Phonon hydrodynamics in frequency-domain thermoreflectance experiments

The hydrodynamic heat transport equation with appropriate boundary conditions and ab initio calculated coefficients is validated by comparing the corresponding analytical and numerical solutions with frequency-domain thermoreflectance experimental measurements in silicon. Special attention is devoted to identifying the resistive effects appearing at the interface between the metal transducer and the silicon substrate. We find that a Fourier model using frequency-dependent effective thermal conductivity cannot simultaneously explain the experimental phase shifts and the amplitude of the temperature oscillations, whereas the hydrodynamic model using intrinsic parameters provides good agreement across a wide temperature range. In addition, phenomenology appearing at reduced length and time scales in this kind of experiment at different temperatures is shown. Specifically, we find hydrodynamic modes of thermal transport that are analogous to pressure- and shear-wave propagation in viscoelastic media.