  Comprehensive understanding of thermal transport in nanostructured materials
needs large scale simulations bridging length scales dictated by different
physics related to the wave versus particle nature of phonons. Yet, available
computational approaches implicitly treat phonons as either just waves or as
particles. In this work, using a full wave-based Non-Equilibrium Green's
Function (NEGF) method, and a particle-based ray-tracing Monte Carlo (MC)
approach, we investigate the qualitative differences in the wave and
particle-based phonon transport at the vicinity of nanoscale features. For the
simple example of a nanoporous geometry, we show that phonon transmission
agrees very well for both methods with an error margin of approximately 15%,
across phonon wavelengths even for features with sizes down to 3-4 nm. For
cases where phonons need to squeeze in smaller regions to propagate, we find
that MC underestimates the transmission of long wavelength phonons whereas wave
treatment within NEGF indicates that those long wavelength phonons can
propagate more easily. We also find that particle-based simulation methods are
somewhat more sensitive to structural variations compared to the wave-based
NEGF method. The insight extracted from comparing wave and particle methods can
be used to provide a better and more complete understanding of phonon transport
in nanomaterials.
