Local-Field Effects in the Optical Spectrum of Silicon

We have calculated the dielectric response matrix ${\epsilon }_{\overrightarrow{G},{\overrightarrow{G}}^{\prime }}(\overrightarrow{\mathrm{q}}=0, \omega )$ for silicon and have obtained the macroscopic frequency-dependent dielectric function. Contrary to recent calculations, local-field corrections do not shift the prominent peak positions of the imaginary part of the dielectric function; further the calculated dielectric function is improved as compared with experiments at higher energies. In particular, agreement with measured energy-loss spectra is significantly better when local-field effects are included.