Potential across the space charge layer

Further, the total potential 5 across the electrode interface is given by the sum of the three potentials across the space charge layer, the compact layer, and the diffuse layer as shown in Eqn. 5-60 ... 

Such a migration of photoexdted electrons and holes induces in the electrode an inverse potential which reduces the potential across the space charge layer and retards the migration of electrons and holes in the opposite direction as shown in Fig. 10-5. This inverse potential, induced by photoexdtation, is called the photopotential. Since the photopotential, AE. = - he,/c, arises in a direction to reduce the potential across the space charge layer, the Fermi level of the semiconductor interior rises by an energy of de j, (the electrode potential lowers... 

In the case of zinc oxide, Dev/ald (2) found that by measuring the capacity he could find the bias on the counter electrode that would correspond to zero electrostatic potential across the space-charge layer (the flat band potential). He could, of course, measure the electrolytic potential for this condition. He found that at low electron density this electrolytic potential depended linearly on the logarithm of the ratio of the electron or hole density to the intrinsic density with the right slope, i. e., (-pr). 

Fig. 2. Same as Fig. 1 except here the potential across the space charge layer in the semiconductor is used. 

An extrapolation of the Mott-Schottky plot to 1/Csc yields the electrode potential at which the potential across the space charge layer becomes zero 0). Accordingly, we have... 

Fig. 26. Variation of cathodic current with potential across the space charge layer for n-ZnO [132]...

In general, in the absence of an oxide the partition of the applied potential across the space charge layer and the Helmholtz layer depends on doping concentration and current range. There are also two different potential distributions depending on whether it is under a forward bias or a reverse bias. Under a forward bias for an anodic process on ap-type semiconductor electrode the current density can be described as follows ... 

Fig. 2.14 Surface recombination, s, vs. potential across the space charge layer A(qualitative description)...

Fig. 3.6 Energy diagram for the semiconductor-vacuum, semiconductor-liquid and liquid-vacuum interfaces 0 , work functions ex, ex surface dipole contributions (neglected at the semiconductor-liquid junction) eA

This equation shows clearly that the space charge capacity Qc depends strongly on the potential across the space charge layer, although in a rather complex way. Before analyzing this relation in more detail it is useful to introduce two further equations. In accordance with Eqs. (5.14) and (5.15) the electron and hole densities at the surface are given by... 

Since the distance between the Fermi level E and the energy bands varies with (see Section 5.3) f is also changed. If Fp = Ft, the surface state is half-occupied (f = 0.5), as shown in Fig. 5.8. Since the charge depends on the potential across the space charge layer, a differential surface state capacity can be defined by... 

Figure 5.5 Accumulation, depletion and inversion layer at the semiconductor-electrolyte interface (a) space charge capacity vs potential across the space charge layer Q (b) energy model.

Figure 5.8 Fermi function f and surface state capacity C55 vs potential across the space charge layer (theoretical curve).

---