Predictions of thermal boundary conductance for systems of disordered solids and interfaces

Abstract

As microsystems grow in their complexity, the number of material layers increases even as the thickness of these layers decreases. As a consequence, energetic transport through material intersections, the so-called thermal boundary conductance (TBC), becomes a greater contributor to the total thermal response of the system as a whole. Consequently, methods are sought that allow for insight into the mechanisms determining the efficiency of this transport, while simultaneously providing predictions with minimal computational investiture. In response, the current study extends the often employed diffuse mismatch model (DMM) to account for disorder that is frequently present in the materials making up the interface as well as the boundary itself. By applying assumptions regarding the scattering rates and mean free paths of phonons within a disordered solid, the resulting modifications of the spectral density of states induce changes in both the number and ratio of forward scattered phonons incident on a surface, and hence predictions of the TBC. Combining these assumptions with an accounting of the distance over which disorder persists, the newly implemented disorder DMM (δ-DMM) is shown to be more capable of predicting the TBC over a range of temperatures and material systems. Additionally, the model demonstrates that TBC is dependent on not only on the material properties but also on the morphology of these materials and the nature of their union.