Anharmonic decay of phonons in silicon from third-order density-functional perturbation theory

Abstract

The Fourier-transformed cubic anharmonic force-constant tensor for silicon has been calculated using the results of density-functional perturbation theory in conjunction with a nonlocal ab initio pseudopotential and the ''2n+1'' theorem of the perturbation theory suggested by Gonze and Vigneron. The response of the conduction electrons to the field of the ions is obtained self-consistently. The anharmonic force-constant tensor has been employed to calculate the line width and the frequency shift of the Raman mode in silicon as a function of temperature. Our results agree well with the experimental data up to 500 K, but indicate that quartic and higher-order terms need to be included at higher temperatures.