Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, andα−Sn: Anharmonic effects

We have measured the temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and $\alpha -\mathrm{S}\mathrm{n}$. The full widths at half maximum of the Raman lines, extrapolated to zero temperature, are 1.24±0.07, 0.75±0.03, and 0.81±0.15 ${\mathrm{cm}}^{-1\mathrm{}}$ for Si, Ge, and $\alpha -\mathrm{S}\mathrm{n}$, respectively. The reliability of the data obtained allows a critical examination of the theoretical calculations published so far. We show that the model assuming the decay of the Raman phonon into two acoustical phonons belonging to the same branch, first proposed by Klemens, does not represent adequately the temperature dependence of the Raman linewidth. The most important decay channels are shown to be combinations of optical and acoustical phonons. However, the more complete calculation by Cowley, which involves all possible decay channels, gives very large zero-temperature linewidths. We show that this arises mainly from the poor description of the phonon dispersion curves by the shell model used by Cowley, and that a better agreement between theory and experiment is to be expected by repeating the calculation with Weber's adiabatic bond-charge model.