[Paper Review] Thermal resistance from non-equilibrium phonons at Si-Ge interface

Xun Li, Jinchen Han+1 more|arXiv (Cornell University)|Dec 3, 2022

Thermal properties of materials49 references4 citations

TL;DR

This study reveals that phonon-phonon scattering of non-equilibrium phonons near Si-Ge interfaces dominates interfacial thermal resistance, exceeding direct interface scattering. Using the Peierls-Boltzmann transport equation, the authors demonstrate that non-equilibrium phonon distributions generate significant entropy and resistance via three-phonon scattering, with phonon dispersion, density-of-states, and group velocity mismatches as key physical origins.

ABSTRACT

As nanostructured devices become prevalent, interfaces often play an important role in thermal transport phenomena. However, interfacial thermal transport remains poorly understood due to complex physics across a wide range of length scales from atomistic to microscale. Past studies on interfacial thermal resistance have focused on interface-phonon scattering at the atomistic scale but overlooked the complex interplay of phonon-interface and phonon-phonon scattering at microscale. Here, we use the Peierls-Boltzmann transport equation to show that the resistance from the phonon-phonon scattering of non-equilibrium phonons near a Si-Ge interface is much larger than that directly caused by the interface scattering. We report that non-equilibrium in phonon distribution leads to significant entropy generation and thermal resistance upon three-phonon scattering by the Boltzmann's H-theorem. The physical origin of non-equilibrium phonons in Ge is explained with the mismatch of phonon dispersion, density-of-states, and group velocity, which serve as general guidance for estimating the non-equilibrium effect on interfacial thermal resistance. Our study bridges a gap between atomistic scale and less studied microscale phenomena, providing comprehensive understanding of overall interfacial thermal transport and the significant role of phonon-phonon scattering.

Motivation & Objective

• To understand the role of non-equilibrium phonons in interfacial thermal resistance at Si-Ge heterojunctions.
• To bridge the gap between atomistic-scale interface scattering and microscale phonon-phonon interactions in thermal transport.
• To quantify the contribution of phonon-phonon scattering to total interfacial thermal resistance beyond traditional interface scattering models.
• To identify general physical parameters—phonon dispersion, density-of-states, and group velocity mismatch—that govern non-equilibrium effects.
• To provide a comprehensive framework for predicting thermal resistance in nanostructured Si-Ge systems using Boltzmann transport theory.

Proposed method

• Employing the Peierls-Boltzmann transport equation (PBTE) to model phonon transport across the Si-Ge interface.
• Solving the PBTE under non-equilibrium conditions to capture the evolution of phonon distribution functions near the interface.
• Applying the Boltzmann H-theorem to quantify entropy generation during three-phonon scattering events.
• Analyzing phonon dispersion, density-of-states, and group velocity mismatch between Si and Ge to explain non-equilibrium phonon generation.
• Decomposing thermal resistance into contributions from interface scattering and phonon-phonon scattering to isolate dominant mechanisms.
• Using numerical simulations to compute the relative magnitude of resistance from non-equilibrium phonon scattering versus direct interface scattering.

Experimental results

Research questions

• RQ1 What is the relative contribution of phonon-phonon scattering to interfacial thermal resistance compared to direct interface scattering at Si-Ge interfaces?
• RQ2 How do non-equilibrium phonon distributions near the interface affect entropy generation and thermal resistance?
• RQ3 What physical parameters—such as phonon dispersion, density-of-states, and group velocity—govern the formation of non-equilibrium phonons at the interface?
• RQ4 To what extent do microscale phonon-phonon interactions dominate over atomistic-scale interface scattering in thermal transport?
• RQ5 Can the non-equilibrium effect be universally predicted using material-specific phonon properties in heterostructures?

Key findings

• Phonon-phonon scattering of non-equilibrium phonons contributes significantly more to interfacial thermal resistance than direct interface scattering.
• Non-equilibrium phonon distributions lead to substantial entropy generation, as quantified by the Boltzmann H-theorem during three-phonon scattering.
• The mismatch in phonon dispersion, density-of-states, and group velocity between Si and Ge is the primary physical origin of non-equilibrium phonons.
• The study identifies that microscale phonon-phonon scattering effects are critical and previously overlooked in modeling interfacial thermal resistance.
• The resistance from non-equilibrium phonons is found to be much larger than the resistance directly attributed to interface scattering.
• The findings provide a generalizable framework for estimating non-equilibrium effects in interfacial thermal transport using material-specific phonon properties.