Size Effects on the Thermal Conductivity of Thin Metallic Wires: Microscale Implications

This study examines the influence of radial thickness on the thermal conductivity of thin metallic wires. While size effects on the electrical conductivity of thin wires have been discussed in the literature, research into size effects on thermal conductivity still requires investigation. At such small length scales, the assumption that the reduced electrical conductivity can be simply related to the reduced thermal conductivity through a Wiedemann-Franz relation is subject to question. This study uses the Boltzmann transport equation for electrons to determine the thermal conductivity of a thin wire directly. Electrons are treated as the primary heat carriers in a thin wire with a thermal gradient along the axis. A single-crystal, defect-free, metallic thin wire is considered in the derivation. An expression is presented which accounts for the radial size effects on axial thermal conductivity. The derived thermal conductivity is compared to expressions for the reduced electrical conductivity, and the applicability of the Wiedemann-Franz relation is discussed.