The effect of ultrasmall grain sizes on the thermal conductivity of nanocrystalline silicon thin films

We report on the thermal conductivity of nanocrystalline silicon thin films with average grain sizes varying from 3 nm to 10 nm. The films were prepared by plasma-enhanced chemical-vapor deposition. The crystallinity and grain sizes of the films are controlled by hydrogen dilution during growth. Thermal conductivity was measured from 80 K to room temperature. The thermal conductivity of the film with 10 nm grain size roughly follows the minimum thermal conductivity predicted for amorphous silicon. As the grain size decreases to 3 nm, its thermal conductivity is reduced to one third of the minimum thermal conductivity. We extend the model of grain boundary scattering of phonons with Debye and Born–von Karman dispersion relations to explain our results. Although our results can still be explained by strong grain boundary scattering, we find the phonon mean-free-path would have to decrease at a faster rate than the reduction of grain size to explain the strong dependence of thermal conductivity on grain size.