A critical path approach for elucidating the temperature dependence of granular hopping conduction
Tsz Chun Wu1, Juhn-Jong Lin2,3, Ping Sheng1()
1. Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 2. Institute of Physics and Department of Electrophysics, Chiao Tung University, Hsinchu 30010, Taiwan, China 3. Center for Emergent Functional Matter Science, Chiao Tung University, Hsinchu 30010, Taiwan, China
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 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.
. [J]. Frontiers of Physics, 2018, 13(5): 137205.
Tsz Chun Wu, Juhn-Jong Lin, Ping Sheng. A critical path approach for elucidating the temperature dependence of granular hopping conduction. Front. Phys. , 2018, 13(5): 137205.
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