A scattering-mediated acoustic mismatch model for the prediction of thermal boundary resistance

Solid-solid thermal boundary resistance (R-b) plays an important role in de termining heat flow, both in cryogenic and room-temperature applications, s uch as very large scale integrated circuitry, superlattices, and supercondu ctors. The acoustic mismatch model (AMM) and the related diffuse mismatch m odel (DMM) describe the thermal transport at a solid-solid interface below a few Kelvin quite accurately. At moderate cryogenic temperatures and above , R-b is dominated by scattering caused by various sources, such as damage in the dielectric substrates and formation of an imperfect boundary layer n ear the interface, making R-b larger than that predicted by AMM and DMM. Fr om a careful review of the literature on R-b it seems that scattering near the interface plays a far more dominant role than any other mechanism. Thou gh scattering near the interface has been considered in the past, these mod els are either far too complicated or are too simple (i.e., inaccurate) for engineering use. A new model, called the scattering-mediated acoustic mism atch model (SMAMM), is developed here that exploits the analogy between pho non and radiative transport by developing a damped wave equation to describ e the phonon transport. Incorporating scattering into this equation and fin ding appropriate solutions for a solid-solid interface enable art accurate description of R-b at high temperatures, while still reducing to the AMM at low temperatures, where the AMM is relatively successful in predicting R-b .