Electrical and thermal conductivity are important fundamental material quantities to establish for understanding and predicting device properties when nanoscale dimensions are involved. Obtaining direct results for electrical resistivity is readily achieved. However, direct measurements of thermal conductivity is extremely difficult due to fabrication and parasitic heat transport issues.
Direct measurements are reported of thermal conductivity for aluminum nanowires. A nanofabricated electrothermal test structure is described for studying the nanowires near room temperature. Nanowires studied are 100 nm thick with 75, 100, and 150 nm widths. The thermal conductivity is found to be substantially lower than for bulk Al, and to decrease as nanowire width is reduced. Measurements of the electrical resistivity show it to increase with reduced nanowire width. These combined measurements allow examination of the Wiedemann-Franz law and to investigate the importance of phonon heat propagation in metals at room temperature.
To aide in the interpretation of the results, we develop an approach for calculating the electron and phonon thermal conductivities, as well as the electrical conductivity. Effects such as surface and grain boundary scattering, which are negligible for larger structures, significantly influence electrical and thermal properties of nanoscale objects. The conventional wisdom for metals holds that thermal transport is predominantly by electrons, and that contribution due to lattice vibrations—that is, thermal transport by phonons—is negligible. Furthermore, it is usually assumed that transport by electrons is identical for describing current and heat. These assumptions are often used to justify the use of the Wiedemann-Franz law to infer thermal conductivity based on measurements of electrical resistivity. Our experiments suggest a breakdown of the Wiedemann-Franz law at the nanoscale. Solution of the Boltzmann transport equation for both electrons and phonons in nanowires will be used to examine the applicability of Wiedemann-Franz law at the nanoscale. It is found that Wiedemann-Franz law can be used to obtain the electronic component of thermal conductivity to good approximation, but that the phonon term must be considered in order to properly estimate total thermal conductivity of metallic nanowires. The calculations are extended to theoretically treat several other metals at room temperature.