  As nanostructured devices become prevalent, interfaces often play an
important role in thermal transport phenomena. However, interfacial thermal
transport remains poorly understood due to complex physics across a wide range
of length scales from atomistic to microscale. Past studies on interfacial
thermal resistance have focused on interface-phonon scattering at the atomistic
scale but overlooked the complex interplay of phonon-interface and
phonon-phonon scattering at microscale. Here, we use the Peierls-Boltzmann
transport equation to show that the resistance from the phonon-phonon
scattering of non-equilibrium phonons near a Si-Ge interface is much larger
than that directly caused by the interface scattering. We report that
non-equilibrium in phonon distribution leads to significant entropy generation
and thermal resistance upon three-phonon scattering by the Boltzmann's
H-theorem. The physical origin of non-equilibrium phonons in Ge is explained
with the mismatch of phonon dispersion, density-of-states, and group velocity,
which serve as general guidance for estimating the non-equilibrium effect on
interfacial thermal resistance. Our study bridges a gap between atomistic scale
and less studied microscale phenomena, providing comprehensive understanding of
overall interfacial thermal transport and the significant role of phonon-phonon
scattering.
