Crossover in Thermal Transport Mechanism in Nanocrystalline Silicon

Using vibrational mode analysis of model structures we demonstrate that lattice vibrations in small grain ($<$ 3 nm) structurally inhomogeneous nanocrystalline silicon are almost identical to those of homogeneous amorphous structures. In particular, the majority of the vibrations are delocalized and unpolarized. As a consequence the principal thermal conductivity mechanism in such nanocrystalline materials is essentially the same as in the amorphous material. With increasing grain size the ability of vibrations to ``homogenize'' over the nanocrystalline structure is gradually lost and the phonon spectra and polarization become progressively more like that of a crystalline material; this is reflected in a crossover in the mechanism of thermal transport. Interestingly, a few of the vibrational modes are localized either on the grain boundary and the grain interiors.