ANHARMONIC SELF-ENERGIES OF PHONONS IN SILICON

We have carried out a realistic ab initio calculation of the contribution of cubic anharmonicity to the inverse lifetime GAMMA and the frequency shift DELTA of phonons in silicon. The cubic coupling constants for phonons throughout the Brillouin zone are obtained from an anharmonic Keating-type lattice-dynamical model, which has been fit to a database of results from local-density-approximation frozen-phonon and elastic-modulus calculations. GAMMA and DELTA have been calculated as a function of temperature T and wave vector. Our results agree reasonably well with experiment, but indicate the need for retention of quartic and higher-order terms, especially at high T.