Semiconductor electrode polarization

We consider a transfer of redox electrons at semiconductor electrodes polarized at an overvoltage t relative to the equilibrium redox potential (the Fermi level cfcredox)). The transfer current of redox electrons is given in Eqn. 8-54 by the arithmetic sum of the electron current via the conduction band, in(ti) - (0(11) > and the hole current via the valence band, ij(ii) - i (Ti) ... 

The discussion of Eq. (4.5.7) has shown that the potential of a polarized semiconductor electrode at sufficiently high electrolyte concentrations is... 

Degeneracy can be introduced not only by heavy doping, but also by high density of surface states in a semiconductor electrode (pinning of the Fermi level by surface states) or by polarizing a semiconductor electrode to extreme potentials, when the bands are bent into the Fermi level region. 

Figure 5-41 illustrates the profile of electron level across the interfadal double layer of a semiconductor electrode (A) in the state of band edge level pinning and (B) in the state of Fermi level pinning. In Fig. 5-41 the cathodic polarization... 

Fig. S-41. Band edge levels and Fermi level of semiconductor electrode (A) band edge level pinning, (a) flat band electrode, (b) under cathodic polarization, (c) under anodic polarization (B) Fermi level pinning, (d) initial electrode, (e) under cathodic polarization, (f) imder anodic polarization, ep = Fermi level = conduction band edge level at an interface Ev = valence band edge level at an interface e = surface state level = potential across a compact layer.

Such an interfacial degeneracy of electron energy levels (quasi-metallization) at semiconductor electrodes also takes place when the Fermi level at the interface is polarized into either the conduction band or the valence band as shown in Fig. 5-42 (Refer to Sec. 2.7.3.) namely, quasi-metallization of the electrode interface results when semiconductor electrodes are polarized to a great extent in either the anodic or the cathodic direction. This quasi-metallization of electrode interfaces is important in dealing with semiconductor electrode kinetics, as is discussed in Chap. 8. It is worth noting that the interfacial quasi-metallization requires the electron transfer to be in the state of equilibrimn between the interface and the interior of semiconductors this may not be realized with wide band gap semiconductors. 

It is characteristic of metal electrodes that the reaction current of redox electron transfer, under the anodic and cathodic polarization conditions, occurs mostly at the Fermi level of metal electrodes rather than at the Fermi level of redox particles. In contrast to metal electrodes, as is discussed in Sec. 8.2, semiconductor electrodes exhibit no electron transfer current at the Fermi level of the electrodes. 

The distribution of the exchange transfer current of redox electrons o(e), which corresponds to the state density curves shown in Fig. 8-11, is illustrated for both metal and semiconductor electrodes in Fig. 8-12 (See also Fig. 8-4.). Since the state density of semiconductor electrons available for electron transfer exists only in the conduction and valence bands fairly away from the Fermi level nsc), and since the state density of redox electrons available for transfer decreases remarkably with increasing deviation of the electron level (with increasing polarization) from the Fermi level CFciiEDax) of the redox electrons, the exchange transfer current of redox electrons is fairly small at semiconductor electrodes compared with that at metal electrodes as shown in Fig. 8-12. 

Fig. 8-aO. State density of redox electrons and reaction current for a redox electron transfer at a semiconductor electrode sli d>tly polarized in anodic direction n = sc dashed curve s band edge levels in equilibrium (Fig. 8-16) solid curve = band edge levels in anodic polarization. 

Fig. 8-24. Redox reaction currents via the conduction and the valence bands of semiconductor electrode as functions of electrode potential of semiconductor anodic polarization corresponds to Figs. 8-20, 8-21 and 8-22. i (i )= anodic (cathodic) current in (ip) = reaction crnrent via the conduction (valence) band BLP = band edge level pinning FLP = Fermi level pinning.

Fig. 8-27. Polarization curves for transfer of redox electrons at n-type and p-type semiconductor electrodes solid curve near Egaxa = reaction with the Fermi level of redox electrons dose to the valence band edge dashed curve near F redok = reaction with the Fermi level of redox electrons dose to the conduction band edge dot-dash curve (FLP)= reaction in the state of Fermi level pinning.

Fig. 8-28. Cathodic polarization curves for several redox reactions of hydrated redox particles at an n-type semiconductor electrode of zinc oxide in aqueous solutions (1) = 1x10- MCe at pH 1.5 (2) = 1x10 M Ag(NH3) atpH12 (3) = 1x10- M Fe(CN)6 at pH 3.8 (4)= 1x10- M Mn04- at pH 4.5 IE = thermal emission of electrons as a function of the potential barrier E-Et, of the space charge layer. [From Memming, 1987.]...

As anodic or cathodic polarization increases, the band level bending in a space charge layer (a depletion layer) becomes steeper, and the electron tunneling through the space charge layer is then ready to occur particularly in semiconductor electrodes of high concentrations of donors or acceptors where the space charge layer is thin. 

Figure 8-42 illustrates the anodic and cathodic polarization curves observed for an outer-sphere electron transfer reaction with a typical thick film on a metallic niobium electrode. The thick film is anodically formed n-type Nb206 with a band gap of 5.3 eV and the redox particles are hydrated ferric/ferrous cyano-complexes. The Tafel constant obtained from the observed polarization curve is a- 0 for the anodic reaction and a" = 1 for the cathodic reaction these values agree with the Tafel constants for redox electron transfers via the conduction band of n-lype semiconductor electrodes already described in Sec. 8.3.2 and shown in Fig. 8-27. 

Fig. 9-10. Polarization curves of anodic dissolution and cathodic deposition of n-type and p-type covalent semiconductor electrodes n-SC (p-SC) = n-type (p-type) semiconductor electrode i (i ) = anodic dissolution (cathodic deposition) current Cp = Fermi level.

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. 

Figure 9-16 illustrates the polarization curves for the anodic oxidative and the cathodic reductive dissolution of ionic compound semiconductors. The anodic oxidative dissolution proceeds readily at p-type semiconductor electrodes in which the mqjority charge carriers are holes whereas, the cathodic reductive dissolution proceeds readily at n-type semiconductor electrodes in which the majority charge carriers are electrons. 

Fig. 9-16. Polarization curves of anodic oxidative dissolution and cathodic reductive dissolution of semiconductor electrodes of an ionic compound MX iiixcp) (iMxh )== anodic oxidative (cathodic reductive) dissolution current solid curve = band edge level pinning at the electrode interface, dashed curve = Fermi level pinning.

Charge transfer reactions on semiconductor electrodes proceed under the condition of anodic and cathodic polarization in which the Fermi level epfsc) is different either from the Fermi level Eputicox) of redox electron transfer reactions or from the equivalent Fermi level ep,ioN) of ion transfer reactions. For redox electron transfer reactions, thermodynamic requirement for the anodic and cathodic reactions to proceed is given by the following inequalities ... 

Fig. 10-10. Polarization curves for electrode reactions at n-type and p type semiconductor electrodes in the dark and in a photoezdted state dashed curve = dark solid curve = photoexcited V (i )= anodic (cathodic) current in the dark tpi, (t ) = anodic (cathodic) current in a photoexcited state.

Fig. 10-14. Energy levels and polarization curves (current vs. potential) for anodic transfer ofphotoexdted holes in oxygen reaction (2 HgO. -t- 4h O24 4 H. ) on a metal electrode and on an n-type semiconductor electrode j = anodic reaction current ep(02 20)- Fermi level of oxygen electrode reaction dCpi, = gain of photoenergy q = potential for the onset of anodic photoexdted ox en reacti . 4 pi, (=-Ae.. le) = shift of potential for the onset of anodic oxygen reaction from equilibrium oxygen potential in the negative direction due to gain of photoenergy in an n-type electrode Eib = flat band potential of an n-type electrode.

Fig. 10-lS. Ehietgy levels and polarization curves of cathodic hydrogen reaction at a metal electrode and at a photoexdted p-type semiconductor electrode = cathodic current ... 

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

Fig. 10-16. Polarization curves for anodic oxygen and cathodic hydrogen redox reactions on an n-type semiconductor electrode of titanium oxide in the dark and in a photoex-cited state i = anodic current in the dark (zero) = anodic current...

Fig. 10-17. Polarization curves for cathodic h3 drogen redox reaction on a photoexdted p-type semiconductor electrode of gallium phosphide equilibrium potential of...

Figure 10-16 shows polarization curves observed for the anodic ox en reaction (anodic hole transfer) and for the cathodic hydrogen reaction (cathodic electron transfer) on an n-type semiconductor electrode of titanium oxide. The data in Fig. 10-16 show that the anodic current due to the transfer of holes (minority... 

Figure 10-17 shows the polarization ciirves for the cathodic hydrogen reaction (cathodic electron transfer) on a p-type semiconductor electrode of galliiun phosphide. The onset potential of cathodic photoexcited hydrogen reaction shifts significantly from the equilibrium electrode potential of the same hydrogen reaction toward the flat band potential of the p-type electrode (See Fig. 10-15.). 

Consequently, by measuring the polarization curves for the transfer reaction of anodic holes both at a photoexdted n-type electrode and at a dark p-type electrode of the same semiconductor, we obtain the relationship between the Fermi level of the electrode (polarization potential E) and the quasi-Fermi level of interfadal holes in the photoexcited n-type dectrode as a function of... 

Fig. 10. Electric potential in semiconductor electrode at flat band situation and at anodic or cathodic polarization relative to the flat band potential...

Finally, if a semiconductor electrode (unlike a metallic one) is polarized, the quantity A

[Pg.312]

Equation (16.40), though rather complex in form, is of remarkable importance because it describes the overall charge transfer process via the valence band at a n-type semiconductor electrode for both anodic and cathodic polarizations. As mentioned earlier, jo represents the generation/recombination rate of holes in the bulk of the semiconductor and jo represents the rate of hole transfer at the interface. The ratio jo/ jy indicates whether the generation/recombination or the surface kinetics of the hole transfer is rate determining. If j0/yv° 1, i.e., the rate is controlled by surface kinetics due to slow hole injection, then... 

Ufb is usually called the flatband potential. The result that the flatband potential differ considerably for n- and p-type electrodes becomes clear by considering the energy scheme in Fig. 7c. In order to reach flatband, an n-type electrode has to be polarized negatively and a p-type positively with respect to equilibrium. In the case of rather strongly doped semiconductors, the two flatband potentials should differ by Eg/e, as actually found for GaP and also for other semiconductor electrodes. The latter conclusion is only valid, however, if the positions of the energy bands are identical for the n- and p-type electrodes. 

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