Phonon transport across hetero-structure boundaries (represented with R p,b, phonon boundary resistance) according to the boundary scattering approximations are modeled as acoustic and diffuse mismatch models. Larger phonon transmission (small R p,b) occurs at boundaries where material pairs have similar phonon properties (u p, D p, etc.), and in contract large R p,b occurs when some material is softer (lower cut-off phonon frequency) than the other.