Piezo-Raman measurements and anharmonic parameters in silicon and diamond

Abstract

Measurements of the frequency shift of optical phonons in Si with uniaxial stress have been performed by Raman spectroscopy using a laser frequency in the region of transparency. A mean deviation of 25% has been found in the phonon deformation potentials as compared with previous results obtained with laser frequencies above the absorption edge. The new values are p/${\mathrm{\omega }}_0^2$=-1.85±0.06, q/${\mathrm{\omega }}_0^2$=-2.31±0.06, and r/${\mathrm{\omega }}_0^2$=-0.71±0.02, and 1.08±0.06 for the Grüneisen parameter ${\gamma }_{\mathit{G}}$. A valence-force-field model with five anharmonic parameters provides a consistency check between the phonon deformation potentials and the third-order elastic constants of Si. On the basis of this model, existing uniaxial-stress data for the optical phonons of diamond and for the pressure dependence of the second-order elastic constants have been reanalyzed and the corresponding five anharmonic parameters have been determined. In this manner, reliable values for the third-order elastic constants have been obtained for diamond.