A critical path approach for elucidating the temperature dependence of granular hopping conduction

Abstract

We revisit the classical problem of granular hopping conduction’s σ∝exp[–(T₀/T)] temperature dependence, where σ denotes conductivity, T is temperature, and T₀ is a sample-dependent constant. By using the hopping conduction formulation in conjunction with the incorporation of the random potential that has been shown to exist in insulator-conductor composites, it is demonstrated that the widely observed temperature dependence of granular hopping conduction emerges very naturally through the immediate-neighbor critical-path argument. Here, immediate-neighbor pairs are defined to be those where a line connecting two grains does not cross or by-pass other grains, and the critical-path argument denotes the derivation of sample conductance based on the geometric percolation condition that is marked by the critical conduction path in a random granular composite. Simulations based on the exact electrical network evaluation of finite-sample conductance show that the configurationaveraged results agree well with those obtained using the immediate-neighbor critical-path method. Furthermore, the results obtained using both these methods show good agreement with experimental data on hopping conduction in a sputtered metal-insulator composite Ag_x(SnO₂)_1–x, where x denotes the metal volume fraction. The present approach offers a relatively straightforward and simple explanation for the temperature behavior that has been widely observed over diverse material systems, but which has remained a puzzle in spite of the various efforts made to explain this phenomenon.

Keywords

granular hopping conduction / insulator-conductor composites / critical path method / immediate-neighbor hopping

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