Conductivity of two-dimensional disordered nanowire networks: Dependence on length-ratio of conducting paths to all nanowires

Abstract

Conducting behavior of two-dimensional (2D) disordered nanowire networks (DNNs) is studied. We find that the length-ratio (ηcp) of conducting paths to all nanowires in the network plays a key role in determining the network conductivity. An algorithm is designated to monitor the formation of conducting paths in the networks and the evolution of network conductance at the same time. As either the area fraction or length of nanowires increases, the length-ratio (ηcp) of the conducting paths expands; meanwhile, the network conductance increases. The network conductance is normalized by the conductance of the regular network so that normalized network conductivity (σ) is obtained. A linear relationship is observed when plotting σ against ηcp. An equation of σ=2(ηcp−0.5) is obtained when ηcp is higher than the threshold. It could fit most part of the simulated plots, except for the region near ηcp∼0.5. 2D transparent and conductive films are built from randomly arranged silver nanowires. Linear behavior is also observed, with the slope less than 2, which is due to the existence of the junction resistance between nanowires. The obtained equation is in agreement with the previous result of the Effective Medium Theory. Finally, the length-ratio (ηcp) could serve as a basic topological parameter in describing the conducting behavior of DNNs.