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We present atomistic valence force field calculations of thermal transport inSi nanowires of diameters from 12nm down to 1nm. We show that as the diameteris reduced, the phonon density-of-states and transmission function acquire afinite value at low frequency, in contrast to approaching zero as in the bulkmaterial. It turns out that this effect results in what Ziman described as the"problem of long longitudinal waves" [1], which states that the thermalconductivity of a material increases as its length is increased due to thevanishing scattering for long-wavelength phonons. We show that this thermaltransport improvement also appears in nanowires as their diameter is decreasedbelow D=5nm (not only as the length increases) originating from the increase inthe density of the long wavevector modes. The observation is present underballistic transport conditions, and further enhanced with the introduction ofphonon-phonon scattering. Because of this, in such ultra-narrow nanowires, asthe diameter is reduced, phonon transport is dominated more and more by lowerenergy phonons with longer mean-free paths. We show that ~80% of the heat iscarried by phonons with energies less than 5meV, most with mean-free paths ofseveral hundreds of nanometers.

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