Nonmonotonic Diameter Dependence of Thermal Conductivity of Extremely Thin Si Nanowires: Competition between Hydrodynamic Phonon Flow and Boundary Scattering.

By carefully and systematically performing Green-Kubo equilibrium molecular dynamics simulations, we report that the thermal conductivity (κ) of Si nanowires (NWs) does not diverge but converges and increases steeply when NW diameter (D) becomes extremely small (dκ/dD < 0), a long debate of one-dimensional heat conduction in history. The κ of the thinnest possible Si NWs reaches a superhigh level that is as large as more than 1 order of magnitude higher than its bulk counterpart. The abnormality is explained in terms of the dominant normal (N) process (energy and momentum conservation) of low frequency acoustic phonons that induces hydrodynamic phonon flow in the Si NWs without being scattered. With D increasing, the downward shift of optical phonons triggers strong Umklapp (U) scattering with acoustic phonons and attenuates the N process, leading to the regime of phonon boundary scattering (dκ/dD < 0). The two competing mechanisms result in nonmonotonic diameter dependence of κ with minima at critical diameter of 2-3 nm. Our results unambiguously demonstrate the converged κ and the clear trend of κ ∼ D for extremely thin Si NWs by fully elucidating the competition between the hydrodynamic phonon flow and phonon boundary scattering.