Fig. 3: Dependence of network resistivity on nanoparticle dimensions.
From: Understanding how junction resistances impact the conduction mechanism in nano-networks
a Resistivity of spray-cast silver nanowire (AgNW) networks versus inverse nanowire length, \({l}_{{{{{{\rm{NW}}}}}}}^{-1}\). The line is a fit to Eq. (2). Here, the carrier density is large, allowing the second square bracketed term in Eq. (2) to be neglected. The uncertainty in \({l}_{{{{{{\rm{NW}}}}}}}^{-1}\) is ±SE in the mean (n = 100−200) and ρNet is the RSS of errors in network cross sectional area, ANet, and LCh. Resistivity of spray-cast nanosheet networks, ρNet, versus nanosheet length, lNS, for networks of (b) AgNSs, (c) graphene, (d) WS2 and (e) WSe2. In b–e, the lines represent fits to Eq. (3). The carrier density is large in b and c allowing the second square-bracketed term in Eq. (3) to be neglected. The behaviour in b and c is counterintuitive as the general expectation is that smaller nanosheets lead to higher resistivity. Fitting the data in a–e yields values for the junction resistance, RJ, and nanoparticle resistivity, ρNP, for each material. The latter parameter, combined with the nanoparticle dimensions yields the nanoparticle resistance, RNP. Values of RJ and ρNP ρNP, as well as ranges of RJ/RNP, are given for each material in a–e and Table 1. The data are presented as means ± SE in the mean for lNS (n = 89–443, Supplementary Note 2) and ρNet (n = 5−29). f Junction resistance, RJ, plotted versus nanoparticle resistivity, ρNP, demonstrating scaling. The uncertainty in RJ is ±the error in the fits to Eqs. (2) and (3). The uncertainty in ρNP is the RSS of errors in RJ and SE in the mean for tNS (or DNW) across each material (n = 135–443).
