Role of dispersion on phononic thermal boundary conductance

Abstract

The diffuse mismatch model (DMM) is one of the most widely implemented models for predicting thermal boundary conductance at interfaces where phonons dominate interfacial thermal transport. In the original presentation of the DMM, the materials comprising the interface were described as Debye solids. Such a treatment, while accurate in the low temperature regime for which the model was originally intended, is less accurate at higher temperatures. Here, the DMM is reformulated such that, in place of Debye dispersion, the materials on either side of the interface are described by an isotropic dispersion obtained from exact phonon dispersion diagrams in the [100] crystallographic direction. This reformulated model is applied to three interfaces of interest: Cr–Si, Cu–Ge, and Ge–Si. It is found that Debye dispersion leads to substantially higher predictions of thermal boundary conductance. Additionally, it is shown that optical phonons play a significant role in interfacial thermal transport, a notion not previously explored. Lastly, the role of the assumed dispersion is more broadly explored for Cu–Ge interfaces. The prediction of thermal boundary conductance via the DMM with the assumed isotropic [100] dispersion relationships is compared to predictions with isotropic [111] and exact three-dimensional phonon dispersion relationships. It is found that regardless of the chosen crystallographic direction, the predictions of thermal boundary conductance using isotropic phonon dispersion relationships are within a factor of two of those predictions using an exact three-dimensional phonon dispersion.