The relaxation of a spatially sinusoidal temperature perturbation in a dielectric crystal at a temperature comparable to or higher than the Debye temperature is investigated theoretically. We assume that most phonons contributing to the specific heat have a mean free path (MFP) much shorter than the thermal transport distance and can be described by the thermal diffusion model. Low-frequency phonons that may have MFP comparable to or longer than the grating period are described by the Boltzmann transport equation. These low-frequency phonons are assumed to interact with the thermal reservoir of high-frequency phonons but not with each other. Within the single mode relaxation time approximation, an analytical expression for the thermal grating relaxation rate is obtained. We show that the contribution of ``ballistic'' phonons with long MFP to the effective thermal conductivity governing the grating decay is suppressed compared to their contribution to thermal transport at long distances. The reduction in the effective thermal conductivity in Si at room temperature is found to be significant at grating periods as large as 10 \ensuremath{\mu}m.

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Onset of nondiffusive phonon transport in transient thermal grating decay

The relaxation of a spatially sinusoidal temperature perturbation in a dielectric crystal at a temperature comparable to or higher than the Debye temperature is investigated theoretically. We assume that most phonons contributing to the specific heat have mean free path (MFP) much shorter than the thermal transport distance and can be described by the thermal diffusion model. Low-frequency phonons that may have MFP comparable to or longer than the grating period are described by the Boltzmann transport equation. These low-frequency phonons are assumed to interact with the thermal reservoir of high frequency phonons but not with each other. Within the single mode relaxation time approximation, an analytical expression for the thermal grating relaxation rate is obtained. We show that the contribution of "ballistic" phonons with long MFP to the effective thermal conductivity governing the grating decay is suppressed compared to their contribution to thermal transport at long distances. The reduction in the effective thermal conductivity in Si at room temperature is found to be significant at grating periods as large as 10 microns.

We report a direct determination of the dynamic behavior of confined acoustic phonons in nanocavities by picosecond acoustics. We provide the broadband, high resolution transmission amplitude curve in the subterahertz range, and we give evidence of resonant transmission peaks in three successive stop bands, in quantitative agreement with acoustic simulations. We furthermore demonstrate transit times in the nanosecond range at the cavity peaks reflecting the strong confinement of resonant phonons within the cavity layer. On the other hand, picosecond transit times are measured in the stop band, shorter than in any of the constituting materials, a tunneling effect well known both in photonic crystals and in macroscopic phononic systems.

Subterahertz phonon dynamics in acoustic nanocavities.

A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3ω dynamic method coupled to a Volklein geometry. The device obtained using micro-machining processes allows the measurement of the in-plane thermal conductivity of a membrane with a sensitivity of less than 10 nW/K (+/−5 × 10−3 Wm−1 K−1 at room temperature) and a very high resolution (ΔK/K = 10−3). A transducer (heater/thermometer) centered on the membrane is used to create an oscillation of the heat flux and to measure the temperature oscillation at the third harmonic using a Wheatstone bridge set-up. Power as low as 0.1 nW has been measured at room temperature. The method has been applied to measure thermal properties of low stress silicon nitride and polycrystalline diamond membranes with thickness ranging from 100 nm to 400 nm. The thermal conductivity measured on the polycrystalline diamond membrane support a significant grain size effect on the thermal transport.

Highly sensitive thermal conductivity measurements of suspended membranes (SiN and diamond) using a 3ω-Völklein method

We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows us to measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this experimental technique is demonstrated in studies of lattice dynamics and relaxation processes in a metallic single grain of AlPdMn quasicrystal, and in rare gas solids neon and argon.

https://hal.archives-ouvertes.fr/hal-00163374/document

Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: application to the stability study of AlPdMn.

We report on the acoustic attenuation in an AlPdMn icosahedral quasicrystal between 15 and 300 K, in the tens of GHz range. High frequency coherent longitudinal acoustic waves are excited and detected by an optical ``pump and probe'' technique, in an interferometric configuration. Our results reveal that, at high temperature $(Tg100\mathrm{K}),$ the acoustic attenuation is rather small, close to the attenuation in crystals and much smaller than in disordered solids. We stress that Akhieser processes (phonon-phonon interactions) must be active in quasicrystals and give the correct behavior and order of magnitude of the acoustic attenuation, at high temperature. At low temperature, departure from the standard behavior arising from phonon-phonon interaction is not understood.

Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency

We present thermal conductivity measurements performed in three short-period (GaAs)_9(AlAs)_5 superlattices. The samples were grown at different temperatures, leading to different small scale roughness and broadening of the interfaces. The cross-plane conductivity is measured with a differential 3w method, at room temperature. The order of magnitude of the overall thermal conductivity variation is consistent with existing theoretical models, although the actual variation is smaller than expected.

https://hal.archives-ouvertes.fr/hal-00422390/document

Thermal conductivity of semiconductor superlattices: Experimental study of interface scattering

We show that the nonlinear behavior of transverse acoustic waves can reveal the anisotropic structure of an icosahedral quasicrystal, at the macroscopic level. We report experiments performed in i-Al-Pd-Mn. We observe that a primary transverse acoustic wave can generate a second harmonic transverse acoustic wave. We also observe a specific relation between the polarization directions of those waves. These observations are manifestations on a macroscopic scale of the long-range order in quasicrystals.

Jean Yves Duquesne

Papers

Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency

Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency

Thermal conductivity of semiconductor superlattices: Experimental study of interface scattering

Anisotropic nonlinear elastic properties of an icosahedral quasicrystal

Interaction of collinear transverse acoustic waves in cubic crystals