Semiconductor-electrolyte interface model

In contrast to metal electrodes, for a semiconductor-electrolyte interface most of the potential drop is located in the semiconductor making it difficult to study interfacial processes using potential perturbation techniques [11,20,55,58,60-65,75-78]. H. Gerischer [76] proposed a model in which electrons and holes are considered as individual interfacial reactants. Distinct and preferential electron transfer reactions involve either the conduction band or valence band as dependent on the nature of the redox reactants of the electrolyte, with specific properties dependent upon the energy state location. 

Salvador [100] introduced a non-equilibrium thermodynamic approach taking entropy into account, which is not present in the conventional Gerischer model, formulating a dependence between the charge transfer mechanism at a semiconductor-electrolyte interface under illumination and the physical properties thermodynamically defining the irreversible photoelectrochemical system properties. The force of the resulting photoelectrochemical reactions are described in terms of photocurrent intensity, photoelectochemical activity, and interfacial charge transfer... 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

Fig. 10.28. Model of charge carrier separation and charge transport in a nanocrystalline film. The electrolyte has contact with the individual nanocrystallites. Illumination produces an electron-hole pair in one crystallite. The hole transfers to the electrolyte and the electron traverses several crystallites before reaching the substrate. Note that the photogenerated hole always has a short distance (about the radius of the particle) to pass before reaching the semiconductor/electrolyte interface wherever the electron-hole pair is created in the nanoporous film. The probability for the electron to recombine will, however, depend on the distance between the photoexcited particle and the tin-coated oxide back-contact. (Reprinted with permission from A. Hagfeldt and Michael Gratzel, Light-Induced Redox Reactions in Nanocrystalline Systems Chem. Rev. 95 49-68, copyright 1995, American Chemical Society.)...

ADSORPTION EXPERIMENTS FOR MODELLING SEMICONDUCTOR/ELECTROLYTE INTERFACES... 

The possible results and limitations of model experiments for semiconductor/electrolyte interfaces are discussed for non-reactive and reactive interfaces and related to the use of UHV techniques for obtaining microscopic information of interfacial processes in photoelectrochemical processes. 

Double layer models for the semiconductor-electrolyte interface... 

A large number of corrective treatments has been derived for the semiconductor-electrolyte interface and we shall consider these below. The complexity of some of the models considered has, however, led to considerable doubt as to the appropriateness of some of the treatments. 

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. 

The exponential dependence of the current on applied potential for p-type silicon and highly doped n-type silicon in the pore formation regime can be analyzed using the Gerischer model of the semiconductor/electrolyte interface [77]. In the absence of surface states, the hole current for a p-type semiconductor is given by ... 

To facilitate a self-contained description, we will start with well-established aspects related to the semiconductor energy band model and the electrostatics at semiconductor electrolyte interfaces in the dark . We shall then examine the processes of light absorption, electron-hole generation and charge separation at these interfaces. Finally, the steady-state and dynamic (i.e., transient or periodic) aspects of charge transfer will be considered. Nanocrystalline semiconductor films and size quantization are briefly discussed, as are issues related to electron transfer across chemically modified semiconductor electrolyte interfaces. 

Figure 20. Comparison of calculated current voltage profiles in the dark (curve d) and under illumination (curves a-c). Curve a is obtained from the basic Gartner model. Curve b considers surface recombination and curve c considers both surface recombination and recombination in the space-charge layer. These simulations are for an n-type semiconductor-electrolyte interface. (Reproduced with permission from Ref [230].)...

Other models taking the above nonidealities to varying extents have been proposed a detailed discussion of these lies beyond the scope of this chapter [233-239], However, it is worth noting here that in some instances involving high-quality semiconductor-electrolyte interfaces the rate-determining recombination step does... 

Fig. 5.5 Accumulation, depletion and inversion layer at thc semiconductor-electrolyte interface a) space charge capacity C e vs. potential across the space charge layer A

In order to describe the photoelectrochemistry of d-band materials it will be necessary to introduce to a higher degree formalisms and energy tenti considerations from coordination chemistry into physical chemical models of the semiconductor/electrolyte interface. 

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. 

In the early stages of study of photoelectrochemical kinetics, two extreme models were presented. One is the model of Bockris and Uosaki,93 108,109 in which the charge transfer step was considered to be the rate-determining step and the other is Butler s model,110 in which the semiconductor/electrolyte interface was considered as a Schottky barrier, i.e., the electrochemical kinetics were neglected and all the potential drop occurred only within the semiconductor. 

Butler s Model—Semiconductor/Electrolyte Interface as a Schottky Barrier... 

Figure 2. Physical model of the semiconductor-electrolyte interface in a photoelec-trochemical cell.

Macroscopic transport equations are commonly used to describe the semiconductor and the electrolyte in the liquid-junction cell. A microscopic model of the semiconductor-electrolyte interface couples the equations governing the macroscopic systems. 

The boundary conditions are specified by the microscopic model of the various interfaces included within the photoelectrochemical cell. A metal-semiconductor interface, for example, can be described in a manner similar to that presented in the preceding section. Consider a semiconducting electrode bounded at one end by the electrolyte and at the other end by a metallic current collector. The boundary conditions at the semiconductor-electrolyte interface are incorporated into the model of the interface. Appropriate boundary conditions at the semiconductor-current collector interface are that the potential is zero, the potential derivative is equal to a constant, determined by the charge assumed to be located at the semiconductor-current collector interface, and all the current is carried by electrons (the flux of holes is zero). These conditions are consistent with a selective ohmic contact.34 The boundary conditions in the electrolytic solution may be set a fixed distance from... 

The semiconductor electrode is typically divided into three regions. Surface-charge and electron and hole-flux boundary conditions model the semiconductor-electrolyte interface. The region adjacent to the interface is assumed to be a depletion layer, in which electron and hole concentrations are negligible. The potential... 

Surface states and crystal imperfections have been found to play an important role in charge-transfer and redox reactions at the semiconductor-electrolyte interface (see Refs. 161-173). Mathematical and conceptual relationships have been developed which describe electrochemical reactions at the semiconductor-electrolyte interface in terms of surface states and potentials (see, e.g., Refs. 17, 71, and 174-182). Electrochemical reaction via surface states has been included within an analytic model,183 but this model is still limited by the restrictions described above. 

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