Band-Structure Effects and Many-Particle Scattering Corrections in the Far-Ultraviolet Spectra of Ge and Si

The band structures of Ge and Si are computed to account for electron and hole states far from the forbidden gap. A Born approximation is employed to compute the contributions of electron-phonon and electron-electron scattering to the imaginary part of the self-energy function. The electron and hole spectral weight functions are evaluated, and the effects of the self-energy function on ${\epsilon }_2\left(\omega \right)$ determined. Our computed dielectric function seems in excellent accord with the recent work of Marton and Toots in the far ultraviolet (5-10 eV).