Lifetimes of Confined Acoustic Phonons in Ultrathin Silicon Membranes

Abstract

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 ...

Thermal conductivity inhibition in phonon engineered core-shell cross-section modulated Si/Ge nanowires

“…Dispersion of acoustic phonons in free-standing Si membranes with the thickness of ~8 nm has been measured directly [33]. The authors observed reduction of the phonon group velocities by more than an order of magnitude.…”

Study of confined coherent acoustic phonon modes in a free-standing cubic GaN membrane by femtosecond spectroscopy

“…A free-standing membrane was chosen due to its potential applications in optomechanics 21,22 and its general interest for fundamental research. [8][9][10]23 The fabrication process of the membrane followed the one in Refs. 24 and 25, and the details are described in the supplementary material.…”

“…Time-resolved pump-probe spectroscopy has been applied to study ultrafast carrier dynamics and phononic properties of various semiconductors, such as GaN, [1][2][3][4] GaAs, [5][6][7] and Si. [8][9][10][11] Among these, GaN is of great importance in optoelectronic and short-wavelength devices because of its widebandgap. [12][13][14] GaN has two crystal structures: wurtzite (hexagonal) and zinc-blende (cubic).…”

Time-resolved detection of propagating Lamb waves in thin silicon membranes with frequencies up to 197 GHz

“…7 Recently, femtosecond lasers have been successfully applied to generate and detect longitudinal acoustic modes in free-standing silicon (Si) membranes with frequencies up to 500 GHz corresponding to 20 nm wavelengths. [8][9][10] As the dispersion relations of propagating Lamb waves are emerging from standing wave resonances, 11 these experiments indicate that propagating Lamb waves in membranes at similarly high frequencies could be monitored all-optically as well, if the conditions for their effective generation and detection are achieved. Recently, Rayleigh waves with wavelengths down to 45 nm (Refs.…”

“…Rayleigh waves are surface acoustic waves on a semi-infinite substrate. 14 Here, we combine the femtosecond pump-probe technique applied earlier to the monitoring of standing wave resonances [8][9][10] and of Rayleigh waves 12 with nanostructuring of the surface 12,13,15 in order to achieve the generation and detection of propagating Lamb waves at frequencies up to 197 GHz and wavelengths down to 50 nm in thin semiconductor membranes. Those high frequencies can be generated because for the same wave vectors the dispersion relations of Lamb waves contain modes of much higher frequencies than those of Rayleigh waves.…”