Effective interface thermal resistance and thermal conductivity of dielectric nanolayers
Résumé
Analytical expressions for the effective interface thermal resistance (ITR) and thermal conductivitykof dielectricnanolayers are derived and analyzed, based on the analytical solution of the phonon Boltzmann transportequation under the gray relaxation time approximation. This is achieved by using accurate expressions for thetemperature and one-dimensional heatflux propagating across nanolayers supporting a diffusive phonon scat-tering at their interfaces. It is shown that the effective ITR between two layers can be symmetric on their thermalproperties, such that its asymptotic value in the ballistic regime is higher than that in the diffusive one. In theballistic-diffusive regime, the effective ITR depends strongly on the ratio=λLl/, between the layer thicknessLand mean free pathlof phonons. Our predictions for the effective ITR in the ballistic regime are in goodagreement with those of the diffuse mismatch model, while they differ by about 16%in the diffusive regime. Onthe other hand,kincreases withλuntil reaching saturation for bulk layers and agrees rather well with previouspredictions reported in the literature. The obtained results could be useful for analytically describing the heattransport in dielectric nanothinfilms and superlattices, in which the gray approximation is valid