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    Nonequilibrium thermal transport across metal-Si interfaces from Boltzmann transport theory

    Jinchen Han and Sangyeop Lee*

    • Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA

    • *Contact author: sylee@pitt.edu

    Phys. Rev. B 112, 235310 – Published 17 December, 2025

    DOI: https://doi.org/10.1103/fndt-fln1

    Abstract

    Efficient heat dissipation across metal–insulator interfaces is critical for the performance and reliability of nanoscale electronic devices. However, the microscopic mechanisms that govern interfacial thermal resistance remain poorly understood, particularly the role of carrier nonequilibrium near the interface. This study investigates how the nonequilibrium distribution of heat carriers influences the metal-Si interfacial thermal resistance. We solve the electron-phonon coupled Boltzmann transport equations with carrier energy dispersion and scattering rates from first principles for three interfaces: Al-Si, Cu-Si, and Au-Si. The carrier nonequilibrium near the interface causes significant thermal resistance in both metal and Si leads, but with different characteristics. In the metal leads, the nonequilibrium exists in a very short distance (∼20 nm) from the interface, but the local thermal resistivity is significantly high, even comparable to those of thermal insulators (∼1 m-K/W). In Si leads, the degree of nonequilibrium is lower compared to the metals but persists over 1–2 µm due to the longer mean free paths of phonons. These factors together make both metals and Si exhibit significant thermal resistance from the carrier nonequilibrium, contributing 30–50% of the total interfacial thermal resistance. Notably, we find that the degree of phonon nonequilibrium and its relaxation length in Si is strongly influenced by the paired metal due to the varying interfacial spectral transmissivity. We further show that the nonequilibrium resistivity cannot be well described with the simple assumption that the carriers with mean free path less than a characteristic length do not contribute to thermal transport. We also evaluate the impact of electrons on interfacial thermal transport and reveal their critical role in shaping carrier nonequilibrium in metals. Lastly, our simulations of Al-Si and Al−Si0.99Ge0.01 interfaces show substantially different resistance despite nearly identical phonon dispersions of Si and Si0.99Ge0.01. This confirms that the difference of experimentally measured interfacial thermal resistance for the two interfaces [R. B. Wilson et al., Nat. Commun. 5, 5075 (2014)] originates from nonequilibrium effects.

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