Anharmonic Phonon Interactions at Interfaces and Contributions to Thermal Boundary Conductance

Abstract

Continued reduction in characteristic dimensions in nanosystems has given rise to increasing importance of material interfaces on the overall system performance. With regard to thermal transport, this increases the need for a better fundamental understanding of the processes affecting interfacial thermal transport, as characterized by the thermal boundary conductance. When thermal boundary conductance is driven by phononic scattering events, accurate predictions of interfacial transport must account for anharmonic phononic coupling as this affects the thermal transmission. In this paper, a new model for phononic thermal boundary conductance is developed that takes into account anharmonic coupling, or inelastic scattering events, at the interface between two materials. Previous models for thermal boundary conductance are first reviewed, including the diffuse mismatch model, which only considers elastic phonon scattering events, and earlier attempts to account for inelastic phonon scattering, namely, the maximum transmission model and the higher harmonic inelastic model. A new model is derived, the anharmonic inelastic model, which provides a more physical consideration of the effects of inelastic scattering on thermal boundary conductance. This is accomplished by considering specific ranges of phonon frequency interactions and phonon number density conservation. Thus, this model considers the contributions of anharmonic, inelastically scattered phonons to thermal boundary conductance. This new anharmonic inelastic model shows improved agreement between the thermal boundary conductance predictions and experimental data at the Pb/diamond and Au/diamond interfaces due to its ability to account for the temperature dependent changing phonon population in diamond, which can couple anharmonically with multiple phonons in Pb and Au. We conclude by discussing phonon scattering selection rules at interfaces and the probability of occurrence of these higher order anharmonic interfacial phonon processes quantified in this work.

Thermal Boundary Conductance: A Materials Science Perspective

“…Among the many proposed extensions to the DMM include, most notably, the effect of interfacial reaction layers (40), the effect of interface roughening (41), and the effect of interfacial inelastic scattering (42). These treatments sometimes allow a good fit of specific results but, when exercised across a broader range of materials and interface types, have a predictive power that is limited at best.…”

Probing and tuning inelastic phonon conductance across finite-thickness interface

“…14,15) Apart from some phenomenological models proposed to accounting for inelastic transmission [16][17][18] , it is only recently that the phonon transmission including inelastic contribution can be directly calculated using the phase-space trajectories in MD simulations. 19) For a well-defined weakly-bonded interface between CNT and silicon, inelastic phonon transmission extending beyond the silicon cut-off frequency has been found.…”

The Role of Electronic and Vibrational Scattering on Thermal Transport Across Multiple Interfaces in Nanostructures

“…Similarly, previous work done from our group has also alluded to similar conclusions by considering various p-p scattering theories [31][32][33]. This supports the e-p interfacial mechanism proposed by Majumdar and Reddy [34] in which e-p coupling in the bulk of the metal must occur before p-p scattering transmits energy across a metal/non-metal interface, and thus, heat conduction across the interface is not driven by e-p coupling mechanisms.…”

“…In these models, the mismatch in acoustic properties or vibrational density of states, limits the interfacial phonon transmission, and therefore restricts the phonon flux that transmits across the interface. As these models and further refinements of these models have been extensively described in the literature [32,33,47,[49][50][51][52][53], these derivations will not be reproduced here. Instead, an analytical formulation of a coupled DMM and quantum mechanical derivation of electron-phonon scattering at free electron metal/nonmetal substrate interfaces will be derived in the following subsection.…”