Mott relationship

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

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... 

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... 

Many authors have discussed a dielectric catastrophe and the Mott transition in terms of the Clausius-Mossotti relationship... 

The relationships between the K-, S- and T-matrices (Mott and Massey, 1965, Chapter 13) are... 

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 example of the type of behaviour encountered for exponential surface-state distributions is provided by n-Fe203 in 1M NaOH [69]. The equivalent conductance and susceptance of the circuit comprising Zss in parallel with C8c clearly show a power law dependence on values obtained from this model again obeyed the Mott-Schottky relationship, although the donor density of 8 x 1018 cm 3 and dielectric constant of 25 suggest that the true flat-band potential may lie rather positive of the value given. 

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. 

If the contribution of a depletion layer in the semiconducting oxide to the interfacial potential is not negligible, the Mott-Schottky relationship holds between the interfacial capacitance and the electrode potential [13]. For an n-type oxide... 

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

Capacitance measurements are generally regarded as the most reliable method for determination of the band edge positions at a sensitized semiconductor-electrolyte interface [14]. The Mott-Schottky relationship, Eq. 7 ... 

Remember 12.4 Mott-Shottky theory provides a relationship between the experimentally measured capacitance, the doping level, and the flat-band potential. 

Show that the capacity can be related to doping level (N — Na) and potential by the Mott-Schottky relationship... 

A certain relationship, which exists between the bulk and surface properties of semiconducting materials and their electrochemical behavior, enables, in principle, electrochemical measurements to be used to characterize these materials. Since 1960, when Dewald was the first to determine the donor concentration in a zinc oxide electrode using Mott-Schottky plots, differential capacity measurements have frequently been used for this purpose in several materials. If possible sources of errors that were discussed in Section III.3 are taken into account correctly, the capacity method enables one to determine the distribution of the doping impurity concentration over the surface" and, in combination with the layer-by-layer etching method, also into the specimen depth. The impurity concentration profile can be constructed by this method. It has recently been developed in greatest detail as applied to gallium arsenide crystals and multilayer structures. 

Although this model is a natural extension of that derived for metal/semi-conductor or p-n junctions, it has proved remarkably difficult to verify it for semiconductors in contact with those electrolytes normally employed by electrochemists. As an example, the electrochemistry of germanium initially proved very difficult to understand in aqueous solution [2] and it was only with DeWaid s studies of n-ZnO [3] that a paradigmatic example of the classical model was discovered. The data found by DeWaid in his study of the ZnO electrolyte interface confirmed quantitatively the behaviour of the a.c. response of the semiconductor/electrolyte as predicted by the classical model. In particular, DeWald confirmed that the series capacitance of the interface obeyed the Mott-Schottky relationship [1]... 

The ratio g/I(0) defines the photocurrent efficiency . In the absence of surface recombination, qg corresponds to the photocurrent density Jphow measured in the external circuit. The Gartner equation has been used successfully to explain the photocurrent-potential characteristics of many semiconductor electrodes under conditions where surface recombination is absent. Plots of ln — O) against dsc (which according to the Mott-Schottky relationship is proportional to (1/ — have... 

Rearrangement yields a very useful relationship (first derived for the metal/semiconductor junction) called the Mott-Schottky equation (54, 55) ... 

The most basic data that the Mott-Littleton and supercell methods provide are the energies and entropies of defect formation. Nevertheless, despite the fact that these techniques are essentially static approaches it can also be possible to deduce information on the dynamic processes of diffusion and conductivity. These two processes are related by the Nemst-Einstein relationship ... 

Structure of the solid are fraught with difficulties. There is disparity in the literature over the values for activation energies, and this is compounded with the problem of identifying the relevant solid-state energies (see Chapter 5 of this volume). The correlations proposed on the basis of Table I depend crucially on the calculated thermal band gaps and first exciton levels. In the calculations, use has been made of the results of de Boer and van Geel [17] and Mott [6], who showed that the thermal energy is always less than that measured optically by an amount which represents lattice relaxation after the optical transition. The relationship between the two is... 

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