A critical path approach for elucidating the temperature dependence of granular hopping conduction
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We revisit the classical problem of granular hopping conduction’s σ ∝ exp[-(To/T)1/2] temperature dependence, where σ denotes conductivity, T is temperature, and To 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 Agx(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.
Keywordsgranular hopping conduction insulator-conductor composites critical path method immediate-neighbor hopping
- 9.Y. N. Wu, Y. F. Wei, Z. Q. Li, and J. J. Lin, Granular hopping conduction in (Ag, Mo)x(SnO2)1-x films in the dielectric regime, arXiv: 1708.04434 (2017)Google Scholar
- 11.N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford: Clarendon, 1979Google Scholar
- 34.C. J. Adkins, Hopping and Related Phenomena, Eds. H Fritzsche and M Pollak, Singapore: World Scientific, 1990, pp 93–109Google Scholar
- 39.P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, Heidelberg: Springer, 2006Google Scholar