Anomalous diameter dependence of thermal transport in ultra-narrow Si nanowires.

We present atomistic valence force field calculations of thermal transport in Si nanowires of diameters from 12 nm down to 1 nm. We show that as the diameter is reduced, the phonon density-of-states and transmission function acquire a finite value at low frequency, in contrast to approaching zero as in the bulk material. It turns out that this effect results in what Ziman described as the "problem of long longitudinal waves" [J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Clarendon, Oxford, 1962)], which states that the thermal conductivity of a material increases as its length is increased due to the vanishing scattering for long-wavelength phonons. We show that this thermal transport improvement also appears in nanowires as their diameter is decreased below D = nm (not only as the length increases), originating from the increase in the density of the long wavevector modes. The observation is present under ballistic transport conditions, and further enhanced with the introduction of phonon-phonon scattering. Because of this, in such ultra-narrow nanowires, as the diameter is reduced, phonon transport is dominated more and more by lower energy phonons with longer mean-free paths. We show that ~80% of the heat is carried by phonons with energies less than 5 me V, most with mean-free paths of several hundreds of nanometers. [ABSTRACT FROM AUTHOR]