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The thermal conductivity reduction due to grain boundary scattering is widely interpreted using a scattering length assumed equal to the grain size and independent of the phonon frequency (gray). To assess these assumptions and decouple the contributions of porosity and grain size, five samples of undoped nanocrystalline silicon have been measured with average grain sizes ranging from 550 to 64 nm and porosities from 17% to less than 1%, at temperatures from 310 to 16 K. The samples were prepared using current activated, pressure assisted densification (CAPAD). At low temperature the thermal conductivities of all samples show a T(2) dependence which cannot be explained by any traditional gray model. The measurements are explained over the entire temperature range by a new frequency-dependent model in which the mean free path for grain boundary scattering is inversely proportional to the phonon frequency, which is shown to be consistent with asymptotic analysis of atomistic simulations from the literature. In all cases the recommended boundary scattering length is smaller than the average grain size. These results should prove useful for the integration of nanocrystalline materials in devices such as advanced thermoelectrics.
Wang et al. (Mon,) studied this question.