Acoustic phonon dispersion relations for several lowest confined branches in a Si NW of side length . The dashed lines are the dispersion curves of the bulk LA and TA waves along the  direction.
Population averaged phonon group velocity as a function of phonon frequency. The overall average values of the phonon group velocity in the Si NWs with square cross section and circular cross section are and , respectively.
Phonon scattering rates in bulk Si and Si NW of square cross section with due to different scattering mechanisms as functions of the phonon frequency. The results are shown for the three-phonon Umklapp, mass difference, phonon electron, and boundary scattering at .
Calculated results of , , and in a NW with square cross section, and in a NW with circular cross section, as a function of specular scattering fraction , for various reduced side lengths as indicated.
(a) Lattice thermal conductivity at room temperature as a function of specular scattering fraction in bulk Si and Si NW of square cross section with . (b) Comparison of the lattice thermal conductivity in a Si NW with square cross section to a NW with circular cross section with the same dimension of , as a function of .
Parameters used for the thermal conductivity calculation for a Si NW with square cross section.
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