The Tortuosity Effect on the Thermal Conductivity of Si Nanowires

ABSTRACT The thermal conductivity of tortuous silicon nanowires with constant cross section at room temperature was investigated in use of full-spectrum Monte-Carlo simulations. Various geometric features that can be possibly used to describe the tortuosity of the nanowires were studied and their relationships with the thermal conductivity were explored. Comparison of simulation results with experimental data shows similar magnitudes and variation trend of the thermal conductivity against the nanowire hydraulic diameter. The more tortuous, the smaller the thermal conductivity is. Among all, data collapse is best when shown against the surface-to-volume ratio and the correlation length of the surface roughness does not affect the thermal conductivity at all. By taking the surface-to-volume ratio into account for the boundary scattering rate, which also depends on the phonon frequency indirectly through the phonon group velocity, we are able to obtain satisfactory predictions based on a linear spectral model, not only about the thermal conductivity but also about the spectral heat flux density distribution. The model also shows that the relative reduction caused by tortuosity decreases with increasing frequency. For highly tortuous nanowires of diameter 22 nm, simply increasing the tortuosity is sufficient to obtain simulated thermal conductivities that are smaller than the experimentally measured value.