  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 both 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.
