Quantitative Derivation of Current-Potential Curves

Since the charge transfer across a semiconductor-electrolyte interface can only occur via the conduction or valence band, the processes via the two bands have to be treated separately. In general anodic and cathodic currents are given by equations similar to 

7 Charge Transfer Processes at the Semiconductor-Liquid Interface 

18a) and (7.18b), but now using boundary conditions which are specific for semiconductors. Since the integral in Eq. (7.18) cannot be solved analytically, we assumed in the case of metal electrodes that the electron transfer occurs mainly around the Fermi level. As proved in Section 7.1, this is a satisfactory approximation. Using an equivalent approach for charge transfer processes at semiconductor electrodes, the anodic current corresponding to an electron transfer from the occupied states of the redox system to empty states of the conduction band, is given by [22] 

Since this equation contains only constant parameters for a given system, the anodic current is independent of the electrode potential. Its absolute value depends essentially on the energy terms in the exponent. 

The reverse current, jl, which corresponds to an electron transfer from the conduction band to the empty states of the redox system, is given by 

The product of and the exponential term corresponds to the density of empty states of the redox system. In this case, f(E)p(E) at = is the density of the occupied states at the bottom of the conduction band on the surface, that is, a number which is equal to the density of free electrons on the surface. Equation (7.46) then turns into 

is the density of energy states at the upper edge of the valence band and 

The anodic current is expected to increase exponentially with the electrode potential provided that the condition AU = A A ) is again fulfilled. In such an anodic reaction in which electrons are transferred into the valence band, holes must be available on the surface. Frequently, scientists then argue in terms of hole transfer. This is only a rather lax description and has no real physical basis for the process at the boundary of two different phases. 

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