<div>The rapid advance in modern electronics and photonics is pushing device design to the micro- and nano-scale, and the resulting high power density imposes immense challenges to thermal management. Promising materials like carbon nanotubes (CNTs) and graphene offer high thermal conductivity in the axial (or in-plane) directions, but their thermal transport in the radial (or cross-plane) directions are poor, limiting their applications. Hierarchical structures like pillared graphene, which is composed of many CNT-graphene junctions, have been proposed. However, thermal</div><div>interfacial resistance is a critical issue for thermal management of these systems. In this work, we have systematically explored thermal transport across interfaces,</div><div>particularly in pillared graphene and silicon/heavy-silicon.</div><div><br></div><div><div>First, by recognizing that thermal resistance of the 3D pillared graphene architecture primarily comes from CNT-graphene junctions, a simple network model of thermal transport in pillared graphene structure is developed. Using non-equilibrium molecular dynamics (NEMD), the resistance across an individual CNT-graphene junction with sp2 covalent bonds is found to be around 6 × 10−11 m2K/W, which is significantly lower than typical values reported for planar interfaces between dissimilar materials. Interestingly, when the CNT pillar length is small, the interfacial resistance</div><div>of the sp2 covalent junction is found to decrease as the CNT pillar length decreases, suggesting the presence of coherence effects. The junction resistance Rj is eventually</div><div>used in the network model to estimate the effective thermal conductivity, and the results agree well with direct MD simulation data, demonstrating the effectiveness of our model.</div></div><div><br></div><div><div>Then we identify three different mechanisms which can lead to thermal resistances across the pillared graphene junction: the material mismatch (phonon propagates from CNT to graphene), the non-planar junction (the phonon propagation direction must change), and defects (there are six heptagons at each junction). The NEMD results show that three mechanisms lead to similar resistance at the CNT-graphene junction, each at around 2.5 × 10−11 m2K/W.</div></div><div><br></div><div><div>Further, we have predicted the transmission function of individual phonon mode using the wave packet method at CNT-graphene junction. Intriguing phonon polarization conversion behavior is observed for most incident phonon modes. It is found that the polarization conversion dominates the transmission and is more significant at larger phonon wavelength. We attribute such unique phonon polarization conversion behavior to the dimensional mismatch across CNT-graphene interface. It is found that the transmission functions at the junction cannot be predicted by the conventional acoustic mismatch models due to the existence of dimensional mismatch. Further analysis shows that, the dimensionally mismatched interface, on one hand tends to reduce the transmission and conductance due to defects and the change of phonon propagation direction at the interface, while on the other hand tends to enhance the transmission and conductance due to the new phonon transport channel introduced by polarization conversion.</div></div><div><br></div><div><div>Finally, we address that many recent experiments have shown that the measured thermal boundary conductances (TBCs) significantly exceed those calculated using the Landauer approach. We identify that a key assumption that an interface is a local equilibrium system (different modes of phonons on each side of the interfaces are at the emitted phonon temperature Te), is generally invalid and can contribute to the discrepancy. We show that the measurable temperature for each individual mode is the ”modal equivalent equilibrium temperature” T rather than Te. Also,</div><div>due to the vast range of transmission functions, different phonon modes are out of local thermal equilibrium. Hence, the total conductance cannot be simply calculated as a summation of individual modal conductance. We modify the Landauer approach to include these effects and name it the ”Nonequilibrium Landauer approach”. Our approach has been used on the carbon nanotube (CNT)/graphene and Si/heavy-Si interfaces which are matched interfaces, and it gives 310% increases in TBC as compared to the conventional Landauer approach at CNT-graphene junction and even higher increase for Si/heavy-Si with small mass ratios. A convenient chart is created to estimate the conductance correction based on our approach, and it yields quite accurate results. Our work indicate that the measured high TBCs in experiments can be due to this nonequilibrium effect rather than the other proposed mechanisms, like inelastic phonon transmission and cross-interface electron-phonon coupling.</div></div><div><br></div><div><div>The results obtained in this study will provide a deeper understanding of nanoscale thermal transport across interfaces. This research also provides new perspectives of</div><div>atomic- and nano-scale engineering of materials and structures to enhance performance of thermal management.</div></div>