Conduction band mechanism

The overall transfer currents of redox electrons can be obtained by integrating these equations with respect to electron energy e from the lower edge of the conduction band to infinity for the conduction band mechanism and firom minus infinity to the upper edge of the valence band for the valence band mechanism. 

Figures 8-16 and 8-17 show the state density ZXe) and the exchange reaction current io( ) as functions of electron energy level in two different cases of the transfer reaction of redox electrons in equilibrium. In one case in which the Fermi level of redox electrons cnxEDax) is close to the conduction band edge (Fig. 8-16), the conduction band mechanism predominates over the valence band mechanism in reaction equilibrium because the Fermi level of electrode ensa (= nREDOK)) at the interface, which is also dose to the conduction band edge, generates a higher concentration of interfadal electrons in the conduction band than interfadal holes in the valence band. In the other case in which the Fermi level of redox electrons is dose to the valence band edge (Fig. 8-17), the valence band mechanism predominates over the conduction band mechanism because the valence band holes cue much more concentrated than the conduction band electrons at the electrode interface.

From these illustrations it follows, in general, that Ihe transfer reaction of redox electrons at semiconductor electrodes occurs via the conduction band mechanism if its equilibrium potential is relatively low (high in the Fermi level of redox electrons) whereas, the transfer reaction of redox electrons proceeds via the valence band mechanism if the equilibriiun redox potential is high (low in the Fermi level of redox electrons). 

TABLE 8-1. Preference for the conduction band mechanism (CB) and the valence band mechanism (VB) in outer sphere electron transfer reactions of hydrated redox particles at semiconductor electrodes (SC) Eo = standard redox potential referred to NHE c, = band gap of semiconductors. [From Memming, 1983.]... 

A further increase in anodic polarization lowers still further the Fermi level ersc)(ti) which gradually approaches the valence band edge Cy at the electrode interface as shown in Fig. 8-21. As the anodic polarization increases, the concentration of interfacial holes in the valence band increases, thus causing the anodic electron transfer to change from the conduction band mechanism to the valence band mechanism. 

Consequently, for the transfer reaction of redox electrons via the conduction band mechanism, the anodic current is constant and independent of the electrode potential whereas, the cathodic current increases with increasing cathodic overvoltage (decreasing electrode potential). 

Fig. 9-8. Potential energy profile for ionization of surface atoms in two steps on a covalent semiconductor electrode c, = band giq> energy tfi s electron level in an intermediate radical S " Ag = activation energy for the first step of radical formation in the conduction band mechanism df = activation energy for the first step of radical formation in the valence band mechanism = activation energy for the second step of radical ionization in the conduction band mechanism Ag = activation energy for the second step of radical ionization in the valence band mechanism beR = CR-Ev. [From Gerischer, 1970.]...

It follows that, when Ptk e, is greater than (e -Ev), the rate of capture of holes is greater than the rate of release of electrons (Vb>Vt). Namely, if the Fermi level ej at the surface is lower than the middle, (ej + Ev)/2, of the band gap (the p-type surface) and if p.b is close to 0.5, the valence band mechanism of Eqn. 9-24b will probably predominate over the conduction band mechanism of Eqn. 9-24a. As the band gap e, of semiconductor electrode increases, the valence band mechanism become more predominant. 

Equation 9-31 indicates that the electron level, er, of the intermediate radical is decisive in determining the ratio of the rates vjv. if the electron level of er is relatively close to the valence band edge Ey, the valence band mechanism, Eqn. 9-24d, will predominate whereas, if the electron level of er is relatively close to the conduction band edge e, the lone pair electron will be excited into the conduction band, and the conduction band mechanism, Eqn. 9-24c, will predominate. As the band gap of semiconductor electrode decreases, the conduction band increasingly participates. 

The same disciission may apply to the anodic dissolution of semiconductor electrodes of covalently bonded compounds such as gallium arsenide. In general, covalent compoimd semiconductors contain varying ionic polarity, in which the component atoms of positive polarity re likely to become surface cations and the component atoms of negative polarity are likely to become surface radicals. For such compound semiconductors in anodic dissolution, the valence band mechanism predominates over the conduction band mechanism with increasing band gap and increasing polarity of the compounds. 

From the Mott-Schottky measurements it follows that the change of the reduction mechanism for copper ions from a valence band to a conduction band mechanism by the addition of 1 M HC l can not be attributed to a shift of the position of the bandedges of the Si. Therefor we suggest that the addition of I M HCI results in the formation of cupric and cuprous chloride species resulting in a shift of the redox Fermi level. 

Estimated by comparison with similar redox systems, c.b., conduction band mechanism. 

According to the electron-transfer mechanism of spectral sensitization (92,93), the transfer of an electron from the excited sensitizer molecule to the silver haHde and the injection of photoelectrons into the conduction band ate the primary processes. Thus, the lowest vacant level of the sensitizer dye is situated higher than the bottom of the conduction band. The regeneration of the sensitizer is possible by reactions of the positive hole to form radical dications (94). If the highest filled level of the dye is situated below the top of the valence band, desensitization occurs because of hole production. 

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

The mechanism involves photochemical production of a free electron in the conduction band (e b ) nd a corresponding hole (h b ) in th valence band. Both of these produce H2O2 and thence hydroxyl radicals. 

All of these one- and two-body models have assumed hard walls for the box (potential V = 00 for r > R). The actual potential energy difference between the lower edge of the conduction band of the macrocrystal and the vacuum level amounts to 3.8 eV. This potential dqpth was used in the quantum mechanical calculation of curve b. It is seen that the energy lowering is substantial, particularly at small diameters. 

We can conclude now that one electron returns to the conductivity band during each act of formation of the vacant site to adsorb sensitizer. Because adsorption centers Zr(. ) are not accounted for by (2.81) the energetics of the process does not depend on the manner in which R is closing in A, i.e. on the fact which recombination mechanism (either Langmuire-Hinshelwood or Ili-Ridil) takes place. 

A mechanism which has been proposed for the operation of this type of photocell is illustrated in Figure 10.7, although it is not fully established in detail. In the proposed mechanism, it is suggested that absorption of light by the dye (or sensitiser, S) raises the dye to its first excited state S. In the excited state, S releases an electron into the conducting band of the titanium dioxide electrode, at the same time forming oxidised sensitiser, S +. At the counter-electrode, an electron is transferred to the... 

The mechanism proposed by the authors is related to the tendency of 02 to capture electrons transferred to the Ti02 conduction band from the excited dye. The dye molecules accept holes and such cationic species react with the negatively charged 02. Such a reaction induces degradation of dye molecules. 

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