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As one simple metamaterial, nanopatterns are often fabricated across a thinfilm so that the thermal transport can be manipulated. The etched sidewalls forthese nanostructures are usually rough due to surface defects introduced duringthe nanofabrication, whereas the top and bottom film surfaces are smoother. Inexisting analytical models, the contrast between these surfaces has not beenaddressed and all boundaries are assumed to be diffusive for phonon reflection.In this paper, a new two-step approach to address this issue is proposed forphonon transport modeling of general thin-film-based structures. In thisapproach, the effective in-plane phonon mean free paths ({\Lambda}_Film) arefirst modified from the bulk phonon MFPs to account for the influence of thetop/bottom film surfaces, with possibly enhanced probability of specular phononreflection at cryogenic temperatures. This {\Lambda}_Film is further modifiedto include the scattering by etched sidewalls with almost completely diffusivephonon scattering. Such a two-step phonon mean free path modification yieldsalmost identical results as frequency-dependent phonon Monte Carlo simulationsfor etched nanowires and representative nanoporous thin films. This simple yetaccurate analytical model can be applied to general thin-film-basednanostructures to combine the phonon size effects along orthogonal directions.

Two-Step Modification of Phonon Mean Free Paths for Thermal Conductivity Predictions of Thin-Film-Based Nanostructures