Davis-Mott model

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).

For the Davis-Mott Model E = E (or Eg). /z(E) drops sharply below E. so that In a more general case the tunnel probabiUty (contained in... 

Figure 5.32 compares the screening potential obtained from a band model such as shown in Figure 5.3 with that predicted by the Davis-Mott model shown in Figure 5.4. In both cases an interface potential U(0) = 1 eV was assumed and a dielectric constant k = 16. Letting tails of localized states in the first model drop exponentially toward Ep as...

The energies E, Eg, E, and E have the same meaning as in the Davis and Mott model. A band of localized acceptor states lies below and a band of donor states above the gap center. In the cases shown, the acceptors are nearly compensated by the donors. As T is increased Ep moves toward the gap center. 

The ideas about conduetion near the mobility edge have changed substantially in recent years and are still in a state of flux, with several different models being developed. It is helpful to begin with the first model developed by Mott around 1965-70 (see Mott and Davis (1979) Chapter 2) to see how the ideas have evolved and to understand the underlying physical concepts. 

The next step in the theory is to calculate the conductivity above and below the mobility edge. In the Anderson model, locali2ed states are defined by a decreasing probability that the electron diffuses a larger distance from its starting point. Mott and Davis (1979 Chapter 1) prove that the dc conductivity in the localized states is zero at T = 0 K. They use the Kubo-Greenwood formula for the conductivity,... 

Figure 8.05 Models for the density of states of an amorphous semiconductor, (a) A true gap in density of states with some band tailing, (b) The Cohen-Fritzsche-Ovshinsky (1969) model of overlapping valence and conduction band tails (After Mott and Davis 1979)...

Figure 8.06 Schematic illustration of the form of the electron wave function in the Anderson model, (a) when states are just localized E < E ) (b) strongly localized (After Mott and Davis, 1979).

Davis and Mott s hypothesis simplifies considerably the following discussions and we shall adopt it. However, its validity is subject to justification in any particular theoretical model of the electronic structure of an amorphous solid. Hindley (1970) has shown that it follows from his random phase model for the wavefunctions in amorphous semiconductors. 

The model of Davis and Mott yields near the interface a constant space charge and hence a parabolic Schottky barrier... 

The most comprehensive attack on the theoretical problems posed by the existence of liquid semiconductors has been made by Mott (1966, 1967, 1970, 1971). TTie essential features of his model are shown in Figure 7.53 and have been described in detail by Cohen, Fritzsche and Ovshinsky (1969) and by Davies and Mott (1970). and separate the extended from the localized states (shown shaded) and mark the energy at which a substantial drop in the mobility occurs. An additional hypothesis is that the energy range of localised states is somewhat greater in the conduction band than in the valence band, thereby explaining the tendency for liquid semiconductors to exhibit positive thermoelectric powers. All the liquids... 

The fundamental optical properties of a fluid metal were defined in Section 3.3. Optical measurements of expanded liquid mercury, like those of the alkali metals, are valuable for the detailed information they provide about the evolution of electronic structure under large changes of temperature and pressure. In terms of the band-overlap model, the optical conductivity cr electronic densities of states of the valence band, N (E), and of the conduction band, N E), according to the relation (Mott and Davis, 1979)... 

Fig. 21.7 (a) Band diagram scheme for n-type doped PPP according to the polaronic-bipolaronic model, (b) Transitions in the Mott-Davis model of an amorphous semiconductor. 

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