Space Mott-Schottky plot

A more reliable method for the determination of the fb potential can be drawn from a thorough investigation of the complete impedance diagram equivalent to the space charge layer. In fact, the main difficulty encountered in the Mott-Schottky plot is the rather wide range potential for the C extrapolation, which necessarily lead to values where electrochemical reactions contribute to changing the surface properties of the substrate. Moreover, the expected linear relationship shows a significant deviation, which is explained... 

The Mott-Schottky plot obtained experimentally for the Ag-modified Ti02 electrode, which satisfy the above requirements, differs from that for the initial electrode by the slope value, with an insignificant shift of the point obtained after extrapolating the plot to the electrode potential axis (Fig. 6.15). Since for the realization of such electrode system we have used a semiconductor characterized by the high concentration of ionized donors, under consideration of Mott-Schottky dependence it is worthwhile to take account of the Helmholtz layer capacity (CH) placed in series with the space charge capacity [100] ... 

Occasionally, the impedance spectra of diamond electrodes are well described by the Randles equivalent circuit with a frequency-independent capacitance (in the 1 to 105 Hz range) [66], Shown in Fig. 11 is the potential dependence of the reciprocal of capacitance squared, a well-known Mott-Schottky plot. Physically, the plot reflects the potential dependence of the space charge region thickness in a semiconductor [6], The intercept on the potential axis is the flat-band potential E whereas the slope of the line gives the uncompensated acceptor concentration NA - Nd in what follows, we shall for brevity denote it as Na ... 

The nature of the frequency dependence of Mott-Schottky plots for semiconductor electrodes has been discussed in the electrochemical literature for more than three decades (see e.g. reviews [6, 84]). It has been speculated that it can be caused by the following factors (1) frequency dependence of dielectric relaxation of the space charge region [85], (2) roughness of the electrode surface [84], (3) slow ionization of deep donors (acceptors) in the space charge region in the semiconductor [86], and (4) effect of surface states. 

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) ... 

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. 8. Mott-Schottky plot of the space charge capacity vs electrode potential at n- and p-type GaP in O.I M H2SO4 [47]...

Deviations from straight lines in Mott-Schottky plots can be attributed to the influence of potential-dependent charging of surface or bulk states. This interpretation is supported by analytic calculations of the contribution of defects to the space charge as a function of applied potential. In principle, the... 

Figure 12.3 Mott-Schottky plot for a thin (80 nm) film of n-CdS on tin oxide-coated conducting glass, showing the transition from Mott-Schottky behaviour to the geometric capacitance limit when the space-charge region extends to the substrate. Electrolyte 0.1 mol dm" Na2S, pH 13. Adapted from Ozsan et al. (1996).

Fig. 5.6 Mott-Schottky plot of the space charge capacity vs. potential across the space charge layer vs. for an n type semiconductor electrode (theoretical curve).

Fig, 5.17 Mott-Schottky plot of thc space charge capacity vs. electrode potential for n-GaAs in aqueous solutions under stationary conditions and after different prcpolarizations scan rate 0.2 Vs-. (After ref. [40])... 

Space-charge capacitance and space-charge resistance of polypyrrole as a function of the potential were shown in Figure 11.19. Similar results can be obtained for polythiophene. The potential dependence of the capacitance values in the cathodic region is typical for ap-type semiconductor. Then one should observe a linear dependence of on the potential (Mott-Schottky plot). Such a plot is shown for polythiophene in Figure 11.21. 

Under certain conditions it may still be possible to determine the donor density of a porous photoelectrode from a Mott-Schottky measurement. This is the case for high donor densities, when the space charge width is small and is therefore stiU able to track the surface contours. An example of this for nanostructured Si-doped Qt-Fe203 photoanodes is shown in Fig. 3.18, reported by Cesar et al. [57], The actual surface area was estimated by dye absorption experiments, and the estimated donor density for this system was 10 ° cm . The concave shape of the Mott-Schottky plot is consistent with a gradual decrease in the effective surface area (cf. (3.5)) as the potential is increased and the depletion layer progressively penetrates into the bulk [58]. 

Fig. 3.18 Mott-Schottky plots of Si-doped (curves a-c) and undoped (curve d) mesoporous hematite photoanode. The capacitances for curves a, b, and c are obtained from an Si-doped sample and models a, b, and c, respectively, shown in the inset of the left-hand plot. Curve d is obtained from the undoped film and model a (series RC). The dashed lines connecting the data points represent the variable active surface area fit. Sketches e-g depict the development of the space-charge layer in a mesoporous semiconductor as function of applied potential, illustrating a decrease in active surface area at advancing space-charge layer width in two dimensions, (e) Near flat band potential with maximum surface area, (f) Total depletion of smaller feature at increased bias potential, (g) Decreased active surface area in concave curved surface. Reprinted with permission from ref. [57], copyright, 2009 American Chemical Society...

To determine the effect of oxidation, a Mott-Schottky plot of the space charge capacitance before and after oxidation was compared. In these plots, which were originally derived for a metal-semiconductor interface (Schottky [ 1939,1942], Mott [1939]) but hold equally well for the metal-electrolyte interface, a linear relationship is predicted between the applied potential and one over the square of the capacitance arising from the space charge layer in the saniconductor. The slope is inversely proportional to the effective donor or acceptor concentration in the semiconductor. For the semiconductor-electrolyte interface (Bard and Faulkner [1980]),... 

Figure 4.3.15. Mott-Schottky plots of the space charge capacitance (curve 1) as derived from data like those shown in Figure 4.3.9a and the capacitance associated with the high-frequency response, Q (curve 2) derived from data like those shown in Figure 4.3.96. The flat-band potential is the same in both cases (0.69 V), but the doping level, as calculated from the slope of the lines, is an order of magnitude lower for curve 2 (polished + etched + oxidized sample) than for curve 1 (polished + etched sample). (Shen et al. [1986]). Reprinted by permission of the publisher, The Electrochemical Society, Inc.

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