Understanding phonon transport across interfaces serves as a major tool to advance a diverse spectrum of fundamental and applied research. Unlike bulk materials, where the three-phonon scattering process is relatively straightforward to investigate, little research has been dedicated to the detailed analysis of the three-phonon scattering process at interfaces due to the complexity of interfaces and the mismatch of phonon dispersions of the two connecting parts. Based on the nonequilibrium molecular dynamics simulation, which is one of the most popular approaches to investigate the thermal conductance, we develop an explicit theoretical framework by considering the full third-order force constants field to quantify the two- and three-phonon scattering at interfaces. Bulk Ar is used as a benchmark to validate the computational scheme by comparing the results with those using the all-order phonon scattering method [frequency-dependent directly decomposed method; Y. Zhou and M. Hu, Phys. Rev. B 92, 195205 (2015)]. Then, Ar–heavy Ar and Si-Ge interfaces are studied and the respective role of two- and three-phonon scattering processes is quantitatively characterized at different temperatures. Moreover, all four different types of the three-phonon scattering process are explicitly evaluated. The method developed herein for splitting the two- and three-phonon scattering processes in the interfacial heat transport is expected to advance our understanding of the phonon process at interfaces, and will facilitate designing high-performance interfacial structures in terms of efficient thermal management.

Probing detailed spectral dependence of phonon transport properties in bulk materials is critical to improve the function and performance of structures and devices in a diverse spectrum of technologies. Currently, such information can only be provided by the phonon spectral energy density (SED) or equivalently, time domain normal mode analysis (TDNMA) methods in the framework of equilibrium molecular dynamics simulations (EMD), but has not been realized in nonequilibrium molecular dynamics simulations (NEMD) so far. In this paper we generate a scheme directly based on NEMD and lattice dynamics theory, called the time domain direct decomposition method (TDDDM), to predict the phonon mode specific thermal conductivity. Two benchmark cases of Lennard-Jones (LJ) argon and Stillinger-Weber (SW) Si are studied by TDDDM to characterize contributions of individual phonon modes to overall thermal conductivity and the results are compared with that predicted using SED and TDNMA. Similar trends are found for both cases, which indicate that our TDDDM approach captures the major phonon properties in NEMD run. The biggest advantage of TDDDM is that it can be used to investigate the size effect of individual phonon modes in NEMD simulations, which cannot be tackled by SED and TDNMA in EMD simulations currently. We found that the phonon modes with mean free path larger than the system size are truncated in NEMD and contribute little to the overall thermal conductivity. The TDDDM provides direct physical origin for the well-known strong size effects in thermal conductivity prediction by NEMD. Moreover, the well-known common sense of the zero thermal conductivity contribution from the Γ point is rigorously proved by TDDDM. Since TDDDM inherently possesses the nature of both NEMD simulations and lattice dynamics, we anticipate that TDDDM is particularly useful for offering a deep understanding of phonon behaviors in nanostructures or under strong confinement, especially when the structure size is significantly smaller than the characteristic mean free path of the dominant phonons.

Pursuing extremely low interfacial thermal resistance has long been the task of many researchers in the area of nano-scale heat transfer, in particular pertaining to improve heat dissipation performance in electronic cooling. While it is well known and documented that confining a macroscopic third layer between two dissimilar materials usually increases the overall interfacial thermal resistance, no research has realized the fundamental decrease in resistance so far. By performing nonequilibrium molecular dynamics simulations, we report that the overall interfacial thermal resistance can be reduced by 6 fold by confining mass graded materials with thickness of the order of nanometers. As comparison we also studied the thermal transport across the perfectly abrupt interface and the widely used alloyed (rough) interface, which shows an opposing and significantly large increase in the overall thermal resistance. With the help of frequency dependent interfacial thermal conductance and wave packet dynamics simulation, different mechanisms governing the heat transfer across these three types of interfaces are identified. It is found that for the rough interface there are two different regimes of interfacial heat transfer, which originates from the competition between phonon scattering and the thickness of the interface. The mechanism of dramatically improved interfacial heat transfer across the nano-confined mass graded interface resides in the minor phonon reflection when the phonons first reach the mass graded area and the rare occurrence of phonon scattering in the subsequent interior region. The phonons are found to be gradually truncated by the geometric interfaces and can travel through the mass graded layer with a high transmission coefficient, benefited from the small mass mismatch between two neighboring layers in the interfacial region. Our findings provide deep insight into the phonon transport across nano-confined mass graded layers and also offer significant guidance for designing advanced thermal interface materials.