Space-charge layer capacitance

Double-layer capacitance Space-charge layer capacitance Capacitance of the Gouy-Chapman layer Capacitance of the Helmholtz layer Madelung constant Sauerbrey constant Distance... 

Three concentrations of each redox couple that ranged over two orders of magnitude were examined as well as a solution containing only electrolyte. The details of these comprehensive experiments will be published elsewhere (22.) however, several pertinent features are described here. The kinetic currents were measured at constant potential. In order to eliminate mass transfer limitations to the current, a jet electrode configuration was utilized (42). The capacitance of the space charge layer (Csc) was measured at the same potentials simultaneously with the kinetic currents. 

The space charge layer capacitance is inversely proportional to the width of the depletion layer w. As the width of the depletion layer approaches zero the capacitance approaches infinity, hence... 

The differential capacitance of the space charge layer, Ca, per unit area is thus given as follows ... 

As seen in Figure 7, the effect of light on the system is to further increase the capacitance in the inversion layer. This, of course, enhances the unpinning effect as the capacitance of the space-charge-layer approaches or exceeds that of the Helmholtz 1ayer. 

In the above analysis, we used the concept of space charge layer, to be more precise, a depletion layer that would form in a doped, wide-gap semiconductor contacting another phase (a metal, an electrolyte solution, or vacuum). The poly crystalline diamond/metal junctions (where metal is Au, Pt, Pd, etc.) often show rectifying properties [67, 68] and their capacitance characteristics resemble those of a diamond/electrolyte solution junction. 

Mott-Schottky plot — is a graphical representation of the relationship between the -> space charge layer - capacitance, and the potential of a semiconducting -> electrode (Mott-Schottky equation) ... 

Figure 16. Equivalent circuit (a) and a simulated Nyquist plot (b) for the charge transfer pathway illustrated in Figure 15. The capacitance C represents that of the space-charge layer and the parallel branch components represent the Faradaic charge transfer process. Refer to the original work for further details. (Reproduced with permission from Ref. [84).)...

The surface state capacitance Css is different from the space charge layer capacitance Csc and the Helmholtz layer capacitance Ch in that there is in general no distance associated with the surface state capacity. 

FIGURE 1.10. An equivalent circuit for the electrical components at the semiconductor/electrolyte interface in the absence of an oxide. represents the resistance of the electrolyte Ch is the capacity of the Helmholtz double layer and Rf is the charge transfer resistance 0, and Ru are the capacitance and resistance associated with the space charge layer in the semiconductor C, and are the capacitance and resistance of the surface states. 

Note that here Cox is given in units of Fcm-2 (capacitance density), tox=df (film thickness) of the oxide. Together with Equation 1.9 for the extension of the space charge layer, we get an expression for (J)ox in terms of the charge NA in the scl ... 

Figure 12.1 Simplest small-signal equivalent circuit representing the semiconductor/electrolyte junction under depletion conditions. = total series resistance, t p = parallel resistance due to charge transfer, Csd = space-charge layer capacitance.

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