Slip Boundary Conditions in Ballistic–Diffusive Heat Transport in Nanostructures

Ballistic–diffusive heat conduction, which is predominantly affected by boundaries and interfaces, will occur in nanostructures whose characteristic lengths are comparable to the phonon mean free path (MFP). Here, we demonstrated that interactions between phonons and boundaries (or interfaces) could lead to two kinds of slip boundary conditions in the ballistic–diffusive regime: boundary temperature jump and boundary heat flux slip. The phonon Boltzmann transport equation (BTE) with relaxation time approximation and the phonon tracing Monte Carlo (MC) method were used to investigate these two slip boundary conditions for the ballistic–diffusive heat conduction in nanofilms on a substrate. For cross-plane heat conduction where the boundary temperature jump is the dominant non-Fourier phenomenon, ballistic transport causes the temperature jumps and thus introduces a ballistic thermal resistance. Importantly, when considering the interface effect, the corresponding model was derived based on the phonon BTE and verified by comparing with the MC simulations. In addition, an interface–ballistic coupling effect was identified, which indicates inapplicability of the standard thermal resistance analysis. In contrast, for the in-plane case that is controlled by boundary heat flux slip, both phonon boundary scattering and perturbation of the phonon distribution function induced by the interface can cause heat flux slip, leading to a variation in in-plane thermal resistance. In addition, a model beyond the Fuchs-Sondheimer formula, which can address both the boundary scattering and the interface effects, was derived based on the phonon BTE. The good agreements with the MC simulations indicate its validity.