Electron transfer at the semiconductor-electrolyte interface

With respect to electron transfer processes, semiconductor electrodes are different from their metal counterparts in two ways. First, the band structure, characterized by a band gap separating the conduction and valence band, will express 

Note that lezyl should not be too small—the Tafel law holds only beyond a bias that satisfies kz k[jT. When rj — 0 the net current which results from the balance between the direct and reverse reactions, must vanish like rj. This imphes that the Tafel behavior is always preceded by a low bias Ohmic regime. 

5 The Tafel slope is defined in the electrochemistry hterature as b = drj/d log /)c,t = 2.3kg7 /(ae) where a is the slope defined above (sometimes referred to as the transfer coefficient), which this theory predicts to take the value 0.5. 

Let us assume for simplicity that all the potential falls on the semiconductor. In this case (Fig. 17.3) the energy levels on the electrolyte side remain rmchanged with 

in taking infinities as limits we assmne that the energy range between the bottom of the valence band and the top of the conduction band fully encompasses the range in which the integrands in (17.17) are nonzero. 

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There is a growing tendency to invoke surface states to explain electron transfer at semiconductor-electrolyte interfaces. Too frequently the discussion of surface states is qualitative with no attempt to make quantitative estimates of the rate of surface state reactions or to measure any of the properties of these surface states. This article summarizes earlier work in which charge transfer at the semiconductor-electrolyte interface is analyzed as inelastic capture by surface states of charge carriers in the semiconductor bands at the surface. This approach is shown to be capable of explaining the experimental results within the context of established semiconductor behavior without tunneling or impurity conduction in the bandgap. Methods for measuring the density and cross section of surface states in different circumstances are discussed. 

As discussed above only surface charging is of real importance for the interpretation of charge transfer at the semiconductor/electrolyte interface. The formation of a conducting layer leads to a solid state device, for which there is no need to be placed directly into the electrolyte. An insulating layer, on the other hand, can not improve charge transfer, except perhaps for very thin layers that allow electron tunneling. The band position at oxidized parts of the surface is not known. 

The thermodynamic feasibility of redox reactions at the semiconductor-electrolyte interface can be assessed from thermodynamic considerations. Since typical redox potentials for many redox couples encountered in electrolytes of natural or technical systems often lie between the band potentials of typical semiconductors, many electron transfer reactions are (thermodynamically) feasible (Pichat and Fox, 1988). With the right choice of semiconductor material and pH the redox potential of the cb can be varied from 0.5 to 1.5 V and that of the vb from 1 to more than 3.5 V (see Fig. 10.4). 

As shown in Fig. 3.13(b) and 3.13(c) when ratio n/nsfl is less than or greater than 1 the system is in non-equilibrium resulting in a net current, with the electron transfer kinetics at the semiconductor-electrolyte interface largely determined by changes in the electron surface concentration and the application of a bias potential. Under reverse bias voltage, Vei > 0 and ns,o > ns as illustrated in Fig. 3.13(b), anodic current will flow across the interface enabling oxidized species to convert to reduced species (reduction process). Similarly, under forward bias, Ve2 < 0 and ns > ns,o as illustrated in Fig. 3.13(c), a net cathodic current will flow. 

Figure 4.12 is an illustration of the potential distribution for n-type semiconductor particles at the semiconductor-electrolyte interface. There are two limiting cases of equation (4.8.11) for photo-induced electron transfer in semiconductors. For large particles the potential drop within the semiconductor is defined by ... 

The electron transfer reactions at the semiconductor/electrolyte interface occur either via the conduction band or the valence band. The total current is therefore given by the sum of four partial currents, denoted as represent electron transfer via the conduction anc valence bands, respectively, and the superscripts, a and c, indicate anodic anc cathodic processes, respectively. Let us assume nereafter that the electron transfer occurs only via the conduction band. In a simple case where the concentration of the electrolyte is sufficiently high and only the overvoltages at the Helmholtz layer (tjh) and in the space charge layer (rjsc) are important, the ica and cc can be given as follows4)... 

We have thus far talked about the chemisorption of ions at the semiconductor/electrolyte interface and charge transfer in the semiconductor surface layer. The main charge transfer process of interest is the transfer of electrons and holes across the semiconductor/electrolyte interface to the desired electrolyte species resulting in their oxidation or reduction. For any semiconductor, electrode charge transfer can occur with or without illumination and with the junction biased in the forward or reverse direction. 

It is generally accepted that three major processes limit the photoelectrochemical current in semiconductors after a bandgap excitation [76]. These processes are schematically illustrated in the band diagram shown in Fig. 3.2. The bold arrows show the desired processes for efficient water splitting PEC cell after a bandgap excitation the transport of electrons to the back contact, the transfer of the hole to the semiconductor surface and the oxidation of water at the semiconductor/electrolyte interface. The three major limiting processes are a) bulk recombination via bandgap states, or b) directly electron loss to holes in the... 

At the semiconductor-electrolyte interface, the electron transfer rate depends on the density of energy states on both sides of the interface. For example, the electron transfer from the redox system to the conduction band of the semiconductor generates an anodic current... 

In this section, we first consider a general model of the faradaic processes occurring at the semiconductor-electrolyte interface due to Gerischer [11]. From Gerischer s model, using the potential distribution at the interface, we may derive a Tafel-type description of the variation of electron transfer with potential and we will then consider the transport limitations discussed above. We then turn to the case of intermediate interactions, in which the electron transfer process is mediated by surface states on the semiconductor and, finally, we consider situations in which the simple Gerischer model breaks down. 

Electron-transfer processes at the semiconductor/electrolyte interface are strongly affected by the density of available carriers (electrons and holes) in the semiconductor at the interface. The observed i-E behavior differs from that at metals and carbon (Chapter 3), where there is always a large density of carriers in the conductor. In the dark, electron-transfer processes involving species in solution with energy levels in the band gap of the semiconductor (Figure 18.2.5Z ) are usually dominated by the majority carrier. Thus, moderately doped w-type materials can carry out reductions, but not oxidations. That is, there are electrons available in the conduction band to transfer to an oxidized solution species, but few holes to accept an electron from a reduced species. The current for a reduction of species O at an w-type semiconductor is given by... 

The pressing need for a detailed description of the semiconductor-electrolyte interface is becoming increasingly apparent Gerischer has given an excellent and timely general account of photoassisted interfacial electron transfer, in which particular attention is paid to the role of surface states at the semiconductor-electrolyte interface. Kowalski et al have used the SCF-A -scattered wave method to calculate the position and character of surface states at various characteristic interfaces, and then used these results to develop a model of photoelectrolysis at Ti02 surfaces. 

R. H. Wilson, Electron transfer processes at the semiconductor-electrolyte interface, CRC Crit. Rev. Solid State Mater. Sci. 10 (1980) 1-41. 

For n-type semiconductors, the fifth requirement implies that hole transfer across the semiconductor/electrolyte interface should be sufficiently fast in order to compete with the anodic decomposition reaction. More generally, interfacial charge transfer should be fast enough to avoid the accumulation carriers at the surface, as this would lead to a decrease of the electric field and a concomitant increase in electron-hole recombination. To improve the kinetics of charge transfer, catalyti-cally active surface species can be added. Examples of effective oxygen evolution catalysts are Ru02 [87], IrO [88], and Co-based compounds [64], whereas Pt, Rh [89], Cr-Rh, RuOa, or NiO [73, 90] are usually employed as a catalysts for hydrogen evolution. 

Figure 1. (A) Schematic representation of electron-hole formation and electron transfer reaction at the semiconductor particle. (B) Thermodynamic constraints for electron exchange at illuminated semiconductor-electrolyte interfaces (A=electron acceptor, D=electron donor).

The reason for the exponential increase in the electron transfer rate with increasing electrode potential at the ZnO/electrolyte interface must be further explored. A possible explanation is provided in a recent study on water photoelectrolysis which describes the mechanism of water oxidation to molecular oxygen as one of strong molecular interaction with nonisoenergetic electron transfer subject to irreversible thermodynamics.48 Under such conditions, the rate of electron transfer will depend on the thermodynamic force in the semiconductor/electrolyte interface to... 

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