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

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Abstract

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.

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Authors and Affiliations

  1. Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Tsz Chun Wu & Ping Sheng

  2. Institute of Physics and Department of Electrophysics, Chiao Tung University, Hsinchu, 30010, Taiwan, China

    Juhn-Jong Lin

  3. Center for Emergent Functional Matter Science, Chiao Tung University, Hsinchu, 30010, Taiwan, China

    Juhn-Jong Lin

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  1. Tsz Chun Wu
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  2. Juhn-Jong Lin
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  3. Ping Sheng
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Correspondence to Ping Sheng.

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Wu, T.C., Lin, JJ. & Sheng, P. A critical path approach for elucidating the temperature dependence of granular hopping conduction. Front. Phys. 13, 137205 (2018). https://doi.org/10.1007/s11467-018-0814-y

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