Hopping conduction variable-range

As described above, the charging energy Eq, which is dependent on the cluster size and on the inter-particle capacitance C, can be determined directly from the temperature-dependence of the dc conductivity. Previous investigation of the electrical properties of these clusters has shown that even at high temperatures thermally activated electron hops instead of hops of variable range dominate charge transport through the samples. 

Another famous hopping model is Mott s variable range hopping [23], in which it is assumed that the localized sites are spread over the entire gap. At low temperatures, the probability to find a phonon of sufficient energy to induce a jump to the nearest neighbor is low, and hops over larger distances may be more favorable. In that case, the conductivity is given by... 

Evidence on this question may be taken by the behavior of the electrical conductivity CT as a function of temperature. A thermally activated process T dependence on log(CT), Arrhenius plot) is expected if doping takes place, whereas j -i/4 dependence, characteristic of a variable range hopping at the Fermi level is expected for a nondoping situation. 

In view of the complexity of the material, it is difficult to unequivocally assign a particular mechanism for electronic conduction in the polymer, although some evidence exists to suggest that it involves three-dimensional variable-range hopping as found for other polymers [213], It has also been suggested that the conductivity of polyaniline is a combination of both ionic and electronic conductivity [207], and is... 

Yu, D. Wang, C. Wehrenberg, B. L. Guyot-Sionnest, P. 2004. Variable range hopping conduction in semiconductor nanocrystal solids. Phys. Rev. Lett. 92 216802-216806. 

At sufficiently low temperatures, under all circumstances where N(EF) is finite but states are localized near the Fermi energy, we expect the phenomenon of variable-range hopping to set in. If interaction between electrons is not taken into account then the conductivity will follow the formula... 

The Hall effect in the temperature range where conduction is by variable-range hopping is not well understood. Evidence from the early work by Fritzsche is discussed by Shklovksii and Efros (1984), who come to the conclusion that the Hall mobility must be small. Hopkins et al (1989) have investigated the behaviour of heavily doped Ge Sb, pushed into the non-metallic regime by magnetic fields up to 7 T, at temperatures down to 100 mK. Below 1 K the... 

Eq. (18) is usually attributed to the variable-range hopping conductivity in presence of the Coulomb gap [34]. However, the analysis [72,75,76] shows that it is unrealistic explanation for the case of nanocomposites, because to fit experimental value on the basis of this theory one has to assume that the length of a single hop is less than the size of granules D and the electron... 

Until the fabrication of the first conductive LB film by Ruaudel-Teixier et al. [20], LB films had been considered as insulators or at most as semiconductors with very low conductivities. This is understandable since the typical film-forming molecules are long-chain fatty acids, which can act only as insulators. It is no wonder that the first systematic investigations of the electrical properties of LB films were carried out for insulating LB films [21-30]. Mott s variable-range-hopping model [31] is employed to explain the results [21,24]. 

Another characteristic feature of disordered systems is the variable range hopping (VRH) mechanism to the electrical conduction, which is observed on the nonmetallic side of the M-NM transition at low temperamres. This arises from the hopping of charge carriers between localized states, or impurity centers. Hence, the phenomenon is also known as impurity conduction. Experimentally, it is indicated by characteristic temperature dependency to the d.c. conductivity. Eor three-dimensional systems with noninteracting electrons, the logarithm of the conductivity and are linearly related, in accordance with the equation given by Mott (Mott, 1968)... 

This form of the conductivity is termed variable range hopping because the average hopping distance is not constant, but decreases as the temperature is raised. The conductivity follows a characteristic 7 law rather than an Arrhenius behavior. More detailed analysis of the hopping mechanism confirms Eq. (7.79), but gives a substantially different value for the prefactor... 

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