Scattering of phonons by edge dislocation and thermal conductivity of nanocrystalline silicon

The temperature dependent thermal conductivity of nanocrystalline silicon with the grain size of 500 nm, 144 nm, and 76 nm, was calculated based on the intrinsic phonon properties using a firstprinciples-based method and recent analytical theory of phonon-dislocation scattering. The results demonstrate, in the nanocrystalline silicon, that the low temperature (T) limit of thermal conductivity is directly proportional to T2 instead of the conventional Casimir limit of T3. Calculated frequency-dependent scattering rates also indicate regimes of dominant scattering mechanisms: frequency-independent boundary scattering dominates in the very low phonon frequency regime of less than 0.6 THz; frequency-dependent boundary scattering dominates in the intermediate phonon frequency regime between 0.6 and 6 THz; and Umklapp scattering dominates in the high phonon frequency regime beyond 6 THz. The thermal conductivity is linear proportional to nanograin size in the region of d < 100nm and it shows independence at d > 1 mu m. This work proves the importance of dislocation-phonon scattering to thermal conductivity when the size of nanograins is small or at low temperature.