Theoretical Phonon Thermal Conductivity of Si/Ge Superlattice Nanowires

The net-radiation method of radiative heat transfer has been combined with the diffuse mismatch interface condition to develop a model for the phonon thermal conductivity of superlattice nanowires. The important size effect is increased classical scattering at interfaces and side walls, which is treated as diffuse and gray (frequency independent). Coherence and quantum confinement effects are neglected, which should be appropriate for typical nanowires at room temperature. An isotropic, sine-type dispersion relation is used which is a significant improvement over the common Debye dispersion. Without any adjustable parameters, the model captures the effects of diameter, segment length, and transmissivity. A simpler picture is offered in terms of Matthiessen’s rule and effective mean free paths. The limitations of the model are also discussed. For a model Si/Ge superlattice nanowire at 300 K, the thermal conductivity is reduced below the alloy limit (7.0 W/m-K) when the diameter is less than 15 nm and/or the segment length is less than 20 nm.