Cross-plane Thermal Conduction in Superlattices: Impact of Multiple Length Scales on Phonon Transport

We report a phonon transport study to elucidate nanoscale thermal conduction in silicon-germanium superlattices considering interactions of phonons with multiple structural length scales. Our results clearly demonstrate the need for quantifying the impact of all relevant length variables in superlattices, i.e., the mean free path and wavelength of phonons, the periodicity of the structure, total size of the superlattice, and the length scale of interfacial disorder, to fully understand the heat conduction in superlattices. Our predictions show that thermal conduction can be ballistic travelling across multiple low roughness interfaces of the superlattice even at room temperatures. In contrast to in-plane transport, we find that the strong surface scattering encountered in the cross-plane direction limits the phonon transport to mean-free-paths of less than 1 μm and wavelengths less than 10 nm even in alloyed superlattices of periods up to 50 nm. This strong role of boundaries also manifests itself in the form of thermal conductivity anisotropy in superlattices. We also investigate the impact of the number of periods and total structural size on the thermal conductivity which is critical for accurate experimental reporting of thermal conductivities.