Thermal Resistance Across Si-Ge Interface from Non-Equilibrium Phonons

As nanostructured devices become prevalent, interfaces often introduce large thermal resistance imposing challenges for thermal management and opening opportunities for developing ultralow-thermal conductivity materials. However, the interfacial thermal transport remains poorly understood due to complex physics and limited methodologies. Although past studies have focused on the atomistic scale phenomena at the interface, the phenomena on a larger scale, for example, the complex interplay between the interfacial scattering and intrinsic phonon-phonon scattering, have not been comprehensively studied. Widely used methods in the past include the Landauer’s formalism which ignores the intrinsic scattering of phonons and molecular dynamics simulation which has a much smaller length scale than the typical mean free paths of phonons.<br/>To explore the role of intrinsic scattering of phonons on the interfacial thermal resistance at micro- and meso-scales, we solve the Peierls-Boltzmann transport equation in both reciprocal and real spaces using a Monte Carlo method with <i>ab initio</i> inputs. Our hypothesis is that the interfacial scattering largely distorts the phonon distribution near the interface, and intrinsic phonon scattering attempts to relax the distorted (non-equilibrium) distribution to a local equilibrium distribution. During this process, a large amount of entropy is generated according to the Boltzmann’s <i>H</i>-theorem. Indeed, our solution for a Si-Ge interface shows a large degree of non-equilibrium in phonon distribution, particularly at Ge side, which makes a significant contribution to thermal resistance. Our study provides a new tool to bridge the gap for <i>ab initio</i> simulation between atomistic scale and less studied microscale. Also, it brings a new insight into the significant role of phonon-phonon scattering on interfacial thermal resistance.