Rate of Electron Transfer Theory

In the first case (conduction band process), the density of unoccupied energy states (Ny n = N c) in the conduction band can be taken to be constant because only a few of them are occupied, even in n -type material, so that the corresponding current is given by 

The situation is different in the case of a valence band process because most of the energy states are occupied by electrons. Here an electron transfer into the valence band is only possible if holes are present at the surface, i.e., the density of empty states, is equal to the density of holes at the surface, Ps. The corresponding current is given by 

In a similar procedure, also the cathodic currents, representing the electron transfer from the electrode to the electrolyte, can be derived. The current 

In this case, the density of occupied states Nocc in the conduction band is given by the density of electrons at the surface ris, whereas the corresponding density of occupied states in the valence band is given by its density of states (Nv) itself. Using the same approximation, one obtains for the conduction band process using also Eq. (24b) 

At equilibrium the Fermi level is constant throughout the system [Ef = F,redox See Eq. (27)]. Polarizing the electrode, the Fermi levels on both sides differ by the externally applied potential Af/. Since any potential variation occurs only across the space of the semiconductor [Af/e = AC/sc see Eq. (13) of Section 2] we have 

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