Fluctuation-induced tunnelling

Third, at high a dopant concentrations the materials become metallic. The total resistivity is a combination of the resistance from the doped metallic islands and resistance rising from the fluctuation-induced-tunneling (FIT) between metallic islands. The latter part has a temperature dependence that follows [111] ... 

P. Sheng, Fluctuation-induced tunneling conduction in disordered materials, Phys. Rev. B, 21, 2180-2195 (1980). 

The parabolic barrier approximation for the fluctuation-induced tunneling gives the following relationship in respect of the temperature dependence of conductivity [49, 50] ... 

CNTs in polymer-CNT composites are efficiently debundled and isotropically dispersed in polymer matrices, the efficient interaction between CNT and polymer provides good dispersion and a low percolation threshold, but only relatively low conductivity near and above percolation, frequently around 10 s cm is achieved at close to 2wt% CNT loading [70, 71], The polymer layer in the intemanotube connections is supposed to be the highest resistance section in the electrical pathway. This polymer layer is a barrier to efficient carrier transport between CNTs, and models for conductivity based on fluctuation-induced tunneling have been proposed [72]. A power law related to percolation theory can be used to model conductivity in the following form ... 

The total behaviour of the sample is determined by the largest resistance. In highly doped samples this will be the resistance from fibre to fibre (/ 3.4) or across grain boundaries found in, for example, the non-fibrillar Durham Graz material. This type of internal contact resistance is well known from metal powders, sputtered metal layers, and polymers compounded with carbon black or metal flakes. Theories of fluctuation-induced tunnelling have been developed to describe this case [83-84]. They show that at finite temperatures the barriers between the individual particles are modulated by statistically fluctuating potential differences. 

Figure 1.40. Temperature dependence of the d.c. conductivity of heavily (iodine) doped polyacetylene and fit of the model of fluctuation-induced tunnelling. Solid curve theoretical fit. (Reprinted with permission from ref 84)...

Figure 3.12. Sheng s model considers the effect of fluctuation-induced tunneling through potential barriers between extended highly conducting regions. In a model circuit the barriers can be treated as capacitances with charging resistances [22b].

The temperature dependence of the electrical conductivity can be fit by the formula of fluctuation induced tunnelling. 

It seems plausible that the inter-fibre resistance behaves similarly to that between metallic grains in evaporated thin films or metallic particles in insulting polymer matrices. For this case a model of fluctuation-induced tunneling has been successfully applied /13/. It also fits perfectly to the temperature dependence of highly doped polyacetylene /lU,9/ (Fig. I8). We assume... 

Fluctuation-induced tunneling model for highly doped polyacetylene (Ref. 9)... 

Sheng P, Sichel E, Gittleman J (1978) Fluctuation-induced tunneling conduction in... 

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