Dispersion of the long-wavelength phonons in Ge, Si, GaAs, quartz, and sapphire

We have used the picosecond ultrasonic technique to measure the dispersion of long-wavelength longitudinal acoustic phonons in Ge, Si, GaAs, z-cut quartz, and sapphire. In these experiments, a subpicosecond light pulse was used to generate a strain pulse at one surface of the sample. After propagation through the sample, the shape of this strain pulse was modified because of the phonon dispersion. From this change in shape, the magnitude of the dispersion could be determined. The results are compared with various lattice dynamical models. We also report on measurements of the temperature dependence of the sound velocity and the acoustic attenuation.