Mott-CFO model

What is the origin of the charge transport phenomena and what do these experimental observations tell us about the material We show that the Mott-CFO model can answer these questions at least to first order, with the additional assumption that the density of localized band-tail states falls off exponentially away from the mobility edges. In this picture, the time-dependent charge transport is dominated by the statistical process associated with the progressive thermalization of electrons (or holes) into the band-tail states. We confine the discussion to electrons and assume that it can be generalized to holes trivially. 

This dramatic drop in can be explained in terms of the Mott-CFO model, (Eggarter (1970)). Briefly, a tail of localized states forms which is associated with density fluctuations. The width of the tail increases with density and becomes comparable to kT at a certain density. At that point the mobility drops precipitously because the electron spends most of its time in localized states which do not contribute to transport. 

This simple analysis confirms the Mott-CFO model in every detail. There is a Gaussian tail of localized states associated with density fluctuations, a mobility edge at = -0.52, channel and resonant extended states just above e, and ordinary extended states further above e. The mobility is of course zero below e. and positive above it. A final comment is in order regarding the behavior of ju (E) for E just above E. Figure 3.7b shows a linear increase which comes from an assumed linear increase in the percolation probability, liowever, we believe it more likely that the percolation probability, and (X)nsequently the classical mobility, would have the critical index behavior of Eq. (3.17a). 

The results stated above constitute a first principle derivation of the Mott-CFO model at least for the system we consider here. Let F be a measure of the spread of the random variables j ej around an average value Cq that will be chosen as zero. Consider first the case where F = 0. From Eqs. (3.26) and (3.27) and the properties of periodic systems one can show that L(E) > 1 for E inside the band with the equality obtaining at the... 

The basic thesis of this review is that the disordered materials show certain universal features in their electronic structure. They are best summarized in the Mott-CFO model there are bands of allowed states within the bands critical energies — mobility edges — occur at which the nature of the states changes abruptly from localized in the tails of the band to extended in the interior of the band bands may overlap although all the extended states... 

Fig. 4.12. Density of states g(E) as function of energy E in amorphous semiconductors, according to the Mott-CFO model (cf. Chapter 3). E P as used in the text is determined by extrapolation of the delocalized states. E and E are mobility edges.

The density of states gj, gf we shall consider is shown in Figure 4.12. This is the model of state densities usually denoted as Mott-CFO model. 

Fig. 5.3. Sketch of Mott-CFO model for covalent semiconductors having three-dimensional cross-linked network structure. The critical energies and define the mobility gap. For T > 0 the mobility m(E) niay be finite in the gap because of thermally assisted tunneling. Ep = Fermi energy. The distribution of localized gap states may be nonmonotonic when defect states of a certain energy are prevalent.

In the following we first discuss the consequences of spatial heterogeneities in terms of the Mott-CFO model and then several phenomenological aspects of heterogeneity. 

Fig. 7,53. The Mott-CFO model for the density of states. The shaded region indicates the extent of the localisation.

I shall use as an updated version of the original Mott-CFO model of the energy bands of an amorphous semiconductor a sketch of the density of states in a-SiH as it is now emerging from a wide variety of experiments. In Fig. la we show n(E) vs E. There is a valence band and within it a mobility edge E, and a conduction band and within it a mobility edge E. . Below Ey and above E the states are extended. Between E and E. the states are localized. Both bands have an... 

Figure 8.09. Density of states for amorphous semiconductors, (a) The CFO model, showing tailing of states causing overlap, (b) The Davis-Mott model, showing a band of compensated levels near the middle of the gap. (c) The Marshall-Owen model, (d) A real glass with defect states (After Nagels, 1979).

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