Mott-Schottky semiconductor

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]. 

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,... 

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 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.]... 

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

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... 

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 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] ... 

For the more accurate description of the Mott-Schottky dependences of semiconductor electrodes modified with small metal particles, it is reasonable to take into account the contribution of the capacity of electronic surface states (C ) induced by the... 

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. 

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 — Figure. Determination of the doping density and flat-band potential from the Mott-Schottky plot of an n-type semiconductor... 

Flat-band potential — In the energy barrier formed for example at metal-semiconductor junctions (- Schottky barrier), metal-insulator-semiconductor junctions, and solution-semiconductor interfaces the flat-band potential corresponds to the potential at which the electric field equals zero at the semiconductor interface, i.e., there is no -+ band bending. In case of solution-semiconductor interfaces, the flat-band potential corresponds to the condition of absence of excess charge and consequently, depletion layer, in the semiconductor. See also -> Mott-Schottky plot, and -> semiconductor. 

Normally, for semiconductors, Csc < CH so CT Csc. Roat may be varied systematically and the decay of j can often be approximated by a single exponential form, i.e. kr 1/RtCi. or kT potentials well positive of V, the long-time transient time-constant t (Rm + Rout)Csc, and a plot of x vs. R]oad (sflin + Rout) is linear, as shown in Fig. 105. Confirmation of this is obtained from the fact that 1/t2 obeys the Mott-Schottky relationship. At potentials close to V, kec becomes much larger and the decay law more complex. 

This result makes it impossible to predict theoretically the position of energy bands without further experiments, since Uh is unknown. Fortunately, however, the position of energy levels can be obtained experimentally by capacity measurements. The differential capacity of the space charge layer below the semiconductor surface can be derived quantitatively by solving the Poisson equation (see e.g. Ref. [6]). For doped semiconductors one obtains the so-called Mott-Schottky equation ... 

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