type semiconductor being in contact with...

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 13. Current- potential curves for an n-type semiconductor in the dark (curve 1) and under band-gap illumination (curves 2 and 3). Two levels of photon fluxes are shown in the latter case.

Referring back to Figure 13, the current-potential curves under illumination of the semiconductor simply appear shifted up relative to the dark i- V counterpart. This, however, is the ideal scenario. Anomalous photoeffects (APEs) are often observed that manifest as a cross-over of light and dark current-voltage curves, as illustrated in Figure 22. Thus, the superposition principle [241] is not obeyed in this instance. The dashed line in Figure 22 is produced by translating the photoeurrent-... 

Figure 2.19 Theoretical current-potential curve for an n-type semiconductor in contact with a redox system, assuming a valence-band process.

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... 

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

This relation is identical to that derived for a pure solid state device which is determined by minority carrier transfer and recombination, such as a pn junction (see Section 2.3) or semiconductor-metal contact (see Section 2.2.3). The corresponding current-potential curves in the dark and under illumination are given by the solid lines in Fig. 7.16. Taking the complete Eq. (7.71), there may be a certain potential range where the recombination current determines the process until the current levels off to a constant jy. For very large jy values, the cathodic current can ultimately be diffusion-limited, which can be checked experimentally by using a rotating electrode. 

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). 

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]. 

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)...

The competition between redox reaction and anodic dissolution became very important in the development of stable regenerative solar cells on the basis of semiconductor-liquid junctions. As shown in the previous section, it is determined by the thermodynamic and kinetic properties of the processes involved. Information on the competitions between these reactions cannot be obtained entirely from current-potential curves, because in many cases they do not look very different upon addition of a redox system, especially if the current is controlled by the light intensity. Therefore, a rotating ring disc electrode (RRDE) assembly consisting of a semiconductor disc and a Pt ring is usually applied, i.e. a technique which makes it possible to determine separately the current corresponding to the oxidation of a redox system [62, 63]. 

Finally, before discussing oscillatory behavior, it is worth noting that a circuit equivalent to that shown in Fig. 1 also arises in semiconductor physics where a semiconductor device takes on the role of the faradaic impedance and the other elements of the circuit are electronic elements. Thus interesting parallels can be drawn between the dynamics of electrochemical and semiconductor systems. Furthermore, stability criteria derived for the latter can be directly applied to electrochemical systems. This is especially interesting for the interaction of S- or Z- shaped current-potential curves with the external circuit, which are not considered here owing to the presence of chemical instabilities. 

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