Interplay of interfacial scattering and internal phonon scattering for thermal transport across a Si/Ge interface

Interfacial resistance between solids has drawn significant interest due to its importance in applications including thermal management in electronic devices. The widely used Landauer formula fails in describing interfacial resistance because it neglects internal phonon scattering. A modified Landauer formula which includes this important contribution, assumes phonons follow the bulk distribution, neglecting the non-equilibrium distribution. Here, we present our examination of interfacial phonon transport by solving the Peierls-Boltzmann equation in both real and reciprocal spaces with inputs from first-principles. The results show that there is a strongly non-equilibrium distribution near the interface due to the complex interplay between the interface scattering and internal phonon scattering. This non-equilibrium distribution decays with distance from the interface and eventually recovers to the bulk phonon distribution. We find that the internal phonon scattering near the interface provides an important contribution to the overall interfacial resistance. Our study provides insights into large discrepancies between experimentally measured interfacial resistances and those calculated from the Landauer formula, thus providing a useful way to interpret experimental data.