Is it related to hopping mechanism in metals? Or analogous ? Is it valid for semiconductors? What is its exact colleration with conductivity?
Hopping assumes localized states and therefore is not useful in metals. It is valid for semiconductors and insulators and historically it was mainly used in the metal-insulator transitions. Intuitively is easy to see that how higher is the frequency of the hopping higher is the conductivity and inversely happens with the hopping length. Its proper definition can be done with different criteria if you in Mott insulators, Anderson insulators or other where the definition of localization length or correlation length is necessary to be introduced properly.
I recommend you the reference:
Hopping transport in solids, edited by M. Pollak,B. Shklovskii in North-Holland 1991.
In amorphous semiconductors, localized states are considered at the band edges where conduction is possible only by hopping process using thermal energy. Mobility in localized states is zero at 0 K. These localized states at the band edges are due to lack of long range order in non- crystalline semiconductors. Localized states are also considered due to inherent structural defects whose energy may lie near the Fermi level in amorphous semiconductors. Mott has suggested variable range hopping concept where hopping of charge carriers not necessarily takes place between two nearby localized states but extends over other localized states also. The conductivity in this case vary with temperature differently as compared to conduction in localized states near band edges. For details see a book " Electronic processes in non - crystalline Solids" by N. F. Mott and E. A. Davis.
We have calculated the hopping length within WO3 structures and approximated it to 9.033 times the average interatomic separation length. We also recorded it varied oppositely to temperature.
Thanks a lot for your contributions and reference suggestions.
Regards.
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