Temperature Dependence of Raman Scattering in Silicon

We have measured the linewidth and the frequency of the q=0 optical phonon in silicon over the temperature range of 20-770\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependence of the linewidth has been interpreted as arising from the decay of the optical phonon to two LA phonons at half the optical frequency. From the observed temperature variation, we deduce an absolute half-width $\ensuremath{\Gamma}$ of 2.1 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 0\ifmmode^\circ\else\textdegree\fi{}K. This value is considerably smaller than that obtained theoretically by Cowley on the basis of numerical calculations which include decay to phonons throughout the Brillouin zone. His numerical calculations also predict a temperature dependence of the linewidth which does not agree with experiment. However, the observed change in frequency with temperature correlates very well with Cowley's theory. We have also studied the relative intensities of Stokes and anti-Stokes components of Raman spectra. The observed temperature dependence of the relative intensities is compared with that predicted on the basis of the Bose-Einstein population factor for the optical phonon.