Thermal resistance across Si–SiGe alloy interface from phonon distribution mismatch

Abstract

Interfacial thermal resistance has often been attributed to the mismatch of phonon spectra between two materials and resulting phonon-interface scattering. However, we use the solution of Peierls–Boltzmann transport equation to reveal a substantial nonequilibrium thermal resistance across the interfaces of Si and SiGe alloys at room temperature, despite their nearly identical phonon dispersion and negligible phonon-interface scattering. The Kapitza length of the Si–Si0.99Ge0.01 interface is approximately 600 nm of Si. This originates from the mismatch in phonon distribution between Si and SiGe alloys due to their distinct scattering rates. The mismatch is relaxed by phonon scattering over a region of 1 μm around the interface, corresponding to the upper bound of mean free path Λx of heat-carrying phonons. The relaxation process leads to the significant entropy generation and increased thermal resistance. Introducing a gradual variation in Ge concentration near the interface markedly reduces thermal resistance when implemented over the 1 μm period. Our finding demonstrates that the interfacial thermal resistance can be significant due to the nonequilibrium phonon distribution, even in the absence of phonon-interface scattering. In addition, among various phonon modes with a wide range of Λx, the relaxation of the nonequilibrium is predominantly governed by the phonons with long Λx.