We study the relaxation of coherent acoustic phonon modes with frequencies up to 500 GHz in ultra-thin free-standing silicon membranes. Using an ultrafast pump-probe technique of asynchronous optical sampling, we observe that the decay time of the first-order dilatational mode decreases significantly from ∼ 4.7 ns to 5 ps with decreasing membrane thickness from ∼ 194 to 8 nm. The experimental results are compared with theories considering both intrinsic phonon-phonon interactions and extrinsic surface roughness scattering including a wavelength-dependent specularity. Our results provide insight to understand some of the limits of nanomechanical resonators and thermal transport in nanostructures.Mechanical and acoustic properties in the nanoscale are receiving increasing attention as they are key properties affecting the limits of ultrasensitive detectors of force [1], mass [2,3], charge [4,5] and spin [6], influencing platforms for biosensing [7] and the investigation of quantum behaviour in extended objects [8]. In particular, phonon lifetimes influence the achievable mechanical quality (Q) -factors in nanomechanical resonators, which often limit device performance [9]. Moreover, they are necessary input parameters for accurate calculations of nanoscale thermal transport, with high-impact applications such as heat management in nanoelectronics [10] and the engineering of novel thermoelectric materials [11]. Despite their importance, phonon lifetimes are perhaps the least well known of all phonon properties due to the challenges associated with their quantitative determination and theoretical modelling. Even though silicon is the most important material for nanoelectronics, MEMS and NEMS, there are few experimental reports of direct measurements of phonon lifetimes in the gigahertz to terahertz range [12] and for all materials open questions remain about the relative contributions of intrinsic and extrinsic scattering processes at high frequencies in both bulk and nanoscale structures [9,[13][14][15][16]. Recent experimental investigations of phonons in superlattice cavities with frequencies of around 1 THz have suggested that lifetimes of high-frequency phonons could be limited by an average interface roughness of just 0.06 nm [17]. On the other hand, phonon wavepackets experiments in bulk silicon with frequencies up to approximately 100 GHz were analysed with a simplified Akhiezer relaxation damping model [12,18] of intrinsic scattering, using an average lifetime of high-frequency thermal phonons of 17 ps. Other intrinsic damping models include clamping losses [19], thermoelastic dissipation [20] and three-phonon interactions [21], which predict a different behaviour depending on the frequency and temperature regimes. In this context, generation and detection of coherent acoustic phonons at high frequencies in different materials and nanostructures is an ideal method to obtain quantitative information on phonon lifetimes and compare with the main theoretical models.Here we use free-standing single-crystalline ...

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