Intraband Raman scattering by free carriers in heavily dopedn−Si

Intraband Raman scattering from free carriers in $n$-type Si has been studied at high-impurity concentrations (${10}^{19}$-${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$). A strong low-frequency tail attributed to intervalley fluctuations is observed. This tail extends to 200 ${\mathrm{cm}}^{-1\mathrm{}}$ and obeys the same selection rules as the scattering between valley-orbit split donor levels. The strength of the tail is found to be independent of exciting frequency. A theoretical study of free-carrier intervalley fluctuations, as has been previously formulated, yields results that are in contradiction with the line shape of the tail and the above experimental observations. The observed scattering cross section is also an order of magnitude larger than that predicted by theory. Ad hoc phenomenological models are proposed which remove some but not all of the contradictions discussed above. The strongest evidence for an intervalley mechanism is provided by measurements under uniaxial stress. Large static uniaxial stresses (up to 20 kbar) were applied along the [001], [111], and [110] crystallographic directions. The results are qualitatively understood on the basis of the simplified ad hoc models and of transverse mass anisotropies induced by the splitting of $X_1$ points by [111] and [110] uniaxial stresses. The contradictions between the present theory and experiment suggest the inadequacy of a free-carrier treatment in the high-impurity regime.