Phonon boundary scattering at a silicon-sapphire interface

The authors have measured the low-temperature thermal conductivity of unusual geometry sapphire bars that have undergone various surface treatments. They show that after careful surface polishing a ten-fold enhancement over the correctly calculated Casimir limit is possible, and that the phonon specular reflection coefficient for such a surface is consistent with phonon scattering from surface asperities. Lightly abrading the surface reduces the specular reflection coefficient as expected; however, in this case the phonon scattering cannot be associated with surface roughness but rather with subsurface dislocations. Silicon deposited epitaxially onto the polished sapphire surface also reduces the ten-fold enhancement of the sapphire above. They show that this is in agreement with the quality of the silicon-sapphire interface and postulate that the thermal conductivity of the composite sample may provide a nondestructive technique for monitoring the average dislocation density at the interface.