Cathodic hole injection reactions

Generation of holes in n-type electrodes may result not only from photoexd-tation but also from cathodic hole iiyection according to Eqn. 10-47  

The current of cathodic hole iiyection, i, can be obtained from Eqn. 10-37. 

The holes injected by a cathodic redox reaction (Eqn. 10-47) diffuse toward the electrode interior and recombine with electrons of the m ority charge carriers in the same way as photogenerated holes, thereby producing a cathodic current inc, which is equivalent to the rate of recombination of holes. The cathodic current i actually observed is the sum of the current of recombination inc and the limiting diffusion current of holes ip.um as shown in Eqn. 10-48  

Equation 10-48 is obtained by excluding the photocurrent ipb from the reaction current of Eqn. 10-44. In the stationary state, the total ciurent i in Eqn. 10-48 equals the transfer current of cathodic redox holes across the electrode interface. 

The Fermi level n r of the electrode corresponds to the polarization potential JE(.i) of the hole-ii jected n-type electrode, and the quasi-Fmmi level pCp of interfacial holes corresponds to the polarization potential pE(i) of a p- q e electrode of the same semiconductor. Then, Eqn. 10-48 becomes Eqn. 10-49  

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For the cathodic reaction of the corrosion, there are two different charge-transfer processes. One involves holes in the valence band as a cathodic hole-injecting reaction and the other involves electrons in the conduction band as a cathodic electron-emitting reaction ... 

Next, we consider the anodic reaction current of redox electron transfer via the conduction band, of which the exchange reaction current has been shown in Fig. 8-16. Application of a slight anodic polarization to the electrode lowers the Fermi level of electrode fix>m the equilibrium level (Ep(sc)( n = 0) = eiiOTSDca)) to a polarized level (ep(8C)( n) = ep(REDox)- n)withoutchanging at the electrode interface the electron level relative to the redox electron level (the band edge level pinning) as shown in Fig. 8-20. As a result of anodic polarization, the concentration of interfacial electrons, n, in the conduction band decreases, and the concentration of interfadal holes, Pm, in the valence band increases. Thus, the cathodic transfer current of redox electrons, in, via the conduction band decreases (with the anodic electron im ection current, ii, being constant), and the anodic transfer current of redox holes, (p, via the valence band increases (with the cathodic hole injection... 

For cathodic hole injection, the overvoltage tip.sc(i) includes both diffusion and recombination of holes in the electrode this overvoltage occurs in the same cathodic direction as the cathodic hole injection so that tip. sc is the usual overvoltage (a negative quantity in the cathodic reaction) rather than the inverse overvoltage. Then, we obtain Eqn. 10-50 ... 

Fig. 10-24. Electron levels and polarization curves for a redox reaction of cathodic holes both at an n-type and at a p-type electrode of the same semiconductor in the dark curve (1) = polarization curve of cathodic hole injection in n -type electrode curve (2)= polarization curve of cathodic hole injection in p-type electrode (equivalent to a curve representing cathodic hole injection current as a i mction of quasi-Fermi level of interfodal holes in n-type electrode) = cathodic hole injection current N = polarization of cathodic hole ixu ection at potential nECi) of n-type electrode, P = polarization of cathodic hole iqjection at potential pE(.i) of p-type electrode.

Photoetching processes do not always consist of a simple superposition of an anodic and a cathodic partial process and may exhibit various types of complications. Firstly, even in the simple case of the photoetching of GaP single crystals in alkaline OBr solutions, the situation is actually more complex than depicted above, since at n-type crystals, it appears that the photoetching process itself induces a hole injection reaction and hence and electroless etching effect [24]. Initially, OBr is reduced at the GaP surface via the current-doubling mechanism (as is concluded from photocurrent measurements at p-type samples) ... 

For homogeneously doped silicon samples free of metals the identification of cathodic and anodic sites is difficult. In the frame of the quantum size formation model for micro PS, as discussed in Section 7.1, it can be speculated that hole injection by an oxidizing species, according to Eq. (2.2), predominantly occurs into the bulk silicon, because a quantum-confined feature shows an increased VB energy. As a result, hole injection is expected to occur predominantly at the bulk-porous interface and into the bulk Si. The divalent dissolution reaction according to Eq. (4.4) then consumes these holes under formation of micro PS. In this model the limited thickness of stain films can be explained by a reduced rate of hole injection caused by a diffusional limitation for the oxidizing species with increasing film thickness. 

Fig. 13 Recombination losses occurring under forward bias in a typical OPV device. Holes injected from the anode Fermi level into the HOMO level ( ) of the donor and electrons injected from the cathode Fermi level ( f,c) into the LUMO level ( J of the acceptor are transported to the D/A interface. Coulombic attraction between holes and electrons yields the (D A ) CT state with energy Ect- Charge recombination reaction (D A ) D + A occurs with rate constant...

Kelly et al., in their study on the behavior of bisymmetrical molecules, such as Br2 and H2O2, at the GaAs surface, observed an Interdependence between the rates of chemical etching and of cathodic reduction, as well as an enhanced anodic dark current at n-type electrodes [79, 80] (see also Sec. 3.2.2). They concluded that hole injection, electron capture, and chemical etching reactions are coupled through a biradical-type common precursor, part of which is Xj, as defined in Sec. 2. The proposed reaction scheme is shown in Fig. 18. Such a mechanism, moreover, ac-... 

Br/Br. Figure 6.19 shows the dark i-Vcurves ofp-Si and -Si for the reactions involving the reduction of Br2 in lOM HF + 0.5M HBr + lOmM Br2 solution.The cathodic current on p-Si in the dark is due to hole injection into the valence band. On the other hand, the cathodic plateau current on n-Si is much larger than on p-Si indicating that the reduction process is mainly a conduction band process. When conduction band electrons are not available, the reduction of Br2 may proceed via the valence band as is the case with -Si in the dark. The current plateau at cathodic potentials on bothp-Si and -Si is limited by the diffusion of Br2. The small plateau current on p-Si indicates that only a small fraction of Br2 is reduced electrochemically and most of the... 

Concerning valence band processes, one observes the opposite effect. Here the anodic current at a p-type electrode rises with increasing anodic overvoltage because sufficient holes are available. At an n-type electrode, only a small current occurs which can be enhanced again by excitation. In the case of a cathodic current at a p-type electrode, the holes injected into the valence band, are easily transported to the rear contact. Accordingly, valence band processes at p-type electrodes are majority carrier reactions. The kinetics of this process are determined by Eq. (7.61b) and the corresponding theoretical /v- curves are given in Fig. 7.14 for various / values. 

Therefore the anodic and cathodic reactions are coupled through the formation of Si sites. The fact that Ni is deposited at pH=8 and not at pH<1 can be explained within the framework of the above set of reactions. At pH<1 two facts are against Ni deposition (i) the Si dissolution rate is very small (<0.1 nm/min), and (ii) dissolution is simply balanced by the HER. The kinetics of HER is actually faster than the reduction of Ni2 ions since the redox potential E0[Ni2+/Ni] < Eo[H+/H2]. In other words, the weak dissociation of Si-H bonds and the strong concentration of protons at low pH favor the HER as cathodic counter-reaction. The mixed potential is thus established without participation of the Niz+ ions, which cannot even withdraw the bonding (VB) electrons of the Si-H bond (hole injection). 

An electrochemical study of platinum and nickel deposition on silicon from fluoride solutions at the open circuit potential is presented. In the steady-state situation, the silicon oxidation current is balanced with a cathodic current such as to yield net zero current. In the case of platinum, the prevailing cathodic process is platinum deposition by hole injection into the valence band. In nickel solutions, a competition is established between nickel reduction and hydrogen evolution at pH=8 metal deposition is the prevailing reaction, either through a valence band process on p-type silicon or through a conduction band process on n-type. On the contrary, at pH<1 the hydrogen evolution reaction is kinetically faster and nickel deposition is not observed. The anodic and cathodic processes are coupled through the formation of silicon surface states. 

Relationships of other type are observed in the case where both the conjugated reactions proceed through the same band (Fig. 13b). For example, the cathodic reaction (42b) can take place with the participation of valence electrons rather than conduction electrons, as was assumed above. Thus, reduction of an oxidizer leads to the injection of holes into the semiconductor, which are used then in the anodic reaction of semiconductor oxidation. In other words, the cathodic partial reaction provides the anodic partial reaction with free carriers of an appropriate type, so that in this case corrosion kinetics is not limited by the supply of holes from the bulk of a semiconductor to its surface. Here the conjugated reactions are in no way independent ones. 

In the case of a cathodic reaction via the valence band, minority carriers are injected into an n-type electrode in the dark. The injected holes diffuse into the bulk of the semiconductor until they recombine with the electrons (Fig. 32), and the current is then determined by the difference of the two quasi-Fermi levels Ep, and Efr.p, i.e. 

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