Length-dependent thermal transport and ballistic thermal conduction

Probing length-dependent thermal conductivity of a given material has been considered as an important experimental method to determine the length of ballistic thermal conduction, or equivalently, the averaged phonon mean free path (l). However, many previous thermal transport measurements have focused on varying the lateral dimensions of samples, rendering the experimental interpretation indirect. Moreover, deducing l is model-dependent in many optical measurement techniques. In addition, finite contact thermal resistances and variations of sample qualities are very likely to obscure the effect in practice, leading to an overestimation of l. We point out that directly investigating one-dimensional length-dependent (normalized) thermal resistance is a better experimental method to determine l. In this regard, we find that no clear experimental data strongly support ballistic thermal conduction of Si or Ge at room temperature. On the other hand, data of both homogeneously-alloyed SiGe nanowires and heterogeneously-interfaced Si-Ge core-shell nanowires provide undisputed evidence for ballistic thermal conduction over several micrometers at room temperature.