Valence 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. 

Similarly, for the transfer reaction of redox holes via the valence band mechanism the anodic and cathodic currents, ip(ii) and ip(ii), are obtained, respectively, as shown in Eqns. 8-64 and 8-65 ... 

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. 

In general, the activation energy for the release of electrons from surface atoms into the conduction band increases with increasing band gap of the semiconductor electrode with this increase the capture of holes by the surface atoms and radicals predominates. Except for germanium, most covalent semiconductors have been found to dissolve anodically through this valence band mechanism [Memming, 1983]. 

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. 

When j AF0 of the redox system is greater than jEp, a valence band mechanism is favored (see mammary in Table II). ft is apparent from the above discussion that for a given system the mechanism can change depending on the degree of polarization. 

Reference numbers are in parentheses, v.b., valence band mechanism. 

In this chapter, we will be dealing mainly with sensitization of n-type semiconductor electrodes where oxidation of the dye takes place through transfer of an electron from the photoexcited dye to the conduction band of the semiconductor. The semiconductor is used as an anode and the charge transfer process monitored as anodic photocurrent. Though not discussed here, reduction of photoexcited dyes is also known to occur through a valence band mechanism. This can only be observed in compounds with a high hole mobility such as SiC or GaP. 

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. 

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. 

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

In order to understand the observed shift in oxidation potentials and the stabilization mechanism two possible explanations were forwarded by Kotz and Stucki [83], Either a direct electronic interaction of the two oxide components via formation of a common 4-band, involving possible charge transfer, gives rise to an electrode with new homogeneous properties or an indirect interaction between Ru and Ir sites and the electrolyte phase via surface dipoles creates improved surface properties. These two models will certainly be difficult to distinguish. As is demonstrated in Fig. 25, XPS valence band spectroscopy could give some evidence for the formation of a common 4-band in the mixed oxides prepared by reactive sputtering [83],... 

No other products were detected in the gas phase. The amount of H2 produced from 85 pmol of m-C16H34 was 4.14 mmol, which is close to the stoichiometric value. One can note that reaction 2.72 stoichiometry resembles that of steam reforming of hexadecane. The authors proposed the following mechanism, which involves the initial generation of active species holes (p+) in the valence band and electrons (e ) in the conduction band of... 

The stable configuration for the H—P pair is predicted by all of the quantum-mechanical calculations to have a hydrogen located at the silicon antibonding site (Si—AB). A model is shown in Fig. 7b, where a phosphorus lone pair lies along the (111) axis and is energetically in the valence band. Here, the theoretical predictions of the H vibrational frequency have been mixed, with the H—Si interaction and frequency overestimated by Hartree-Fock and Hartree-Fock-like methods and lower by local-density calculations. 

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