Localization, the mobility edge and

An increasing disorder potential causes first strong electron scattering and eventually electron localization, in which the wave-function is confined to a smaU volume of material rather than being extended. The form of the localized wavefunction is illustrated in Fig. 

Anderson s theory of localization uses the model illustrated in Fig. 

8 (Anderson 1958). The crystal is described by an array of identical atomic potential wells and the corresponding band of electronic states is broadened to a band width B by the interaction between atoms. The disordered state is represented by the same array of sites to which a random potential with average amplitude is added. Anderson showed that when VJB exceeds a critical value, there is zero probability for an electron at any particular site to diffuse away. All of the electron states of the material are localized and there is no electrical conduction at zero temperature. 

The critical value of VJB for complete localization is about three. Since the band widths are of order 5 eV, a very large disorder potential is needed to localize all the electronic states. It was apparent from early studies of amorphous semiconductors that the Anderson criterion for localization is not met. Amorphous semiconductors have a smaller disorder potential because the short range order restricts the distortions of the bonds. However, even when the disorder of an amorphous semiconductor is insufficient to meet the Anderson criterion, some of the states are localized and these lie at the band edges. The center of the band comprises extended states at which there is strong scattering and 

The electronic structure is illustrated in Fig. 1.9. The energy of the mobiUty edge within the band depends on the degree of disorder and is typically 0.1-0.5 eV from the band edge in all amorphous semiconductors. The properties of states near the mobility edge are actually more complicated than in this simple model of an abrupt mobiUty edge and are described in more detail in Chapter 7. Nevertheless, the model of Fig. 1.9 provides a good description of amorphous semiconductors. 

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