  We numerically investigate thermal transport at solid-solid interfaces with
graded intermediate layers whose masses vary exponentially from one side to the
other. Using Non-Equilibrium Green's Function and Non-Equilibrium Molecular
Dynamics simulations, we show that an exponentially mass-graded junction with a
finite thickness can result in 68\% of enhancement in thermal conductance
larger compared to a single bridging layer (29\%) and a linear mass-graded
junction (64\%) of similar thickness. We examine how the thermal conductance at
such interfaces is influenced by geometric qualities and strength of
anharmonicity. For geometric properties, we tested the effects from number of
layers and the junction thickness. In the absence of anharmonicity, increasing
the number of layers results in better elastic phonon transmission at each
individual boundary, countered by the decrease of available conducting
channels. Consequently, in the harmonic regime, conductance initially increases
with number of layers due to better bridging, but quickly saturates. The
presence of slight anharmonic effects (at ultra-low temperature T = 2 K) turns
the saturation into a monotonically increasing trend. Anharmonic effects can
facilitate interfacial thermal transport through the thermalization of phonons.
At high temperature, however, the role of anharmonicity as a facilitator of
interfacial thermal transport reverses. Strong anharmonicity introduces
significant intrinsic resistance, overruling the enhancement in thermal
conduction at the boundaries. Our analysis shows that in our model
Lennard-Jones system, the influence of a mass-graded junction on thermal
conductance is dominated by the phonon thermalization through anharmonic
effects, while elastic phonon transmission plays a secondary role.
