Role of phonon coupling and non-equilibrium near the interface to interfacial thermal resistance: The multi-temperature model and thermal circuit

Abstract

Interfacial thermal transport between two semi-infinite leads has been widely assumed to be independent from bulk transport in the two leads. However, here we show that due to the mismatch of phonon modal interfacial conductance and modal thermal conductivity, thermal interfacial transport is affected by the bulk thermal transport, and phonons near the interface can be driven into strong non-equilibrium, causing an additional resistance that is lumped into the interfacial resistance. This is captured using a multi-temperature model (MTM) that we introduce. Using thermal properties predicted from first-principles calculations and interfacial transmission coefficients predicted from the acoustic mismatch model, we present a case study of thermal transport across the Si-Ge interfaces using our MTM. The results show that phonon branches are in non-equilibrium near the interface due to energy redistribution caused by different thermal properties of the materials and the corresponding transmission coefficients, and the overall interfacial thermal conductance is 5.4% smaller than the conventional prediction, due to the phonon non-equilibrium resistance. We present a thermal circuit to include this new resistance due to phononphonon coupling and non-equilibrium near the interfaces. The thermal circuit also shows that increasing the phonon-phonon coupling factor G pp can reduce this resistance. Our MTM is a general and simple analytical approach expected to be useful for investigating the coupling between thermal transport across interfaces and in the bulk leads.

Computational predictions of quantum thermal transport across nanoscale interfaces

“…59 In this scenario, the electron temperature differs from that of phonons in metal. Hence, two temperature models 60,61 and even multi-temperature models 62 have been proposed to characterize the nonequilibrium states between the phonons and other heat carriers near the interface. This temperature difference between the electrons and phonons can explain the measured thermal rectification.…”

Dramatic increase in the thermal boundary conductance and radiation limit from a Nonequilibrium Landauer Approach

“…However, it was pointed out in previous modal NEMD simulations [27] and multi-temperature model [36] that, in a typical experimental interface between two semi-infinite solids, the thermostats are placed far enough from the interface, so different phonon modes arrive at the interface at different emitted temperatures although they leave the thermostat with the same temperature. On the other hand, different phonon modes will not share the same T λ either, similarly due to the coupling between interfacial transport and bulk transport in the leads [36]. A rigorous approach will calculate TBC by using G λ in the multi-temperature model [36] that covers both the interface and two leads.…”

“…On the other hand, different phonon modes will not share the same T λ either, similarly due to the coupling between interfacial transport and bulk transport in the leads [36]. A rigorous approach will calculate TBC by using G λ in the multi-temperature model [36] that covers both the interface and two leads. However, here without going into too much detail in the two leads, we can assume the same T eλ and T λ as two limiting cases, to derive the TBC respectively.…”

Multitemperature Modeling of Thermal Transport across a Au–GaN Interface from Ab Initio Calculations

“…To capture the nonequilibrium phenomena of the phonons, a multitemperature model (MTM) generalization has been developed. , MTM describes a nonthermal lattice by partitioning the vibrations into individual phonon branches with distinct equilibrium temperatures. So far, MTM has been utilized to model thermal transport originating from the electron–phonon coupling in different situations, such as the thermal transport in pulse-laser-irradiated single-layer graphene, thermal transport in nanosized graphene, and phonon–phonon coupling across the Si–Ge interfaces . To the best of our knowledge, no MTM has been yet developed to capture the thermal energy transport and nonequilibrium originating from electron–phonon coupling at the Au–GaN interface.…”

“…19,23 phene, 24 thermal transport in nanosized graphene, 25 and phonon−phonon coupling across the Si−Ge interfaces. 26 To the best of our knowledge, no MTM has been yet developed to capture the thermal energy transport and nonequilibrium originating from electron−phonon coupling at the Au−GaN interface.…”