Effective interface thermal resistance and thermal conductivity of dielectric nanolayers

Analytical expressions for the effective interface thermal resistance (ITR) and thermal conductivity k of dielectric nanolayers are derived and analyzed, based on the analytical solution of the phonon Boltzmann transport equation under the gray relaxation time approximation. This is achieved by using accurate expressions for the temperature and one-dimensional heat flux propagating across nanolayers supporting a diffusive phonon scattering at their interfaces. It is shown that the effective ITR between two layers can be symmetric on their thermal properties, such that its asymptotic value in the ballistic regime is higher than that in the diffusive one. In the ballistic-diffusive regime, the effective ITR depends strongly on the ratio λ=L/l, between the layer thickness L and mean free path l of phonons. Our predictions for the effective ITR in the ballistic regime are in good agreement with those of the diffuse mismatch model, while they differ by about 16% in the diffusive regime. On the other hand, k increases with λ until reaching saturation for bulk layers and agrees rather well with previous predictions reported in the literature. The obtained results could be useful for analytically describing the heat transport in dielectric nanothin films and superlattices, in which the gray approximation is valid.