Semiconductor faradaic currents

If the potential on the semiconductor has imposed on it an a.c. component, then the effect is to change the accumulated charge in the depletion layer according to eqn. (38). Assuming that no faradaic current is passing, i.e. the semiconductor is deep in depletion, the capacitive response of the semiconductor layer may be approximated as... 

The expressions for the components of the total faradaic current at the semiconductor surface as given in eqns. (173) (176) show that this current is given as the product of factors intrinsic to the electron transfer process taking place, to the concentration and thermal energy distribution of the redox couple, and to the concentration of carriers or the density of states. If we restrict attention to an n-type semiconductor and assume that only electron transfer to and from the conduction band is significant, then the nett current can be written... 

THE A.C. THEORY OF SEMICONDUCTORS WITH FARADAIC CURRENT FLOWING... 

In the presence of a faradaic current, the a.c. response of a semiconductor becomes significantly more complex. Nevertheless, using the theory of Sect. 3, it is possible to derive expressions for the a.c. response of the semiconductor-electrolyte interface both in the simple case of electron transfer from CB to electrolyte and in the case where surface states play an intermediate role. 

These devices are based on the measurement of either electrochemical potential or faradaic current associated with redox reactions at an electrode. They are particularly suitable for enzyme-substrate receptor systems by virtue of the ionic products often produced in such reactions. The sensing membranes of the ion-selective electrodes previously described have been combined with semiconductor devices for miniaturization, low-impedance output, signal amplification, and capability of on-chip processing. The ion-sensitive field effect transistor (ISFET) is based on replacement of the conventional transistor gate with the ion-... 

The rather high values of the faradaic resistance RF are due to the above-mentioned low background currents and negligible corrosion rate of diamond in aqueous solutions. Relatively high a values, as compared with other semiconductor electrodes [6], reflect the higher doping level of diamond films the acceptor concentration Na would be no less than 1018 cm-3. 

The potential distribution at the surface of the semiconductor is such that the bulk of the potential change is accommodated within the depletion layer. It follows, as discussed in Sect. 4, that ns will be a strong function of the applied potential. However, the corollary of this is that the matrix element V and the thermal distribution parameters ox(Ec) and Qrei(Ec) will be much weaker functions of potential. Although, therefore, we would expect to find an exponential or Tafel-like variation of current with potential for a faradaic reaction on a semiconductor, the underlying situation is quite different from that of a metal. In the latter case, the exponential behaviour arises from the nature of the thermal distribution function Q and the concentration of carriers at the surface of the metal varies little with potential. To see this more clearly, we may expand eqn. (179) assuming that the reverse process of electron injection into the CB can be neglected eqn. (179) then reduces to... 

The semiconductor electrode must be ideally polarizable over the potential range of interest. This means that there is no leakage current or Faradaic reaction to allow charge transfer across the semiconductor-electrolyte interface. This restriction is not too important if measurements are taken at sufficiently high frequency that the effects of Faradaic reactions are suppressed. 

EIS has been used to study the kineties of outer-sphere redox reactions at semiconductors in the dark (Meier et al., 1991 Meier et al., 1999). The reactions involve majority carriers (electrons for n-type materials), and the electrode behaves like a metal with a low and potential-dependent electron density. The EIS response can be modelled by the equivalent circuit shown in Eig. 12.1, where is interpreted as the faradaic resistance obtained by linearising the potential dependence of the current associated with electron transfer to the redox species. 

Electrocatalysis at metal electrodes in aqueous (1.2) and non-aqueous ( ) solvents, phthalocyanine ( ) and ruthenium ( ) coated carbon, n-type semiconductors (6.7.8),and photocathodes (9,10) have been explored in an effort to develop effective catalysts for the synthesis of reduced products from carbon dioxide. The electrocatalytic and photocatalytic approaches have high faradaic efficiency of carbon dioxide reduction (1,6). but very low current densities. Hence the rate of product formation is low. Increasing current densities to provide meaningful amounts of product, substantially reduces carbon dioxide reduction in favor of hydrogen evolution. This reduction in current efficiency is a difficult problem to surmount in light of the probable electrostatic repulsion of carbon dioxide, or the aqueous bicarbonate ion, from a negatively charged cathode (11,12). 

Finally, before discussing oscillatory behavior, it is worth noting that a circuit equivalent to that shown in Fig. 1 also arises in semiconductor physics where a semiconductor device takes on the role of the faradaic impedance and the other elements of the circuit are electronic elements. Thus interesting parallels can be drawn between the dynamics of electrochemical and semiconductor systems. Furthermore, stability criteria derived for the latter can be directly applied to electrochemical systems. This is especially interesting for the interaction of S- or Z- shaped current-potential curves with the external circuit, which are not considered here owing to the presence of chemical instabilities. 

Bocarsly and co-workers [149,150] reported the mechanistic pathway for the electrochemical conversion of CO2 to methanol. They described the selective conversion of CO2 to methanol at a p-GaP semiconductor electrode, catalysed by pyridinium ions, where the reaction was driven by light energy, to yield Faradaic efficiencies near 100%, at potentials well below the standard potential. At illuminated electrodes, cathodic currents of --20 mA/cm could be maintained, without an applied bias. At metal electrodes, formic... 

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