Mott-Schottky

As outlined above, electron transfer through the passive film can also be cmcial for passivation and thus for the corrosion behaviour of a metal. Therefore, interest has grown in studies of the electronic properties of passive films. Many passive films are of a semiconductive nature [92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102 and 1031 and therefore can be investigated with teclmiques borrowed from semiconductor electrochemistry—most typically photoelectrochemistry and capacitance measurements of the Mott-Schottky type [104]. Generally it is found that many passive films cannot be described as ideal but rather as amorjDhous or highly defective semiconductors which often exlribit doping levels close to degeneracy [105]. 

C/pB estimated by both electrical (Mott-Schottky) and optical (photocurrent voltammetry) methods in the media studied, for (11 l)-oriented ZnSe electrode surfaces. A different variation was observed for the (110) orientation at pH >6. At pH 0, for both (110) or (11 l)-oriented electrode surface, the flat band potential value was -1.65 V (SHE) and the measured potential stability range (no detected current) was -0.35 to +2.65 V (SHE). A comparison of band levels with the other II-VI compounds as well as decomposition levels of ZnSe is given in Fig. 5.6. 

In Eq. (4.5.5), describing an n-type semiconductor strongly doped with electron donors, the first and third terms in brackets can be neglected for the depletion layer (Af0 kT/e). Thus, the Mott-Schottky equation is obtained for the depletion layer,... 

The Mott-Schottky plot following from Eqs (4.5.12) and (4.5.14) is the relationship... 

Figure 7.5 Mott-Schottky plot for the depletion layer of an n-type semiconductor the flat-band potential Eft, is at 0.2 V. The data extrapolate to Eft, + kT / eo-...

Semiconductors that are used in electrochemical systems often do not meet the ideal conditions on which the Mott-Schottky equation is based. This is particularly true if the semiconductor is an oxide film formed in situ by oxidizing a metal such as Fe or Ti. Such semiconducting films are often amorphous, and contain localized states in the band gap that are spread over a whole range of energies. This may give rise... 

Figure 8.4 Mott-Schottky plot for n-type SnC>2 for various donor concentrations (data taken from Ref. 5).

The interfacial capacity follows the Mott-Schottky equation (7.4) over a wide range of potentials. Figure 8.4 shows a few examples for electrodes with various amounts of doping [5]. The dielectric constant of Sn02 is e 10 so the donor concentration can be determined from the slopes of these 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]. 

The potential dependence of the SCR capacity Csc on applied potential V is described by the Mott-Schottky relation ... 

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 ).

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

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).

Figure 12. Mott-Schottky plots as in Figure 11 but for p-type GaP in 0.5M HgSO. Symbols have the same meaning as in Figure 11 (IQ).

Equation (3.4.28) is commonly known as Mott-Schottky equation. 

Fig. 3.10 Mott-Schottky plot for n-type and p-type semiconductor of GaAs in AlCls/n-butylpyridinium chloride molten-salt electrolyte [79],...

Thapar R, Rajeshwar K (1983) Mott-Schottky analyses on n- and p-GaAs/room temperature chloroaluminate molten-salt interfaces. Electrochim Acta 28 195-198... 

The flat band potentials of a semiconductor can be determined from the photocurrent-potential relationship for small band bending [equation (4.2.1)], or derived from the intercept of Mott-Schottky plot [equation (4.2.2)] using following equations... 

Fig. 4.5 Mott-Schottky plot of n-Ti02 prepared at different temperatures. AC frequency 1000 Hz. Reprinted with permission from Ref. [47].

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