We revisit the classical problem of granular hopping conduction＇s σ∝exp[-（To/T）1/2] temperature dependence, where a denotes conductivity, T is temperature, and To is a sample-dependent constant. By using the hopp...We revisit the classical problem of granular hopping conduction＇s σ∝exp[-（To/T）1/2] temperature dependence, where a 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 configuration- averaged 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 expla- nation 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.展开更多
文摘We revisit the classical problem of granular hopping conduction＇s σ∝exp[-（To/T）1/2] temperature dependence, where a 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 configuration- averaged 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 expla- nation 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.
