Phonon hydrodynamics in frequency-domain thermoreflectance experiments

Abstract

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 frequencydomain 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.

Observation of second sound in a rapidly varying temperature field in Ge

“…In our experiments, ∣Δ T ∣ max < 20 K; thus, the observed deviations between the theoretical predictions and the measured values at very low temperatures are expected (see section S8 for details). We note that similar experiments ( 25 , 26 ) were explained in terms of nonlocality as described by the Guyer-Krumhansl equation, which reduces to Eq. 1 in the absence of nonlocal effects.…”

Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

“…The temperature-dependent parameter values are listed Table 1. The resistive relaxation time and MFP are taken from Beardo et al [9].…”

“…Although EFMs provide important insights into thermoreflectance experiments, they are bound to the assumption of diffusive transport and, as a result, can fail to provide consistent interpretations of the data. For example, fitting an EFM to data of the amplitude of oscillations in the surface temperature results in a thermal conductivity that monotonically increases with frequency; however, fitting to data of the phase of the oscillations leads to a conductivity that monotonically decreases with frequency [9].…”

“…Kovács [17] also considered a one-dimensional geometry and modelled heat flow using the GK equation. Beardo et al [9] studied three-dimensional heat conduction in thermoreflectance experiments using a model based on the GK equation which accounted for the thin metal film that is bonded to the surface of a semiconductor. They developed an analytical solution by assuming that the laser heating is harmonic in time.…”

Temperonic Crystal: A Superlattice for Temperature Waves in Graphene

“…Coherent control of wavelike phenomena via metamaterials is driving, ever since four decades, a technological revolution in fields ranging from electronics, photonics, to phononics [1][2][3][4][5][6]. Although temperature has been historically considered as the paradigmatic example of an incoherent field, undergoing diffusive as opposed to wavelike propagation, on short space and timescales Fourier law fails [7][8][9][10][11] and the possibility for temperature wavelike propagation sets in [12][13][14][15][16]. The ultimate goal is to devise metamaterials, addressed as temperonic metamaterials, enabling coherent control of temperature oscillations arising in the hydrodynamic heat transport regime and operating at above liquid nitrogen temperature.…”