Using Amorphous Material Properties in Scattering-Mediated Acoustic Mismatch Model for Predicting Thermal Boundary Resistance

Abstract

Solid-solid thermal boundary resistance (Rb) plays an important role in determining the heat flow between materials. The acoustic mismatch model (AMM) and the diffuse mismatch model (DMM), work pretty well in describing and predicting the thermal energy transport at solid-solid interface at very low temperatures (in the range of few Kelvin). At moderate cryogenic temperatures they do not perform that well, and the reason may be attributed to the dominance of scattering in determining Rb. Scattering mediated acoustic mismatch model (SMAMM) was developed on this principle. Though SMAMM works well, it has some fundamental problems. SMAMM’s assumption of U-processes, for amorphous layer formed between materials, is physically unexplainable. It also assumes unrealistically small scattering time. We propose a modified version of SMAMM called Amorphous SMAMM, which takes into account amorphous material properties for the interstitial layer formed, to find the scattering time to be used in SMAMM. This model performs better than all the models in the range of 25 to 60 K in predicting Rb. Above this temperature, original SMAMM performs better, but Amorphous SMAMM always performs better than the AMM. Amorphous SMAMM does not run into any physical problems with the assumptions made, hence the results have a better physical significance than SMAMM’s.