Dispersion relations for LA phonon modes of freestanding GaN nanowires with diameters of (a) and (b) . Several lowest phonon branches are shown. The dashed lines indicate the dispersion relation for LA phonon modes in bulk GaN.
Phonon group velocity as a function of phonon angular frequency calculated for each dispersion branch. The results are shown for (a) and (b) . The dashed lines indicate the sound velocity for LA phonon modes in bulk GaN.
Branch-averaged phonon group velocity as a function of phonon angular frequency for and 40 nm. The horizontal dashed-dotted line indicates the sound velocity in bulk GaN for LA phonon modes. The results for are obtained in two methods: using the isotropic assumption (solid curve) and assuming phonon propagation in the  direction of wurtzite GaN (dashed curve).
(a) Thermal conductivity of GaN nanowires at room temperature as a function of wire diameter; (b) rate of change in thermal conductivity, , with respect to wire diameter. Circles indicate calculated data and the dashed and solid curves are results after interpolation. Square symbols represent experimental data extracted from Ref. 10. The simulation results are obtained in two cases: in case 1 (solid), we consider the change in the nonequilibrium phonon distribution due to diffuse scattering at the wire surfaces; whereas in case 2 (dashed), we do not. Both cases have included phonon confinement, boundary scattering, and scattering on impurities and electrons. It can be seen that the results obtained in case 1 are in excellent agreement with the experimental data. Calculated thermal conductivity of pure and doped bulk GaN is also shown. Material parameters used include and Si and O impurity concentrations at 0.13 and , respectively.
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