By Nevill F. Mott, Edward Arthur Davis
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Extra resources for Electronic Processes in Non-Crystalline Materials
9. Mobility and percolation edges Classical percolation theory has been applied to electrons in non-crystalline materials by many authors. A wavy potential energy function such as that illustrated in Fig. 11 is envisaged, and it is supposed that the (b) Fig. 11. Potential energies in conduction and valence bands with long-range fluctuations due to (a) electrostatic charges and (b) fluctuations in density. conductivity can be calculated by considering the fraction PI of the volume available to an electron of energy E and the fraction P2 in connected channels.
12; Pi(E) represents the total volume available for the electron of energy E. Curve P2, representing the volume available for conduction, has been shownt to behave like (E—Ep) 1'6 near the percolation edge. If the tLast and Thouless (1971), Stinchcombe (1973, 1974), Kirkpatrick (1971, 1973a); for a review see Esser (1972) and Kirkpatrick (19736). 40 T H E O R Y OF ELECTRONS IN A NON-CRYSTALLINE MEDIUM Fig. 12. PI is the volume available to an electron of energy E in the potential of Fig. 11; P2 is the volume in connected channels.
This behaviour is discussed in more detail in connection with the behaviour of the wavefunctions at the mobility edge, and these indices are perhaps open to doubt. The Anderson criterion in two dimensions is discussed by Licciardello and Thouless (1975) and by Yoshino and Okazaki (1977), who obtain similar results, Vo/B~l. 16); in two and three, as we have seen, a criterion exists for localization; in four according to Toulouse (1975) and Toulouse and Pfeuty (1975) localization cannot occur. 4.
Electronic Processes in Non-Crystalline Materials by Nevill F. Mott, Edward Arthur Davis