Quasi-Fermi level concept

In the theory of non-equilibrium processes at solid state junction and also semiconductor-liquid interfaces, as developed in the previous section, frequently quasi-Fermi levels have been used for the description of minority carrier reactions [90, 91], A concept for a quantitative analysis for reactions at n- and p-type electrodes has been derived [92, 93], using the usual definition of a quasi-Fermi level (Eqs. (3a) and (3b)). Taking a valence band process as an example, the quasi-Fermi level concept can be illustrated as follows ... 

More insight into the quasi-Fermi level concept and its application has been obtained by the following example [93]. In Fig. 16, curve a) represents the current-potential curve as obtained with p-GaAs in an electrolyte without any redox system. The anodic current corresponds to the decomposition of GaAs. After addition of Cu " as an oxidizing agent, a corresponding cathodic current is visible (curve b)). At the mixed potential Um, i = 0.34 V (j == 0), the two currents are equal. The position of the quasi-Fermi level Ep, p in the p-electrode... 

These examples show very nicely how well the quasi-Fermi concept operates. There are various results given in the literature which can be interpreted on the basis of this concept. Especially the investigations of reactions of [FefCN) ] -/ - at GaAs and the etching behaviour confirm this model [97, 98]. The quasi-Fermi level concept also explains multiple step redox reactions. 

Interestingly, no charge transfer between S and Red occurs, although a considerable concentration of S has been found under stationary illumination. It should be mentioned that similar results have been obtained with p-type electrodes in the dark, which the same authors evaluated on the basis of the quasi-Fermi level concept. 

The direction of the electric field at the interface (Figure 6, Section 1.3.2) is such that the minority carriers (holes in this case) are swept to the surface and the electrons are driven to the rear ohmic contact. How fast the holes are drained away (by Faradaic reactions involving the redox electrolyte) will dictate how the Fermi levels compare with the equilibrium situation discussed earlier. The departure from equilibrium has been quantified in terms of the quasi-Fermi level concept discussed later. 

The quasi-Fermi level concept for electron-transfer processes... 

In the present derivation we take a valence-band process as an example. According to the quasi-Fermi level concept, it is assumed that the same reaction with identical rates, i.e. equal currents, takes place at n- and p-type semiconductor electrodes of the same material if the density p of holes at the surface—or equivalently the quasi-Fermi levels Fp p —are equal at the surface of the two types of electrodes, as illustrated for an illuminated n-electrode and a p-electrode in the dark in Fig 2.21. This model is applicable if three conditions are fulfilled ... 

Reineke R. and Memming R. (1992), Comparability of redox reactions at n-type semiconductor electrodes. 1. The quasi-Fermi level concept , J. Phys. Chem. 96, 1310-1317. 

The quasi-Fermi level concept makes it possible to quantitatively relate intensity-modulated photocurrent spectroscopy (IMPS) and impedance data as follows. 

The Limits of Applicability of the Quasi-Fermi Level Concept in Photoelectrochemical Kinetics Alternative Approaches... 

It is clear from the above considerations that the quasithermody-namic approach, based on the concept of quasi-Fermi levels, is sufficiently widespread and what is most important is that it is efficient. Obviousness and simplicity—here are its indisputable advantages. At the same time, it should be noted that the use of the quasi-Fermi-level concept cannot be justified in all cases. At any rate, the applicability of this concept requires that the following inequalities,... 

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