Wiedemann-Franz law of Cu-coated carbon fiber

We investigate the thermal and electrical conductivities of Cu-coated carbon fiber (Cu-CF), which is designed to reduce the weight of metal wires. The electrical and thermal properties of Cu-CF are assessed using the 3ω method. This material is formed by depositing a thin layer of Cu, approximately 100–200 nm thick, on a core of CF with a diameter of 7μm. This structure grants the wire metal-like electrical properties, i.e., a positive temperature coefficient of resistance (TCR), with phonon-driven heat conduction behavior. Therefore, metal-like electrical conduction and insulator-like thermal conduction are combined in the Cu-CF wire. Electrical conduction is completely dominated by the Cu layer regardless of temperature. In contrast, heat conduction is dominated by the inner-core CF near 300 K, but the Cu layer dominates at lower temperatures. Thus, the deviation of Lorenz number L of Cu-CF from its theoretical value of Lo = 2.44 × 10−8 W Ω/K2 increases as the Cu layer becomes thinner and the temperature increases.