Intra- and interband Raman scattering by free carriers in heavily dopedp-Si

Raman scattering from the free carriers in $p$-Si has been studied at high doping levels ($p=1.5\mathrm{}\times {10}^{19} {\mathrm{cm}}^{-3\mathrm{}} \mathrm{and} 1.5\times {10}^{20} {\mathrm{cm}}^{-3\mathrm{}}$). The features observed in the Raman spectra at low frequency are similar to those for $n$-Si: a strong tail which can be seen only in ${\Gamma }_{{25}^{\prime }}$ scattering symmetry. A theory of the Raman cross section is formulated and it is found that this tail is due to fluctuations of the effective mass of the free carriers in the warped upper valence band. the observed selection rule can be accounted for. For the more lightly doped samples (1.5×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$) the dependence of the Raman spectra on uniaxial stress in the [111] and [100] directions and on the exciting frequency has been studied. It can be explained in terms of the stress-dependent band structure of Si and the frequency-dependent interaction for the scattering process, respectively. Superimposed on the intraband tail a hump is also found, whose spectral position varies for lower stress as the stress-dependent splitting of the topmost valence bands. Therefore this hump is attributed to interband transitions. At higher stresses the hump gets pinned at a frequency of about 400 ${\mathrm{cm}}^{-1\mathrm{}}$. This feature cannot be understood in terms of the stress-dependent band structure.