Helmholtz layer surface states

Fig. 6-99. An interfacial electric double layer on semiconductor electrodes a = charge of surface states 0.1 = interfadal charge of adsorbed ions IHP = inner Helmholtz plane.

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

As discussed previously, the surface states responsible for the reduction peak could be intrinsic surface states or states associated with a surface-attached intermediate in the series of reactions leading to O-evolution. The latter possibility was deemed to be more likely since no change in voltage across the Helmholtz layer (no change in capacitance) was observed when these states are in the oxidized form. 

This picture is subject to two caveats. First, in the metal, the potential difference is indeed negligible in the bulk, but directly inside, for about 1 A, there is a potential difference. Correspondingly, some semiconductors will have surface states (Section 10.5.2) and then the Helmholtz layer returns. 

Fig. 10.8. A schematic diagram of a p-type semicon-ductor/solution interface at two applied potentials, I/, and V2, in the absence of surface states. The diagram shows the potential drop in the solution s Helmholtz layer and exhibits no variation in Helmholtz layer potential difference with applied potentials. The Fermi level is not pinned.

Fig. 10.15. p-Type semiconductor/solution interface in the presence of high-density surface states. The potential difference in the Helmholtz part of the double layer, (i.e., that in the solution) is greatly increased compared with a situation with a negligible number of surface states. Correspondingly, the potential difference within the semiconductor is greatly diminished compared with one containing negligible surface states. 

It is possible to determine how surface states affect the distribution of potential in the interface if one assumes that the solution concerned is relatively concentrated so that the excess electric charge on the solution side of the interface is predominantly in the Helmholtz (H) layer. Then... 

The relative changes in VH and Vsc as a function of surface state density are shown in Fig. 10.20. At low surface state density (<1012), the potential drop across the Helmholtz layer is small and remains almost constant with a change in electrode potential. However, at high surface state densities (>1013), the potential drop in the Helmholtz region increases and exceeds the potential drop in the space charge region for surface state densities greater than 5 x 1013 cm 2. 

Jaegerman (1997) calls photoelectrochemical reactions that occur at high surface state configurations Bardeen model reactions because Bardeen was the first to discuss surface states. Here they are called Helmholtz reactions because the potential difference at interfaces at which they predominate is largely in the Helmholtz layer. 

Calculate the potential difference in the Helmholtz layer in the solution for a semiconductor in which the surface state density is 1014 cm-2 (assume the effective dielectric constant is 6 and the thickness of the double layer 5 A). As an approximation, neglect the contribution due to oriented dipoles of adsorbed water. (Bockris)... 

Typical values of transfer coefficients a and ji thus obtained are listed in Table 4 for single crystal and polycrystalline thin-film electrodes [69] and for a HTHP diamond single crystal [77], We see for Ce3+/ 41 system (as well as for Fe(CN)63 /4 and quinone/hydroquinone systems [104]), that, on the whole, the transfer coefficients are small and their sum is less than 1. We recall that an ideal semiconductor electrode must demonstrate a rectification effect in particular, a reaction proceeding via the valence band has transfer coefficients a = 0, / =l a + / = 1 [6], Actually, the ideal behavior is rarely the case even with single crystal semiconductor materials fabricated by advanced technologies. Departure from the ideal semiconductor behavior is likely because the interfacial potential drop is located in part in the Helmholtz layer (due e.g. to a high density of surface states), or because the surface states participate in the reaction. As a result, the transfer coefficients a and ji take values intermediate between those characteristic of a semiconductor (0 or 1) and a metal ( 0.5). 

Oskam et al. [66] have used IMPS to investigate the role of surface states at the n-Si(lll)/NH4F interface. In this case, the redox reaction is simpler, and appears not to involve holes trapped at surface states. This is probably due to the presence of a surface oxide layer. Electron transfer is evidently exceptionally slow in this case, since these authors observed a modulated photocurrent even at potentials far from the flatband potential where recombination is expected to be negligible. Accumulation of holes modifies the potential drop across the Helmholtz (and presumably also surface oxide region), leading to a capacitive charging current. This effect has also been treated in more detail by Peter et al. [71]. 

The solvent molecules form an oriented parallel, producing an electric potential that is added to the surface potential. This layer of solvent molecules can be protruded by the specifically adsorbed ions, or inner-sphere complexed ions. In this model, the solvent molecules together with the specifically adsorbed, inner-sphere complexed ions form the inner Helmholtz layer. Some authors divide the inner Helmholtz layer into two additional layers. For example, Grahame (1950) and Conway et al. (1951) assume that the relative permittivity of water varies along the double layer. In addition, the Stern variable surface charge-variable surface potential model (Bowden et al. 1977, 1980 Barrow et al. 1980, 1981) states that hydrogen and hydroxide ions, specifically adsorbed and inner-sphere... 

Type II. Equilibrium is established between the surface states and the majority carriers within the semiconductor. Under these circumstances, a fraction of the potential change will be dropped across the depletion layer and a fraction across the Helmholtz layer. If a redox couple is present in solution, and the kinetics of electron transfer between this and the surface states are also rapid, then a large dark current will be found. 

The expected Tafel slope of 60mV/decade is not always found. There are a number of reasons for this, aside from kinetic effects in the bulk of the semiconductor. The kinetic effects associated with faradaically active surface states is of considerable significance, as shown below, but another common problem is that part of the potential change may appear across the Helmholtz layer rather than across the depletion layer. A well-known case in point is germanium, for which the surface is slowly converted from "hydride to "hydroxylic forms as the potential is ramped anodically. This conversion gives rise to a change in the surface dipole and hence Aij/ AT. In fact, the anodic dissolution of p-germanium is found to follow a law [106]... 

If Nt rises above 1013cm 2, it may be anticipated that the complete emptying of such states will affect the potential drop in the Helmholtz layer. From above, the change in potential is rO = rNtfJNM, where Nm is the maximum possible number of surface states. Writing y = riVt/iVM, we may approximate y from the estimated double-layer capacitance of 10-20/iFcm-2 this gives y (0.08-0.16) x 10"13 Nt V. The rate constants k, and ka will also depend on yft specifically... 

At oxide semiconductor electrode-electrolyte interfaces, with no contribution from surface states, the electrical potential drop exhibits three components the potential drop across the space-charge region, sc, across the Helmholtz layer, diffuse double layer, d, the latter becoming negligible in concentrated electrolytes... 

In the non-steady state, changes of stoichiometry in the bulk or at the oxide surface can be detected by comparison of transient total and partial ionic currents [32], Because of the stability of the surface charge at oxide electrodes at a given pH, oxidation of oxide surface cations under applied potential would produce simultaneous injection of protons into the solution or uptake of hydroxide ions by the surface, resulting in ionic transient currents [10]. It has also been observed that, after the applied potential is removed from the oxide electrode, the surface composition equilibrates slowly with the electrolyte, and proton (or hydroxide ion) fluxes across the Helmholtz layer can be detected with the rotating ring disk electrode in the potentiometric-pH mode [47]. This pseudo-capacitive process would also result in a drift of the electrode potential, but its interpretation may be difficult if the relative relaxation of the potential distribution in the oxide space charge and across the Helmholtz double layer is not known [48]. 

When the Fermi level is shifted in the semiconductor under very high anodic polarization, degeneracy of surface states sets in. The surface then behaves like that of a metal and an effective Helmholtz double layer forms at the surface. 

Figure 29. Calculated current-potential characteristics for direct (dashed lines, 0/cm ) and surface state mediated electron transfer between an -type semiconductor electrode and a simple redox system. The plots show the transition from ideal diode behavior to metallic behavior with increasing density of surface states at around the Fermi-level of the solid (indicated in the figures). This is also clear from the plots below, which show the change of the interfacial potential drop over the Helmholtz-layer (here denoted as A(Pfj) with respect tot the total change of the interfacial potential drop (here denoted as A(p). Results from D. Vanmaekelbergh, Electrochim. Acta 42, 1121 (1997).

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