The phonon thermal conductivity of a multilayer is calculated for transport perpendicular to the layers. There is a cross over between particle transport for thick layers to wave transport for thin layers. The calculations shows that the conductivity has a minimum value for a layer thickness somewhat smaller then the mean free path of the phonons.
@article{arxiv.cond-mat/9907368,
title = {Minimum Thermal Conductivity of Superlattices},
author = {M. V. Simkin and G. D. Mahan},
journal= {arXiv preprint arXiv:cond-mat/9907368},
year = {2009}
}