Solution Fermi level

Fig. 11-2. Electron energy leveb for a mixed electrode reaction of iron corrosion in acidic solution = Fermi level of iron electrode Sfw/hj) = Fermi level of hydrogen redox...

Figure 1.7 Dye-sensitised solar cell (a) cell architecture (b) electronic energy levels. The placement of the semiconductor band-edge energy and the solution Fermi levels S/S, S /S and 1713 on the same scale, the vacuum scale of electronic energy, is explained in Appendix lA at the end of this chapter.

Figure 1.8 Cell schematics for a regenerative solar cell based on (a) an n-type photoelectrode (b) ap-type photoelectrode. The top diagrams show the cell reactions under illumination, the middle diagrams the electronic energy levels and band bending, and the bottom diagrams the cell current-voltage (I-U) characteristics with the photoelectrode and counter electrode (CE) currents shown in the same quadrant. The maximum power point is located at the point on the current-voltage curve at which the rectangle of maximum area may be inscribed in this quadrant. The photovoltage V, the electron and hole quasi-Fermi levels E and fip and the solution Fermi level f o.R, the open-circuit potential Ugc of the photoelectrode and the standard redox potential 17 ° of the 0,R redox couple are also shown.

The concept of the solution Fermi level is discussed in Appendix lA at the end of this chapter. 

THE VACUUM SCALE OF ELECTRODE POTENTIAL AND THE CONCEPT OF THE SOLUTION FERMI LEVEL... 

The concept of the solution Fermi level is very useful in photoelectrochemistry, althongh it strikes some as strange at first, because the term Fermi level was first introduced and defined for an electronically conducting phase, such as a metal or semiconductor, which contains free electrons. In this context, the Fermi level is defined as the energy, measured with respect any convenient reference level, for which the probability that an electronic energy level is occupied is one-half. The most convenient reference level to use in photoelectrochemistry is the local vacuum level of the solution. The Fermi level of any conducting phase a is then synonymous with the electrochemical potential of an electron in that phase, i.e. E = fi . 

We are now in a position to relate the electronic energy levels of the solution and the electrode on the same scale. It follows from the definition of absolute electrode potential and its value for the SHE, given in eq. 1A.14, that the solution Fermi level qr of a redox couple 0,R is related to its electrode potential Uq r (SHE) on the SHE scale by... 

Figure 4.24 shows how the band bending adjusts when the potential t/ of an n-type semiconductor electrode is altered. This changes the position of the semiconductor Fermi level E with respect to the solution Fermi level at the same time adjusting the band bending across the space-charge layer, but the valence and conduction band-edge... 

This behaviour is observed only for reasonably defect-free semiconductors. Such a solution semiconductor junction behaves like a metal semiconductor Schottky junction, with the electrolyte solution playing the role of the metal. The other extreme of behaviour, a Bardeen junction in which the band bending is fixed and the band edges float with respectto the solution Fermi level, is observed in solution semiconductor junctions with a high density of interfacial states. 

Hence, the use of the determination of solution Fermi level from standard redox potential (cf. Figure 16) is not applicable in the absence of the value of (/> However, the question is whether the Fermi level in solution is... 

A Le Chatelier concentration effect raises or lowers the solution Fermi level by the relative concentrations of the reduced and oxidized forms. 

Thus when using the she scale one chooses as the reference state of electrons (and assigns the zero value to it) the state of an electron at the Fermi level of a metal electrode in equilibrium with an aqueous solution of pH=0 and Ph2=1 atm at 25°C. 

Singh P, Singh R, Gale R, Rajeshwar K, DuBow J (1980) Surface charge and specific ion adsorption effects in photoelectrochemical devices. J Appl Phys 51 6286-6291 Bard AJ, Bocarsly AB, Pan ERF, Walton EG, Wrighton MS (1980) The concept of Fermi level pinning at semiconductor/liquid junctions. Consequences for energy conversion efficiency and selection of useful solution redox couples in solar devices. J Am Chem Soc 102 3671-3677... 

Knowledge of the Volta potential of a metal/solution interface is relevant to the interpretation of the absolute electrode potential. According to the modem view, the relative electrode potential (i.e., the emf of a galvanic cell) measures the value of the energy of the electrons at the Fermi level of the given metal electrode relative to the metal of the reference electrode. On the other hand, considered separately, the absolute value of the electrode potential measures the work done in transferring an electron from a metal surrounded by a macroscopic layer of solution to a point in a vacuum outside the solotion. ... 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

Because of the excess holes with an energy lower than the Fermi level that are present at the n-type semiconductor surface in contact with the solution, electron ttansitions from the solution to the semiconductor electrode are facilitated ( egress of holes from the electrode to the reacting species ), and anodic photocurrents arise. Such currents do not arise merely from an acceleration of reactions which, at the particular potential, will also occur in the dark. According to Eq. (29.6), the electrochemical potential, corresponds to a more positive value of electrode potential (E ) than that which actually exists (E). Hence, anodic reactions can occur at the electrode even with redox systems having an equilibrium potential more positive than E (between E and E ) (i.e., reactions that are prohibited in the dark). 

Figure 9.14 Kinetic current density (squares) at 0.8 V for O2 reduction on the Pt monolayer deposited on various metal single-crystal surfaces in a 0.1 M HCIO4 solution, and calculated binding energies (circles) of atomic oxygen (BEq), as a function of calculated d-band center (relative to the Fermi level, ej — sp) of the respective surfaces. The data for Pt(lll) were obtained from [Markovic et al., 1999] and are included for comparison. Key 1, PIml/ Ru(OOOl) 2, PtML/Ir(lll) 3, PtML/Rh(lH) 4, PtML/Au(lll) 5, Pt(lll) 6, PIml/ Pd(lll). (Reproduced with permission from Zhang et al. [2005a].)...

Substituting (1.66) into expression (1.64) leads to the fact that far from the equilibrium position owing to either full occupation of adsorption surface states or with leveling off in Ea with the Fermi level of adsorbent Ep solution of the latter can be written as... 

Another possibility of the appearance of a quasimetallic behaviour of metal oxides occurs with thin oxide films on metals. If the film thickness is sufficiently small (less than ca. 3nm), the electrons can tunnel through the oxide film, and the charge transfer actually proceeds between the level of solution species and the Fermi level of the supporting metal (Fig. 4.12). 

Bradley et al.109 have combined a p-Si photocathode and homogeneous catalysts (tetraazamacrocyclic metal complexes, which had been shown to be effective catalysts for C02 reduction at an Hg electrode110) to reduce the applied cathode potential. The catalysts showed111 reversible cyclic voltammetric responses in acetonitrile at illuminated p-Si electrodes at potentials significantly more positive (ca. 0.4 V) than those required at a Pt electrode, where the p-Si used had surface states in high density and Fermi level pinning112 occurred. Electrolysis of a C02-saturated solution (acetonitrile-H20-LiC104 1 1 0.1 M) in the presence of 180 mM... 

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