Study of Phonon Dispersion in Silicon and Germanium at Long Wavelengths Using Picosecond Ultrasonics

Abstract

We have studied the dispersion of long wavelength longitudinal phonons in silicon and germanium using ultrasonic techniques. For long wavelengths, the acoustic phonon dispersion relation is of the form $\omega \left(k\right)\approx ck-\gamma k^3$, where $c$ is the speed of sound and $\gamma$ measures the lowest-order phonon dispersion. By sending an ultrasonic pulse of length a few hundred angstroms into a crystal and measuring the change of the pulse shape with propagation distance, we are able to determine the parameter $\gamma$. The results are compared with lattice dynamics models.