Effect of Electrical Contact Resistance on Measurement of Thermal Conductivity and Wiedemann-Franz Law for Individual Metallic Nanowires

The electrical and thermal properties of metallic nanostructures have attracted considerable fundamental and technological interests. Recent studies confirmed a dramatic decrease in the electrical and thermal conductivities when the dimension is comparable or even smaller than the electron mean free path. However, the verification of the Wiedemann-Franz law in these nanostructures remains hotly debated. The Lorenz number obtained from the two-probe measurement is found to be much larger than that from the four-probe measurement. Here, we reported the electrical and thermal properties of the individual silver nanowires measured by the two-probe and four-probe configurations. The measured electrical contact resistance is found to be nearly temperature-independent, indicating a ballistic-dominant electronic transport at the contacts. When the effect of thermal contact resistance is diminished, the Lorenz number measured by the four-probe configuration is comparable to the Sommerfeld value, verifying that the Wiedemann-Franz law holds in the monocrystalline-like silver nanowire. Comparatively, the derived electrical conductivity becomes smaller and the thermal conductivity becomes larger in the two-probe measurement, confirming that the electrical contact resistance will introduce a large error. The present study experimentally demonstrates a reasonable explanation to the discouragingly broad span in the Lorenz number obtained from different metallic nanostructures.