Vibrational and Raman-scattering properties of crystallineGe1−xSixalloys

First- and second-order Raman-scattering measurements have been performed in the crystalline ${\mathrm{Ge}}_{1-x}{\mathrm{Si}}_x$ alloy series from low frequencies (∼ 40 ${\mathrm{cm}}^{-1\mathrm{}}$) to high frequencies (∼ 1100 ${\mathrm{cm}}^{-1\mathrm{}}$). The second-order optical-like spectra indicate appreciable structure in the phonon density of states not predicted by the coherent-potential-approximation theory, but are in accord with recent cluster calculations. The first-order low-frequency acoustic spectra provide a direct identification of one-phonon disorder-induced scattering in semiconductors resulting from mass disorder. The optical-mode first-order spectra are interpreted in terms of $k\simeq 0$ as well as density-of-states contributions. Comparison with the second-order spectra allows an estimate of the relative importance of the $k\simeq 0$ and density-of-states contributions. The results indicate that the first-order scattering from the Ge-derived optical mode is primarily associated with the $k\simeq 0$ component except at rather large values of $x$. Measurements at low frequencies and in the elastic continuum range also demonstrate an explicit frequency dependence of the Raman coupling parameter for the disorder-induced acoustic phonon scattering.