We determine the size effect on the lattice thermal conductivity of nanoscale wire and multilayer structures formed in and by some typical semiconductor materials, using the Boltzmann transport equation and focusing on the Knudsen flow effect. For bo
th types of nanostructured systems we find that the phonon transport is reduced significantly below the bulk value by boundary scattering off interface defects and/or interface modes. The Knudsen flow effects are important for almost all types of semiconductor nanostructures but we find them most pronounced in Si and SiC systems due to the very large phonon mean-free paths. We apply and test our wire thermal-transport results to recent measurements on Si nanowires. We further investigate and predict size effects in typical multilayered SiC nanostructures, for example, a doped-SiC/SiC/SiO$_2$ layered structure that could define the transport channel in a nanosize transistor. Here the phonon-interface scattering produces a heterostructure thermal conductivity smaller than what is predicted in a traditional heat-transport calculation, suggesting a breakdown of the traditional Fourier analysis even at room temperatures. Finally, we show that the effective thermal transport in a SiC/SiO$_2$ heterostructure is sensitive to the oxide depth and could thus be used as an in-situ probe of the SiC oxidation progress.
SiC is a robust semiconductor material considered ideal for high-power application due to its material stability and large bulk thermal conductivity defined by the very fast phonons. In this paper, however, we show that both material-interface scatte
ring and total-internal reflection significantly limit the SiC-nanostructure phonon transport and hence the heat dissipation in a typical device. For simplicity we focus on planar SiC nanostructures and calculate the thermal transport both parallel to the layers in a substrate/SiC/oxide heterostructure and across a SiC/metal gate or contact. We find that the phonon-interface scattering produces a heterostructure thermal conductivity significantly smaller than what is predicted in a traditional heat-transport calculation. We also document that the high-temperature heat flow across the metal/SiC interface is limited by total-internal reflection effects and maximizes with a small difference in the metal/SiC sound velocities.
