Temperature-dependent thermal conductivity and suppressed Lorenz number in ultrathin gold nanowires

Abstract

The values of material parameters required for quantitative electrothermal modeling of nanoscale structures typically differ strongly from those of the bulk material. In this work, we apply a simple experimental technique that allows us to estimate values for thermal conductivity of both a metal nanowire and its insulating substrate by measuring the increase in resistance due to small amounts of dc self-heating. We measure gold nanowires with widths between 24 and 55 nm using this technique, and extract relevant material parameters as a function of temperature. Electrical resistivities of our nanowires are width dependent and much higher than bulk gold values, and enhanced temperature dependence of the resistivity indicates a depressed Debye temperature due to significant phonon softening. The fit thermal conductivity versus temperature of our 21-nm ${\mathrm{SiO}}_{2}$ on Si substrate is highly consistent with literature values for oxide thin films. We find the thermal conductivity of the nanowires increases rapidly with temperature and width and is well below the value for bulk gold, which can be qualitatively explained by the dominance of structural scattering. The Lorenz number is relatively constant over temperature, as in the Wiedemann-Franz theory, but it is significantly lower than reported values for bulk gold and exhibits some width dependence.