Model resistor conduction mechanism

All models of resistor conduction mechanism are based on a network of conductive chains in the microstructure with segments of different couplings [5-7]. 

A considerable amount of research has been done in attempts to understand conduction mechanisms in thick-fihn resistors. However, there is no common agreement among researchers in explaining these mechanisms. Pike and Seager proposed a tunneling barrier model to explain the small activation energy associated with the shallow minimum in resistance... 

It has been demonstrated that, by considering simple resistor microstructures and utilizing the multipath model, conduction mechanisms with very high activation energies (0.5 eV) can be used to explain the temperature dependence of resistors which exhibit very low activation energies. However, no single quantitative model developed thus far completely explains the conduction mechanism of thick-film resistors. 

An explanation of the observed relaxation transition of the permittivity in carbon black filled composites above the percolation threshold is again provided by percolation theory. Two different polarization mechanisms can be considered (i) polarization of the filler clusters that are assumed to be located in a non polar medium, and (ii) polarization of the polymer matrix between conducting filler clusters. Both concepts predict a critical behavior of the characteristic frequency R similar to Eq. (18). In case (i) it holds that R= , since both transitions are related to the diffusion behavior of the charge carriers on fractal clusters and are controlled by the correlation length of the clusters. Hence, R corresponds to the anomalous diffusion transition, i.e., the cross-over frequency of the conductivity as observed in Fig. 30a. In case (ii), also referred to as random resistor-capacitor model, the polarization transition is affected by the polarization behavior of the polymer matrix and it holds that [128, 136,137]... 

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