Effect of sample size on the temperature dependence of the resistivity of copper below 4.2K

Abstract

The electrical resistivity rho (d,T) of single-crystalline copper whiskers with diameters d between 7 and 81 mu m and residual electron mean free path le=240 mu m has been measured in the temperature range 0.4K<or=T<or=4.2K. The magnitude of the temperature-dependent part Delta rho (d,T) turns out to increase linearly with the residual resistivity, rho (d,0), of the samples. Moreover Delta rho (d,T) is found to be substantially smaller after the sample surfaces had been roughened by chemical etching. These results are in quantitative agreement with recent size-effect calculations of Sambles et al. (1982) at temperatures where Delta rho ( infinity ,T)<< rho ( infinity ,0). The conclusion to be drawn is that in the low-temperature limit in conjunction with the theoretical predictions, surface scattering simply enhances the temperature dependence of the bulk resistivity by a constant factor.