Effect of interfacial roughness on thermal boundary conductance: An elastic wave model using the Kirchhoff approximation

Abstract

Interfacial roughness plays an important role in nanoscale thermal transport, while this issue still lacks a theoretical description due to the difficulty in quantifying the phonon scattering at the disordered interface. We report an elastic wave model (EWM) that describes the phonon–interface interaction by the interface elasticity. The transmissivity calculation based on the interfacial displacement and stress continuity incorporates the mode conversion and nonlinear vibration spectra of phonon waves, and the resulting cut-off frequency. Compared with the acoustic mismatch model that also assumes specular scattering of phonons waves, the applicable range of EWM is extended to room temperature and shows better accuracy. Based on this model, we use a statistical method with the Kirchhoff approximation and introduce the tangent plane slope distribution to determine the phonon scattering at a Gaussian-distributed rough interface. And the effective transmission coefficient is calculated by integrating the contributions of all points to the energy transmission. Calculated thermal boundary conductance (TBC) by a Landauer formula agrees well with the experiments of Al/SiO2/Si and Au/SiO2/Si rough interfaces. And the results show that the TBC of interface with sub-nanometer RMS roughness (10−10 m) is close to that of the smooth interface. After this transition, the increasing σ can significantly impact the interfacial heat transfer. Compared with existing models, the EWM can quantitatively estimate the effect of roughness on TBC and give a transmission image of wave-like phonons at the interface. This work contributes to an in-depth understanding of phonon wave effects in nanostructures.