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Systematic measurements by light scattering of the linewidth and frequency shift of the q=0 optical phonon in silicon over the temperature range of 5-1400 K are presented. Both the linewidth and frequency shift exhibit a quadratic dependence on temperature at high temperatures. This indicates the necessity of including terms in the phonon proper self-energy corresponding to four-phonon anharmonic processes.
Bałkanski et al. (Mon,) studied this question.