Gerischer diagram

Figure 7.6 Gerischer diagram for a redox reaction at an n-type semiconductor (a) at equilibrium the Fermi levels of the semiconductor and of the redox couple are equal (b) after application of an anodic overpotential.

If the electronic properties of the semiconductor - the Fermi level, the positions of the valence and the conduction band, and the flat-band potential - and those of the redox couple - Fermi level and energy of reorganization - are known, the Gerischer diagram can be constructed, and the overlap of the two distribution functions Wox and Wred with the bands can be calculated. 

Fig. 15. Diagram illustrating the thermodynamic stability of a semiconductor against corrosion and photocorrosion (a) semiconductor is absolutely stable, (b) stable against cathodic decomposition, (c) stable against anodic decomposition, and (d) unstable. [From Gerischer (1977a).]...

To illustrate the above approach, we present here the energy diagrams (taken from the paper by Gerischer, 1977a) for two of the most widely used semiconductor materials in aqueous solutions. 

Fig. 18. Diagram of electrochemical potentials for reactions at 2 electrode in an aqueous solution (pH = 7). The potentials are given relative to the NHE. [From Gerischer (1977a).]...

Figure 4. A Gerischer s diagram for a sensitizer, S , and its excited state, S. ...

Figure 7. Gerischer s diagram for sensitization of a n-type semiconductor by an excited state sensitizer S. ...

Figure 33 shows a Gerischer-like diagram which summarizes the kinetic processes that can be initiated with light excitation of a dye-sensitized nanocrystalline anatase... 

Figure 33. Gerischer-like diagram that summarizes the kinetic rate constants measured experimentally upon light excitation of a dye sensitized nanocrystalline TiO (anatase) film.

A more modern visualization of the factors entering the calculation of the anodic and cathodic currents has been developed by Gerischer and Schmickler (Fig. 28) [66, 69-71]. In this diagram, Wox and Wred are proportional to the Gaussian terms in Eqs (48) and (49), corresponding... 

FIGURE 12.13 Gerischer-type diagram for interfacial electron transfer. The rate constants for interfacial electron transfer are dependent on the overlap of the sensitizer and the semiconductor density of states. Note that the density of states of the semiconductor is not a singular parameter and can shift with a change in environment, that is, pH, ionic strength, solvent, and so on. 

The diagram shown in Fig. 3.10 is now widely used to describe electron transfer processes at electrodes, and it has the merit that it can be extended readily to the discussion of electron transfer at semiconductor and insulator electrodes [16]. The theoretical basis for the diagram is to be found in the fluctuating energy level model of electron transfer which has been discussed by Marcus [12,13], Gerischer [17-19], Levich [20], and Dogonadze [21]. 

Figure 9.26 Schematic diagrams for energy vs. density of states for semiconductor-electrolyte interface (SEI). (a) An ideal interface described by Gerischer s model, where direct transfer of charge between bulk energy states of semiconductor and redox takes place, and (b) transfer of charge mediated through surface states. The hashed curves represent filled states. 2 represents solvent reorganization energy from Marcus theory. Adapted from reference (40).

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