Semiconductor electrodes anodic polarization

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. 

Fig. 8-21. State density of redox electrons and reaction current ibr a redox electron transfer at a semiconductor electrode further polarized beyond that in Fig. 8-20 in anodic direction T =T gc.

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.

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. 

Fig. 8-16. Electron state density for a redox electron transfer reaction of h3rdrated redox particles at semiconductor electrodes (a) in the state of band edge level pinning and (b) in the state of Fermi level pinning dashed curve = band edge levels in reaction equilibrium solid curve = band edge levels in anodic polarization e p,sq = Fermi level of electrode in anodic polarization e v and c c = 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.

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.

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...

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... 

Fig. 10-23. Energy levels and polarization curves for a redox reaction of anodic redox holes at a photoexdted n-type electrode and at a dark p-type electrode of the same semiconductor curve (1) = polarization curve of anodic transfer of photoexdted holes at an n-type electrode curve (2)= polarization curve of anodic transfer of holes at a p-type electrode in the dark (equivalent to a curve representing anodic current as a function of quasi-Fermi level of interfadal holes in a photoexdted n-type electrode) i = anodic transfer current of holes Eredox = equilibriiun potential of redox hole transfer N = anodic polarization at potential n (t) of a photoexdted n-type electrode P = anodic polarization at potential pE(i) of a dark p-type electrode.

Fig. 10-32. Polarization curves of cell reaction for photoelectrolytic decomposition of water at a photoexdted n-type anode and at a photoezdted p-type cathode solid curve n-SC s anodic polarization curve of oxygen evolution at photoexdted n Qpe anode (Fermi level versus current curve) dashed curve n-SC = anodic polarization curve of oxygen evolution at dark p>type anode of the same semiconductor as photoexdted n-type anode (equivalent to the curve of current versus quasi-Fermi level of interfadal holes in photoezdted n-type anode) solid curve p-SC = cathodic polarization curve of hydrogen evolution at photoexdted p-type cathode (Fermi level versus current curve) dashed curve n-8Cr = cathodic polarization curve of hydrogen evolution at dark n-type electrode of the same semiconductor as photoezdted p-type cathode (equivalent to the curve of current versus quasi-Fermi level of interfadal electrons in photoexdted p-type cathode) > > = flat band potential of n-type (p-type) electrode nn.sc (v p sc) = inverse overvoltage for generation of photoexdted electrons (holes) in a p-type (n-type) electrode.

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

An interesting example of the kinetic effect in semiconductor photocorrosion is photopassivation and photoactivation of silicon (Izidinov et al., 1962). Silicon is an electronegative element, so it should be dissolved spontaneously and intensively in water with hydrogen evolution. But in most of aqueous solutions the surface of silicon is covered with a nonporous passivating oxide film, which protects it from corrosion. The anodic polarization curve of silicon (dashed line in Fig. 20) is of the form characteristic of electrodes liable to passivation as the potential increases, the anodic current first grows (the... 

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... 

A shift in the band edge position also explains the observed dependence of the hole injection rate on the electrode polarization. Fig. 11 exempliHes this by the total current-potential behavior of a (111) n-GaP electrode in alpine Fe(CN) solutions (pH = 13), together with the partial current due to the injection of holes (revealed by rotating ring-disk experiments, see ref. [73]). Also at p-GaP, it was shown that the hole injection rate is lower with anodic polarization than with cathodic polarization. The potential-dependent position of the band edges is ascribed to a potential-dependent accumulation of positive charges (holes, surface decomposition intermediates,. ..) at the semiconductor surface [62, 73]. 

It is further clear from Fig. 5.19 that the n-electrode has to be polarized cathodically with respect to the equilibrium potential, and the p-electrode anodically, in order to reach the corresponding flatband situation (see lower part of Fig. 5.19), provided that the positions of the energy bands at the surface are the same for the two types of electrodes. Keeping in mind that the electrode potential refers to the Fermi level of the electrode, then the difference of flatband potentials corresponds exactly to the difference of the two Fermi levels. Since the Fermi level in the bulk of a semiconductor with the usual doping (>1() cm ) is rather close to the corresponding band, the difference in the flatband potentials approximates the bandgap of the semiconductor as found with GaP. 

The same type of arguments prove that the anodic decomposition reaction occurs via the valence band. Here we see that the corresponding anodic current at p-GaAs increases steeply with increasing anodic polarization whereas a very small anodic current is found with n-type electrodes. The latter could be increased by light excitation. Accordingly, holes from the valence band are required for the anodic decomposition of the semiconductor. It should be emphasized here that not holes but electrons are actually transferred across the interface, but an injection of electrons into the valence band is only possible if holes are present at the semiconductor surface. 

Interestingly, the anodic dark current at n-Ge electrodes increases considerably upon addition of the oxidized species of a redox system, for instance Ce" ", to the electrolyte, as shown in Fig. 8.4 [7]. The cathodic current is due to the reduction of Ce. The latter process occurs also via the valence band (see Chapter 7), i.e. since electrons are transferred from the valence band to Ce", holes are injected into the Ge electrode. Under cathodic polarization these holes drift into the bulk of the semiconductor where they recombine with the electrons (majority carriers) and the latter finally carry the cathodic current. In the case of anodic polarization, however, the injected holes remain at the interface and are consumed for the anodic decomposition of germanium, as illustrated in the insert of Fig. 8.4. Accordingly, the cathodic and anodic current should be compensated to zero. Since, however, the anodic current is increased upon addition of the redox system there is obviously a current multiplication involved, similarly to the case of two-step redox processes (see Section 7.6). Thus, in step (e) (Fig. 8.1) electrons are injected into the conduction band. This experimental result is a very nice proof of the analytical result presented by Brattain and Garrett [3]. 

Table 8.1 Decomposition products of various semiconductor electrodes during anodic and cathodic polarization...

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