  The Boltzmann transport equation is one of the most relevant framework to
study the heat transport at the nanoscale, beyond the diffusive regime and up
to the micrometer-scale. In the general case of three-dimensional devices, the
particle Monte Carlo approach of phonon transport is particularly powerful and
convenient, and requires reasonable computational resources. In this work, we
propose an original and versatile particle Monte Carlo approach parametrized by
using ab-initio data. Both the phonon dispersion and the phonon-phonon
scattering rates have been computed by DFT calculation in the entire 3D
Brillouin zone. To treat the phonon transport at rough interfaces, a
combination of specular and diffuse reflections has been implemented in phase
space. Thermal transport has been investigated in nanowires and thin films made
of cubic and hexagonal Silicon, including edge roughness, in terms of effective
thermal conductivity, phonon band contributions and heat flux orientation. It
is shown that the effective thermal conductivity in quasi-ballistic regime
obtained from our Monte Carlo simulation cannot be accurately fitted by simple
semi-analytical Matthiessen-like models and that spectral approaches are
mandatory to get good results. Our Full Band approach shows that some phonon
branches exhibiting a negative group velocity in some parts of the Brillouin
zone may contribute negatively to the total thermal flux. Besides, the thermal
flux clearly appears to be oriented along directions of high density of states.
The resulting anisotropy of the heat flux is discussed together with the
influence of rough interfaces.
