Electrode Mott-Schottky plots

If VEB is increased, IEB increases and the current density at the electrode eventually becomes equal to JPS. It has been speculated that this first anodic current peak is associated with flat-band condition of the emitter-base junction. However, data of flat-band potential of a silicon electrode determined from Mott-Schottky plots show significant scatter, as shown in Fig. 10.3. However, from C-V measurement it can be concluded that all PS formation occurs under depletion conditions independent of type and density of doping of the Si electrode [Otl]. 

Fig. 10.2 Mott-Schottky plots of an n-type and a p-type silicon electrode in an electrolyte composed of 0.5 mol I"1 HF and 0.5 mol I-1 NH4CI. Dotted lines correspond to ND = l.l xlO15 cm" and NA=3.4xl015 cm-3.

Figure 5-47 shows the Mott-Schottky plot of n-type and p-type semiconductor electrodes of gallium phosphide in an acidic solution. The Mott-Schottl plot can be used to estimate the flat band potential and the effective Debye length I D. . The flat band potential of p-type electrode is more anodic (positive) than that of n-type electrode this difference in the flat band potential between the two types of the same semiconductor electrode is nearly equivalent to the band gap (2.3 eV) of the semiconductor (gallium phosphide). 

Fig. 6-47. Mott-Schottky plot of electrode capacity observed for n-type and p-type semiconductor electrodes of gallium phosphide in a 0.05 M sulfuric add solution. [From Meouning, 1969.]...

Fig. 5-61. Mott-Schottky plot of an n-type semiconductor electrode in presence of a surface state ib = flat band potential with the surface state fully vacant of positive charge Eft, - flat band potential with the surface state fully occupied by positive charge Q = maximum charge of the surface state e, = surface state level, s capacity of the surface state ( Ch ).

Pig. 10-18. (a) PolarizatioD curves of anodic dissolution and (b) Mott-Schottky plots of an n-type semiconductor electrode of molybdenum selenide in the dark and in a photo-excited state in an acidic solution C = electrode capacity (iph) = anodic dissolution current immediately after photoexdtation (dashed curve) ipb = anodic dissolution current in a photostationary state (solid curve) luph) = flat band potential in a photostationary state. [From McEv( -Etman-Memming, 1985.]... 

Figure 11. Mott-Schottky plots of reciprocal square of differential capacitance of n-type TiO electrode in 0.5M HfSO, vs, electrode potential. (O) In the dark (O) under illumination as in Figure 10. Intercept at C = oo gives the value of the flat-band potential (19).

Where Vs is the potential value at the surface of the electrode. Then plotting the value of 1/Csc versus the applied potential E should yield a straight line whose intercept with the E axis represents the flat band potential, and the slope is used for the calculation of N, the charge carrier density in the semiconductor. A typical example of Mott-Schottky plot is given in Fig. 2 [7] in this graph, the extrapolated values of the fb potential are -1-0.8 V and —0.6 V vs. SCE for p-Si and n-Si respectively. 

The experiments were performed with single crystal (111) p-Si electrodes with a resistivity of about 5.5 ohm cm non-aqueous electrolytes were used consisting of absolute methanol containing tetramethylammonium chloride (TMAC) or acetonitrile containing tetraethyl ammonium perchlorate (TEAP). The flat-band potentials or p-Si in the two electrolytes were determined from Mott-Schottky plots (in the dark) in the depletion range of the p-Si electrode, from open-circuit photopotential measurements, and from the values of electrode potential at which anodic photocurrent is first observed in n-type Si electrodes. These three methods all yielded consistent flat-band potential values for p-Si of + 0.05V (vs SCE)... 

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] ... 

Fig. 11.12. The results of Hall measurements of mobility are shown in Table 11.3. The Mott-Schottky plot showed a flatband potential of -0.23 V on the NHS. Some electrode kinetic measurements (Miller, 1992) are shown in Fig. 11.13.

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 ... 

Fig. 11. Mott-Schottky plot for a polycrystalline diamond electrode with tance in 0.5 M H2S04. Solid line shows a linear fitting [66], Reproduced chemical Society, Inc.

Fig. 13. Mott-Schottky plot for a singlecrystal thin-film electrode in 0.5 M H2SO4. Experimental curves, frequency/Hz (1) 21,544, (2) 10,000, (4) 4642, (5) 2154, (6) 1000, (7) 215 (3) calculated curve for Ccaic (discussed in section 5.3, below). Potential vs. Ag/AgCl electrode [78],...

The problem of the frequency dependence of the differential capacitance of diamond electrodes, which manifests itself in the frequency dependence of the slope of Mott-Schottky plots, can be subdivided into two aspects (1) by the process(es) causing the frequency dependence and (2) the most convenient format for the presentation of this dependence. 

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. 

Thus, we have to conclude that, without knowing the physical nature of the frequency dependence of the differential capacitance of a semiconductor electrode, the donor (or acceptor) concentration in the electrode cannot be reliably determined on the basis of the Schottky theory, irrespective of the Mott-Schottky plot presentation format. Therefore, the reported in literature acceptor concentrations in diamond, determined by the Schottky theory disregarding the frequency effect under discussion, must be taken as an approximation only. However, we believe that the o 2 vs. E plot (the more so, when the exponent a approaches 1), or the Ccaic 2 vs. E plot, are more convenient for a qualitative comparison of electrodes made of the same semiconductor material. 

Moderately doped diamond demonstrates almost ideal semiconductor behavior in inert background electrolytes (linear Mott -Schottky plots, photoelectrochemical properties (see below), etc.), which provides evidence for band edge pinning at the semiconductor surface. By comparison in redox electrolytes, a metal-like behavior is observed with the band edges unpinned at the surface. This phenomenon, although not yet fully understood, has been observed with numerous semiconductor electrodes (e.g. silicon, gallium arsenide, and others) [113], It must be associated with chemical interaction between semiconductor material and redox system, which results in a large and variable Helmholtz potential drop. 

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]...

Fig. 11. Mott-Schottky plot upperfigure) smii photocurrent vs. electrode potential (tower gurc) for H-RuSa [79]...

Figure 7. Mott-Schottky plots for n- and p-type GaAs electrodes in an AlCfi-n-butylpyridinium chloride molten-salt electrolyte. (Reproduced with permission from Ref. [32].)...

Capacity measurements (represented as Mott-Schottky plots), performed by Ferrer et al. for a thin film TiOj electrode immersed in a less alkaline (pH 11.3) Na2S04 solution, have shown that the addition of H2O2 caused effectively the shift of the flat-band potential closely similar to that of the onset potential in Fig. 12. 

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