Temperature dependence of the resistance of metallic nanowires (diameter $\geq$ 15 nm): Applicability of Bloch-Gr\"{u}neisen theorem

Abstract

We have measured the resistances (and resistivities) of Ag and Cu nanowires of diameters ranging from 15nm to 200nm in the temperature range 4.2K-300K with the specific aim to assess the applicability of the Bloch-Gr\"{u}neisen formula for electron phonon resistivity in these nanowires. The wires were grown within polymeric templates by electrodeposition. We find that in all the samples the resistance reaches a residual value at T=4.2K and the temperature dependence of resistance can be fitted to the Bloch-Gr\"{u}neisen formula in the entire temperature range with a well defined transport Debye temperature ($\Theta_{R}$). The value of Debye temperature obtained from the fits lie within 8% of the bulk value for Ag wires of diameter 15nm while for Cu nanowires of the same diameter the Debye temperature is significantly lesser than the bulk value. The electron-phonon coupling constants (measured by $\alpha_{el-ph}$ or $\alpha_{R}$) in the nanowires were found to have the same value as that of the bulk. The resistivities of the wires were seen to increase as the wire diameter was decreased. This increase in the resistivity of the wires may be attributed to surface scattering of conduction electrons. The specularity p was estimated to be about 0.5. The observed results allow us to obtain the resistivities exactly from the resistance and gives us a method of obtaining the exact numbers of wires within the measured array (grown within the template).