Space charge layer potential distribution

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

The potential i sc of the space charge layer can also be derived as a fixnction of the surface state charge Ou (the surface state density multiplied by the Fermi function). The relationship between of a. and M>sc thus derived can be compared with the relationship between and R (Eqn. 5-67) to obtain, to a first approximation, Eqn. 5-68 for the distribution of the electrode potential in the space charge layer and in the compact layer [Myamlin-Pleskov, 1967 Sato, 1993] ... 

Fig. 6-40. An interfadal potential, distributed to Msc in the space charge layer and to in the compact layer as a function of the concentration of surface states, D . [From Chandrasekaran-Kainthla-Bockris, 1988.]...

Fig. 5-42. Potential across an interlace of semiconductor electrode distributed to the space charge layer, At>sc, and to the compact layer,. as a function of total potential,...

The frontier between the depletion and the accumulation situations of the space charge layer is defined by the flat band potential. In fact, when the potential is constant all along the thickness of the electrode, the mobile charge (and naturally the fixed charge) distribution is uniform. In the case of the interface of Si electrode with an electrolyte, the corresponding bias potential has to be determined with respect to the reference electrode. The value of the flat band potential Vfb is expected... 

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form ... 

In an improved model (1) it is assumed that the ions are distributed in the electrolyte in a space charge layer near the electrode surface. The distribution of the ions and the corresponding potential are ruled by Boltzmann statistics and the Poisson equation. 

The charge distribution and electrolytic potential within the diffuse space charge layer in a solid electrode, as well as the capacity of this layer, can be treated in the same manner as in an electrolyte as shown by Rice (3, Verwey and Niessen (12) and Grimley (13). In the case of a semiconductor with electrons and holes, the charge distribution obeys the Boltzmann equations... 

POTENTIAL AND CHARGE DISTRIBUTION IN SPACE CHARGE LAYER... 

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 ... 

Figure 5.41 shows that the passivation potential decreases with doping concentration and is largely independent of orientation. The change in the values of passivation potential is more than 1 V from low to high. The distribution of this extra potential associated passivation in the Helmholtz layer, in the space charge layer, in a preexistent oxide, or in the substrate has not been determined. The passivation overpotential. 

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