Reducing thermal conductivity of thermoelectric materials by using a narrow wire geometry

Abstract

The dependence of the thermal conductivity of narrow wires made from bismuth and covalently bonded materials on wire diameter was numerically calculated by considering contributions of mean free paths of carriers and phonons. The results suggest that a reduction in the thermal conductivity should be observable in a bismuth wire having a diameter of less than 1 μm sample. A reduction of nearly 20% in the temperature range of 150–300 K is expected due to the use of a narrow wire geometry. Such a geometry reduces the mobility and the thermal conductivity of the carriers, which is the dominant component, while the thermal conductivity due to phonons was dramatically reduced by using narrow wires at temperatures under 50 K due to the longer mean free path phonons. The thermal conductivity of materials with covalent bonding such as silicon was also estimated, and it is expected that the thermal conductivity of a silicon wire could be reduced due to the mean free path of phonons being longer than that of the carriers. The results suggest that it should be possible to enhance the figure of merit by reducing the thermal conductivity through using wire geometries having diameters of less than 100 nm in materials having low mobilities, high thermal conductivities, and high Debye temperatures.