Modulated heat conduction in a two-layer dielectric system with dynamical interface thermal resistance
Résumé
Heat conduction in a two-layer dielectric system excited with a laser beam of modulated intensity is studied in terms of a dynamical interface thermal resistance predicted by the phonon Boltzmann transport equation under the gray relaxation time approximation. This is done by using accurate expressions for both the modulated temperature and heat flux profiles, which describe both the diffusive and ballistic regimes of heat transport. It is shown that (i) for modulation frequencies much smaller than the phonon collision frequency f1 of the finite layer, the values of this dynamical resistance in the pure ballistic regime agree well with those of the diffuse mismatch model, while they differ by about 10% in the diffusive one. (ii) In the diffusive regime, the thermal resistance reaches a maximum at the characteristic modulation frequency fc≃(10⎯⎯⎯⎯√/2π)(l1/L)2f1, where l1 and L are the phonon mean free path and thickness of the finite layer, respectively. This maximum thermal resistance is associated with the minimum of the modulated heat flux at the interface. The theoretical basis is used to establish a methodology to determine the dominant thermal relaxation time and phonon mean free path of the finite layer. The obtained results can thus be applied for describing the modulated heat conduction in dielectric thin films through the comparison of our theoretical model with experimental data measured by thermoreflectance or other relevant photothermal techniques.