Analytical model for thermal boundary conductance based on elastic wave theory

Abstract

Interfacial phonon-mediated heat transport plays a key role in nanoscale materials and devices. We propose a model based on elastic wave theory, that considers the mode conversion of acoustic waves transmitted across an interface and combines isotropic dispersion relations to describe the interfacial phonon thermal transfer process and estimate the thermal boundary conductance (TBC). In this model, we calculate the amplitude ratios of all reflected and transmitted acoustic waves using the frequency-dependent interfacial displacement and stress components of the continuity equation; we then determine the energy transmission coefficient of the three modes of incident waves. Consequently, our model can produce the complete angular and frequency spectra of the phonon transmission coefficients for the three acoustic modes. These results show that the specular scattering dominates the transmission of low-frequency phonons at interfaces (e.g., the transmission coefficients of the Al–Si interface are close to 1 below 4 THz, and due to different elastic properties, the phonons at frequencies below 5 THz dominate the heat transfer for Al–diamond interfaces). In addition, the TBC numerical results by our model for Al–Si and Al–diamond interfaces are consistent with those found in previous experimental works. Compared with existing theoretical models, better prediction values were obtained at temperatures higher than 100 K, which verified the model’s feasibility for phonon transmission coefficients and TBC prediction. Finally, we quantitatively analyze the differences between various theoretical models by considering the mode conversion of interfacial acoustic waves, models using acoustic mismatch simplifications, and the importance of phonon dispersion relations for TBC analysis at high temperatures.