Variations of acoustic and diffuse mismatch models in predicting thermal-boundary resistance

Solid-solid thermal-boundary resistance plays an important role in determining heat flow, in both cryogenic and room-temperature applications. The acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) have traditionally been used to predict the thermal boundary resistance R_b across the interface of two adjoining materials at temperatures well below the Debye temperatures of the materials in question. Both the AMM and DMM use the Debye density of states (DOS) in both contacting solids. Here, the use of a measured DOS is made in conjunction with the DMM. This shows an improvement in the prediction of R_b relative to that based on the Debye DOS. Another approach considered is to predict R_b from measured specific heat per unit volume C data. The measured C automatically includes the effect of temperature on the DOS. This leads to a marginal improvement in R_b above that predicted when using the measured DOS. The AMM describes the thermal transport at a solid-solid interface below a few Kelvin quite accurately. The DMM, theoretically more suitable for interfacial transport above a few Kelvin, is no better than AMM for predicting the thermal-boundary resistance at a solid-solid interface. This raises the possibility that both diffuse and specular reflections are taking place at the interface. This kind of mixed reflection is very common in radiative transport. Owing to the similarity in phonon transport and radiative transport a mixed model, considering both specular and diffuse reflection, is developed, which is able to predict R_b values between those of the AMM and DMM. Further, a regime map is developed which delineates three predominant regimes describing the dominance of the R_b predictions made by the AMM, DMM, and mixed models.