Improvements in 3-omega measurement of thermal conductivity for nanostructured materials

Nanostructured materials have reduced thermal conductivity in order to enhance the thermoelectric figure of merit (ZT). The 3$\omega$ method is widely used for vertical thermal conductivity measurements in the nanostructure materials, especially layered materials. The challenge for this method is to measure the small 3$\omega$ voltage at the third harmonic, above the comparably large $\omega$ voltage from the sample at the fundamental frequency, complicated by the nonlinear signal from other components in the measurement circuit. We carefully study the 3$\omega$ method [Cahill, Rev. Sci. lnstrum. 61 (2), 802 (1990)] and develop a strategy to increase the signal to noise ratio of the data, for more accurate results. We also investigate an alternate sample preparation geometry for the 3$\omega$ measurement, so that the heat flow is vertical and linear through the thin film instead of cylindrical as is standard for this method. This results in a direct measurement of the vertical thermal conductivity in such an anisotropic material. New geometries for measuring lateral thermal conductivity will also be proposed and explored.