Current-Potential Behavior

Let us return to the equilibrium situation of an n-type semiconductor in contact with a redox electrolyte and reconsider the situation in Fig. 9(a). This is shown again in Fig. 12(a) to underscore the fact that the interface is in a state of dynamic equilibrium. That is, the forward and 

ket is the rate constant for electron transfer, Cqx is the concentration of empty (acceptor) state in the redox electrolyte, Hs and Hjo are the surface concentrations of electrons, the subscript o in the latter case denoting the equilibrium situation. Thus, as long as the semiconductor-electrolyte interface is not perturbed by an external (bias) potential, Ug = n o and the net current is zero. The voltage 

A few words about the units of the terms in Eq. (14) are in order at this juncture. The term i /CqA may be regarded as a flux (/) in units of number of carriers crossing per unit area per second [1, 3, 8]. The concentration terms are in cm thus ket has the dimensions of cm s because of the second-order kinetics nature stemming from the two multiplied concentration terms in Eq. (14) [1, 3, 8]. 

Consider now the application of a bias potential to the interface. Intuitively when it is such that g go, a reduction current (cathodic current) should flow across the interface such that the oxidized redox species are converted to reduced species (Ox Red). On the other hand, when ngo g, the current flow direction is reversed and an anodic current should flow. Once again the situation here is somewhat 

The assumption is inherent in the preceding discussion that all of the applied bias (V) drops across the space charge layer such that we are modulating only the majority carrier population at the surface (and not the potential drop across the Helmholtz layer). In other words, the band edge positions are pinned or there is no Fermi level pinning (see Sect. 1.3.4). 

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The concentration of an electroactive species is changing with time and distance in such a way that a temporal evolution equation is needed for analyzing the current-potential behavior. This evolution is typically given by Eq. (1.173) ... 

The current-potential behavior shown in Figure 5.22 is claimed to be characteristic of a clean platinum surface in a clean test solution,99 and can be used as a criterion of solution and electrode cleanliness in aqueous 0.5 M H2S04. The presence of organic material generally will cause a decrease in the hydrogen adsorption peaks and the appearance of new peaks. 

Hydrodynamic and stirred-solution electrodes. Certain advantages result when the electrode is moved past the solution or vice versa. The increased mass transport increases the current and often increases the sensitivity (although not necessarily the signal-to-noise ratio). In addition, hydrodynamic electrodes such as the rotated platinum electrode and rotated-disk electrode exhibit a current-potential behavior similar to that of the DME. That is, they give the familiar plateau when the current is limited by mass transport to the electrode surface and the current is proportional to the solution concentration of the electroactive species. 

The effect of illumination seen in the current/potential behavior is reflected also in capacity measurements as evaluated in the form of Mott/ Schottky-plots (Fig. 2). Illumination leads to a parallel shift of this plot in the same direction and by about the same amount as in I/E curves. The plot is shifted back to its dark position if the appropriate redox couple is added. Other minority carrier acceptors on the other hand are not able to shift the light-plot back onto the plot obtained in the dark. 

Fig. 4 Dark current/potential behavior of GaAs and InP (both n- and p-type) in the presence of Eu2+...

Consider now the current-potential behavior of a system close to E. Assuming that the two partial currents are in their respective linear Tafel region, we can write... 

A shift in the band edge position also explains the observed dependence of the hole injection rate on the electrode polarization. Fig. 11 exempliHes this by the total current-potential behavior of a (111) n-GaP electrode in alpine Fe(CN) solutions (pH = 13), together with the partial current due to the injection of holes (revealed by rotating ring-disk experiments, see ref. [73]). Also at p-GaP, it was shown that the hole injection rate is lower with anodic polarization than with cathodic polarization. The potential-dependent position of the band edges is ascribed to a potential-dependent accumulation of positive charges (holes, surface decomposition intermediates,. ..) at the semiconductor surface [62, 73]. 

Figure 13 shows schematically the current- and partial current-potential behavior of p-GaP ((a) and (b)) and n-GaP ((c) and (d)) in alkaline Fe(CN) solutions. In Fig. 13 (a) and (c), the partial current density at rest-potential or under open-circuit, and hence the etch rate, is limited by the cathodic partial reaction rate. This is the case for (111) GaP (for which the cathodic reaction is under kinetic control) and for (ITT) GaP at low Fe(CN) concentrations (for which the cathodic reaction is under diffusion control). In Fig. 13 (b) and (d), the partial current density at rest-potential or under open-circuit is limited by the anodic partial reactioi rate, which is limited by the OH diffusion rate (see Sec. 2.1) this is the case for (111) GaP at... 

That the shape of the curve on the rising portion of the wave remains the same as in polarography can be understood from the factors that govern the current-potential behavior in these voltammetric techniques. Throughout the voltammetric curve the cur-... 

Kilsa K., Mayo E. L, Kuciauskas D., Villahermosa R., Lewis N. S., Winkler J. R. and Gray H. B. (2003), Effects of bridging ligands on the current-potential behavior and interfacial kinetics of ruthenium-sensitized nanocrystalline TiOa photoelectrodes , J. Phys. Chem. A 107, 3379-3383. 

Tafel lines obtained on the metals Pt, Pd, Ir, Rh, and Au (Fig. 22) for the electroreduction of oxygen in acid solutions indicate that Au with no unpaired d electrons has a significantly lower exchange current density than other metals (10 amp cm" on Au as compared with 10 amp cm ) Rh and Ir, which are expected to have the same number of unpaired electrons, show essentially an identical current-potential behavior Pd and Pt with virtually the same number of unpaired electrons show the same Tafel behavior 90). 

The observed current-potential behavior is a function of the simultaneous processes of film formation, its dissolution, and metal dissolution. The latter seems to be mostly responsible for the magnitude of the current at all potentials. In the active potential region dissolution is hindered by a decrease in the free electrode area, and in the passive region dissolution depends entirely on the properties of the passivating film. 

This finally brings us to the comparability of the current-potential behavior... 

Figure 15.4 illustrates the origin of the corrosion potential and also the principles of cathodic and anodic protection for a single oxidation reaction (M M ) and a single reduction reaction (H H2) occurring at the metal surface (the dashed lines represent the current-potential behavior of the reverse reactions and are not important to the present discussion). Because charge balance must be maintained, the potential is pinned at a value, Ecom where the cathodic current and the anodic current are equal (i.e., where the two curves intersect). This corrosion potential (Ecorr) is called a mixed potential, as it is determined by a mixture of two (sometimes more) electrochemical reactions. The anodic current (also the cathodic current, as they are equal) at this potential is the corrosion current (torr)- It is important to note that E orr and icorr are influenced by both the thermodynamics of the two reactions, manifested by the equilibrium potentials E(h+/h2) and E(m/m+)> and by the kinetics of the two reactions, manifested by the exchange current densities io(H+/h2) and o(m/m+)> and by the slopes of the two linear curves (the Tafel slopes). 

Finally it should be mentioned that, in principle, the same current-potential behavior can be obtained from Marcus s or Levich s " theory. Although not mentioned in these theories, one can actually derive from them the same distribution functions of energy states, since the exponential terms in Eqs. (32) and (34) are equal in all theories. This result is entirely due to the assumption of a harmonic oscillation model of the motion in the ion s solvation shell. The main advantage of Gerisher s model is the description of electron transfer reactions in terms of an energy picture (Figure 11), which is especially useful for the processes occurring at semiconductor or insulator electrodes. The same description, of course, can also be applied for metal electrodes,t which will not be discussed here (see, e.g.. Ref. 91). 

A typical current-potential behavior of a semiconductor electrode is shown in Figure 12 for n- and Here the cathodic process corres-... 

In Section 4.2 we have described electrode reactions which were partly limited by the deficiency of electrons or holes in the corresponding energy bands. A typical example was the current-potential behavior in Figure 12. The anodic current at the n-type electrode was limited by the diffusion of holes and the cathodic current at the p-type electrode by the diffusion of electrons toward the surface. It was further mentioned that these currents could be enhanced by light absorbed by the electrode. 

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