Fermi level of redox systems

Standard Potential and Fermi Level of Redox Systems... 

Figure 10. p- and -type semiconductors in contact with an electrolytic solution. Ep = Fermi level = so-called Fermi level of redox system in solution (activation barrier energy). 

Figure 4.16a illustrates the charge separation model from a thermodynamic perspective. As soon as the photoexcited electrons are trapped at the unoccupied d orbital states, the apparent Fermi level of the system will shift from Ep to Ep due to accumulation of electrons. This is the most recognised model to explain the role of promoters. It is therefore not difficult to predict that the metal NPs, which can trap the most electrons in quantity, win the competition based on this assumption. Unfortunately, experimental results disagree with this prediction, as Au NPs can trap more electrons than Pt but show relative poor performance compared to that of Pt in photoinduced reduction reactions. Apparently, a more precise model that takes the kinetics of the trapped electrons into cmisideration is needed, as shown in Fig. 4.16b. In this model the kinetics of trapped electrons for redox reaction (kred) and reverse trapping to the trap state of semiconductor (krev) were taken into account. These two rate constants can be extracted by in situ UV-vis spectrometry...

Typically the contributions of the two bands to the current are of rather unequal magnitude, and one of them dominates the current. Unless the electronic densities of states of the two bands differ greatly, the major part of the current will come from the band that is closer to the Fermi level of the redox system (see Fig. 7.6). The relative magnitudes of the current densities at vanishing overpotential can be estimated from the explicit expressions for the distribution functions Wled and Wox ... 

Consider the interface between a semiconductor and an aqueous electrolyte containing a redox system. Let the flat-band potential of the electrode be fb = 0.2 V and the equilibrium potential of the redox system o = 0.5 V, both versus SHE. Sketch the band bending when the interface is at equilibrium. Estimate the Fermi level of the semiconductor on the vacuum scale, ignoring the effect of dipole potentials at the interface. 

In Figure 6, the case of n-type Ti02 and a metal cathode is depicted, with an applied potential difference (E - E )/e, either to ensure that the Fermi level of electrons in tJie metal is higher than the H2O/H2 redox system so that hydrogen... 

Figure 6, Schematic showing energy correlations for photoassisted electrolysis of water using n-type TiOg as a photoanode and a metal cathode. Symbols as in Figures 3, 4, and 5, except Epis Fermi level for metal contact to TiO and E/ is higher Fermi level in metal cathode, polarized by an external source to a potential negative to the semiconductor anode. EF(Hi) and Ep(02) are abbreviated forms for Fermi energies for redox systems of Figure 3 (13j.

Similar photovoltaic cells can be made of semiconductor/liquid junctions. For example, the system could consist of an n-type semiconductor and an inert metal counterelectrode, in contact with an electrolyte solution containing a suitable reversible redox couple. At equilibrium, the electrochemical potential of the redox system in solution is aligned with the Fermi level of the semiconductor. Upon light excitation, the generated holes move toward the Si surface and are consumed for the oxidation of the red species. The charge transfer at the Si/electrolyte interface should account for the width of occupied states in the semiconductor and the range of the energy states in the redox system as represented in Fig. 1. 

In the presence of a redox system dissolved in the electrolyte, as long as there exists an energy difference between the Fermi level of the semiconductor and the redox couple, to reach the equilibrium conditions charge-carrier transfer occurs across the semiconductor-liquid interface via the energy bands, i.e., the conduction or valence band of the semiconductor. At the equilibrium point, the Fermi level of the redox... 

As for semiconductor/metal contacts, a change in the Fermi level of the liquid phase should result in a different amount of charge transferred across the semicondnctor/liqnid junction. For semiconductor/liquid junctions, the important energetic trends for a series of different liqnid contacts can thns be determined by measuring the solntion redox potential relative to a standard reference electrode system. Within this model, solutions with more positive redox potentials shonld indnce greater charge transfer in contact with n-type semicondnctors. 

Combining a semiconductor with an electrolyte containing a redox system, equilibrium is achieved if the electrochemical potential is constant throughout the whole system, i.e. the Fermi-levels of the semiconductor and the redox system must be equal on both sides of the interface ... 

Fig. 13. Electrode potential and energy bands of a semiconductor being in contact with a redox system a redox couple with a relatively negative standard potential b with positive standard potential c the Fermi-level of the redox system occurs around the middle of the energy gap...

Figure 29. Calculated current-potential characteristics for direct (dashed lines, 0/cm ) and surface state mediated electron transfer between an -type semiconductor electrode and a simple redox system. The plots show the transition from ideal diode behavior to metallic behavior with increasing density of surface states at around the Fermi-level of the solid (indicated in the figures). This is also clear from the plots below, which show the change of the interfacial potential drop over the Helmholtz-layer (here denoted as A(Pfj) with respect tot the total change of the interfacial potential drop (here denoted as A(p). Results from D. Vanmaekelbergh, Electrochim. Acta 42, 1121 (1997).

Having located the semiconductor band-edge positions (relative to either the vacuum reference or a standard reference electrode), we can also place the Fermi level of the redox system, E f, redox, on the same diagram. Energy diagrams such as those... 

Figure 13. Schematic outline of a dye-sensitized photovoltaic cell, showing the electron energy levels in the different phases. The system consists of a semiconducting nanocrystalline Ti02 film onto which a Ru-complex is adsorbed as a dye and a conductive counterelectrode, while the electrolyte contains an I /Ij redox couple. The cell voltage observed under illumination corresponds to the difference, AF, between the quasi-Fermi level of Ti02 and the electrochemical potential of the electrolyte. S, S, and S+ designate, respectively, the sensitizer, the electronically excited sensitizer, and the oxidized sensitizer. See text for details. Adapted from [69], A Flagfeldt and M. Gratzel, Chem Rev. 95, 49 (1995). 1995, American Chemical Society.

Some authors have asserted that the quasi-Fermi level model requires a threshold with respect to light intensity. This problem has been discussed for photoconversion systems such as photoelectrolysis of FI2O (Gregg and Nozik, 1993 Shreve and Lewis, 1995). Since the discussion on the threshold problem has frequently led to misinterpretations, we want to clarify the situation by considering a simple charge-transfer between an n-type semiconductor and redox system, as illustrated in Fig. 2.23. The system is at equilibrium (i = 0) if the overvoltage is zero (rj = 0). Flere the quasi-Fermi levels of electrons and holes are both equal to Ap,redox (not shown). Assuming that the redox process occurs entirely via the valence band, then only the quasi-Fermi level of holes at the surface, Sp, is of interest. Anodic polarisation of the electrode in the dark produces a very small anodic current (lower i-rj curve in the centre of Fig. 2.23). As mentioned in the previous section, is practically pinned close to fip,redox (Fig. 2.23A) whereas p, differs from Ap,redox by qr]. On illumination, the anodic... 

The model can be further tested by varying the concentration of one of the species as illustrated in Fig. 6.9. In this case, the Fermi level of the redox system is shifted according to the Nernst equation. One can easily prove by using Eqs. (6.37), (6.38) and (640) that in this case and >red are equal at = Ep,redox. 

---