low temperatures ($\sim 1 $ K), in which heat is carried predominantly by phonons with frequencies less than 1 THz.[@klitsner_phonon_1987; @Swartz1987] At these low temperatures and for pristine, ordered interfaces, transmission coefficients can be obtained from continuum elastic theory in an analogy with Snell’s law for light; this model is known as the acoustic mismatch model (AMM).[@Khalatnikov1952; @Little1959] The AMM was shown to explain the experimentally measured values of TBR at various solid-solid interfaces.[@Swartz1987] At higher temperatures (above 1 K), heat transport across the interfaces was found to be sensitive to surface roughness. For the limit of completely diffuse scattering in which transmitted and reflected phonons cannot be distinguished, Swartz constructed the diffuse mismatch model (DMM).[@swartz_thermal_1989] Despite the success of these models at explaining TBR at low temperatures, they generally fail at temperatures larger than 40 K and are unable to account for the atomistic structure of the interface.

Recent works have focused on remedying these deficiencies. Optical methods enable the routine measurement of TBR over a wide range of temperatures for various metal-dielectric interfaces [@Lyeo2006; @Norris2009; @Cheaito2015; @Schmidt2010; @duda_role_2010] as well as at interfaces with variable bonding strength. [@OBrien2012; @Losego2012] Other works have examined the temperature dependence of the 