Theory of the anharmonic damping and shift of the Raman mode in silicon

A theoretical investigation has been made of the damping constant and frequency shift of the Raman mode in silicon due to cubic anharmonic interactions between nearest-neighbor atoms. The normal-mode frequencies and eigenvectors for the harmonic crystal were calculated using a model containing short-range forces out to fourth neighbors and long-range nonlocal dipole interactions. The Raman-mode linewidth and frequency shift were calculated as functions of both temperature and frequency, and the results are compared with experimental data on the temperature dependences of these quantities.