Nanostructured electronic and photonic devices include a high density of material interfaces, which can strongly impede heat conduction and influence performance and reliability. Thermal conduction through interfaces is a very mature field as long as the interface dimensions are large compared to the phonon wavelength. In nanostructures, however, the confinement of phonons in the directions parallel to the interface may strongly influence heat conduction. The present work investigates a model problem consisting of an abrupt junction between a harmonic 1D and 2D square lattice. The results show that energy couples to phonon modes localized near the free surface and that the energy transmission coefficient across the interface into these surface modes is less than unity even for materials with identical bulk impedances. The lattice dynamics calculations performed here provide an initial perspective on the impact of phonon confinement on the acoustic mismatch resistance and lay the groundwork for more detailed studies involving 3D molecular dynamics.

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