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  • Open Access

Scattering matrix formalism for interface heat conduction based on Monte Carlo evaluation of the phonon Boltzmann transport equation

Yifei Li1,2, Yichong Chen1, Guihua Tang2,*, Livio Gibelli1, and Matthew K. Borg1,†

  • 1Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom
  • 2MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

  • *Contact author: ghtang@mail.xjtu.edu.cn
  • †Contact author: Matthew.Borg@ed.ac.uk
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Phys. Rev. B 113, 205304 – Published 6 May, 2026

DOI: https://doi.org/10.1103/kz9s-y611

Abstract

As electronic devices continue to advance, accurate thermal management at the nanoscale is becoming increasingly crucial in engineering design. While the phonon Boltzmann transport equation (BTE) is commonly used for this purpose, conventional boundary conditions, such as the acoustic mismatch model (AMM) and diffuse mismatch model (DMM), fail to accurately predict nanoscale heat transport. In this work, we evaluate an interfacial boundary condition based on the scattering matrix (S-matrix) formalism within a low-variance direct simulation Monte Carlo (DSMC) solution of the BTE. The S-matrix framework resolves frequency- and polarization-dependent phonon transmission and reflection, enabling us to examine how microscopic details, including anisotropic scattering neglected by traditional models, lead to large differences in interfacial thermal resistance at ideal and disordered silicon/germanium interfaces. We further demonstrate that while S-matrix data can be used to accurately tune DMM for larger systems of known materials, DMM remains unsuitable for simulating nanoscale devices. Our predictions show good agreement with experimental measurements, and can be used for more accurate nanoscale thermal design of real-world devices.

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Phys. Rev. B 113, 205304– Published 6 May, 2026
  • Received 7 November 2025
  • Revised 17 February 2026
  • Accepted 31 March 2026
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