Picosecond ultrasonic measurements of attenuation of longitudinal acoustic phonons in silicon

We report ultrafast optical measurements of the attenuation of 50 and 100 GHz longitudinal acoustic-phonon pulses in Si. Picosecond acoustic measurements were made at temperatures 50 < T < 300 K on thinned (50-mu m-thick) wafers. The measured phonon lifetimes at 300 K, approximate to 5-7 ns, are an order of magnitude less than expected based on three-phonon scattering rates derived from thermal conductivity data. We find instead that relaxational damping is the dominant mechanism in this frequency and temperature range. This attenuation sets an intrinsic limit on the quality factor of nanomechanical resonators that operate near room temperature.