Temperature-Dependent Thermoelectric Properties of Individual Silver Nanowires

Individual highly pure single crystalline silver nanowires (Ag NWs) were investigated with regard to the electrical conductivity $\sigma$, the thermal conductivity $\lambda$ and the Seebeck coefficient $S$ as function of the temperature $T$ between $1.4\,\mathrm{K}$ and room temperature (RT). Transmission electron microscopy was performed subsequently to the thermoelectric characterization of the Ag NWs, so that their transport properties can be correlated with the structural data. The crystal structure, surface morphology and the rare occurrence of kinks and twinning were identified. The thermoelectric properties of the Ag NWs are discussed in comparison to the bulk: $S_{\mathrm{Ag,Pt}}(T)$ was measured with respect to platinum and is in agreement with the bulk, $\sigma(T)$ and $\lambda(T)$ showed reduced values with respect to the bulk. The latter are both notably dominated by surface scattering caused by an increased surface-to-volume ratio. By lowering $T$ the electron mean free path strongly exceeds the NW's diameter of $150\,\mathrm{nm}$ so that the transition from diffusive transport to quasi ballistic one dimensional transport is observed. An important result of this work is that the Lorenz number $L(T)$ turns out to be independent of surface scattering. Instead the characteristic of $L(T)$ is determined by the material's purity. Moreover, $\sigma(T)$ and $L(T)$ can be described by the bulk Debye temperature of silver.