  We present a calculation of the lattice thermal conductivity of Si-Ge
nanowires (NWs), based on solving the Boltzmann transport equation by the Monte
Carlo method of sampling the phonon mean free paths. We augment the previous
work with the full phonon dispersion and a partially diffuse momentum-dependent
specularity model for boundary roughness scattering. We find that phonon
flights are comprised of a mix of long free-flights over several {\mu}m
interrupted by bursts of short flights, resulting in a heavy tailed
distribution of flight lengths, typically encountered in L\'{e}vy walk
dynamics. Consequently, phonon transport in Si-Ge NWs is neither entirely
ballistic nor diffusive; instead, it falls into an intermediate regime called
superdiffusion where thermal conductivity scales with the length of the NW as
$\kappa \propto L^{\alpha}$ with the exponent of length dependence
$\alpha\approx 0.33$ over a broad range of wire lengths 10 nm$<L<$10 $\mu$m
regardless of diameter and roughness. We conclude that thermal conductivity in
Si-Ge alloy NWs is length-dependent up to 10 $\mu$m and therefore can be tuned
for thermoelectric applications.
