Ballistic-diffusive heat conduction in multiply-constrained nanostructures

Abstract

Ballistic-diffusive heat conduction in multiply-constrained nanostructures is theoretically studied based on the phonon Boltzmann transport equation. The results show that different constraints influence the thermal transport in different ways. In the direction parallel to the heat flow, the phonon ballistic transport can cause temperature jumps at the boundaries in contact with the phonon baths. In contrast, for lateral constraint, the heat flux is reduced near the boundaries due to phonon-boundary scattering. A thermal conductivity model for multiply-constrained nanostructures is then derived from the phonon Boltzmann transport equation. The influences of different constraints are combined on the basis of Matthiessen's rule. The model accurately characterizes the thermal conductivities of various typical nanostructures, including nanofilms (in-plane and cross-plane) and finite length nanowires of various cross-sectional shapes (e.g. circular and rectangular). The model predictions also agree well with Monte Carlo simulations and experimental data for silicon nanofilms and nanowires.