Space charge layer potential drop

Figure Bl.28.9. Energetic sitiration for an n-type semiconductor (a) before and (b) after contact with an electrolyte solution. The electrochemical potentials of the two systems reach equilibrium by electron exchange at the interface. Transfer of electrons from the semiconductor to the electrolyte leads to a positive space charge layer, W. is the potential drop in the space-charge layer.

There are five possible physical phases in the current path in which the current conduction mechanisms are different as illustrated in Figure 19. They are substrate, space charge layer, Helmholtz layer, surface oxide film, and electrolyte. The overall change in the applied potential due to a change of current density in the current path is the sum of the potential drops in these phases ... 

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 applied anodic potential may mostly or partially drop in the space charge layer or in the Helmholtz layer depending on doping type and concentration as well as on the potential range. 

For moderately doped substrates, when the surface is free of oxide the change of potential is mostly dropped in the space charge layer and in the Helmholtz double layer. The reactions are very sensitive to geometric factors. The reaction that is kinetically limited by the processes in the space charge layer is sensitive to radius of curvature, while that limited by the processes in the Helmholtz layer is sensitive to the orientation of the surface. Depending on the relative effect of each layer the curvature effect versus anisotropic effect can vary. 

From the energy diagram shown in Fig. 10-33, the operating cell voltage, V,, is obtained, as expressed in Eqn. 10-60, by subtracting from the electromotive force AEph the potential barrier of the space charge layer, the cathodic overvoltage t h, and the iR drop in the electrolyte ... 

Upon immersion of the CdSe semiconductor into the electrolyte, electron exchange at the interface occurs until equilibrium is attained. At equilibrium, the Fermi level of the semiconductor is adjusted by the presence of a space charge layer at the semiconductor surface. This layer is due to the difference between the Fermi level of the semiconductor and the Fermi level of the electrolyte which is measured at the redox couple (X) The potential drop at the space charge layer and the amount of band bending also depend on the degree of Fermi level mismatch at the semiconductor-... 

Fig. 5.1 Schematic energy band bending for (A) large particle, (B) small particle, and (C) metal-deposited particle. R, radius of the particle Lsc, space charge layer E(red/ox), redox level in solution E , Fermi level in semiconductor

Fig. 38. (a) Potential diagram (potential drop at the interfaces including the space charge layer Aipsc and Helmholtz layer Asemiconductor model of a metal with a n-type passive layer, with the band gap Eg, space charge layer dsc, conduction band CB, and valence band VB. 

Elegant studies of electrocapillarity of a nonpolarized ITIES by Gavach et al. [48] showed that the tetraethyl-, tetrapropyl- and tetrabutylammonium ions are not adsorbed within the compact layer and suggested that the interface is made of two space charge layers, described by the Gouy-Chapman theory, on either side of a central compact layer [49-51]. In a nonpolarized ITIES, the potential drop across the interface cannot be altered independently of the chemical potential of a salt of ionic constituents in either of the phases. The degree of specific adsorption cannot therefore be quantitatively estimated at a nonpolarized interface [28]. 

The Mott-Schottky regime spans about 1 V in applied bias potential for most semiconductor-electrolyte interfaces (i.e., in the region of depletion layer formation of the semiconductor space-charge layer, see above) [15]. The simple case considered here involves no mediator trap states or surface states at the interface such that the equivalent circuit of the interface essentially collapses to its most rudimentary form of Csc in series with the bulk resistance of the semiconductor. Further, in all the discussions above, it is reiterated that the redox electrolyte is sufficiently concentrated that the potential drop across the Gouy layer can be neglected. Specific adsorption and other processes at the semiconductor-electrolyte interface will influence Ffb these are discussed elsewhere [29, 30], as are anomalies related to the measurement process itself [31]. Figure 7 contains representative Mott-Schottky... 

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