Thermal resistance between low-dimensional nanostructures and semi-infinite media

Abstract

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 discipline for the traditional geometry, in which the lateral interface dimensions are large compared to the phonon wavelength. In nanostructures, however, the localization of phonons in the directions parallel to the interface may strongly influence the effective thermal resistance. The present work investigates model problems of abrupt junctions between a harmonic one-dimensional (1D) and a three-dimensional (3D) fcc lattice and between a 1D and a two-dimensional square lattice. The abrupt change in geometry modifies the phonon modes participating in energy transmission and creates an additional thermal resistance that is comparable with that occurring due to the acoustic mismatch at the interface of bulk media. For both cases, varying the impedance mismatch at the junction suggests that engineering an intentional impedance mismatch at a nanostructured interface may enhance the transmission of energy. The lattice dynamics calculations are used to develop qualitative arguments for the interface resistances in the practical geometries involving carbon nanotubes, silicon nanopillars, and graphene. This research provides foundations for detailed investigations of the impact of localized phonon modes on the acoustic mismatch resistance.