Energy Dependence of the Single-Particle Self-Energy Correction for Ge and Si

The energy dependence of the self-energy correction $\Delta \mathrm{}\left(E\right)\mathrm{}$ to local-density-functional pseudopotential theory has been determined for Si and Ge from -15 to 16 eV above the Fermi energy $E_F$, and compared to recent calculations. The real part of $\Delta \mathrm{}\left(E\right)\mathrm{}$ was determined from the shift, relative to calculations, of detailed x-ray bremsstrahlung isochromat spectra, which exhibited many new higher-energy features, and x-ray photoemission spectra; the imaginary part was estimated from escape-depth data and the widths of conduction-band features. The real part changes abruptly at $E_F$ and is otherwise roughly constant, even up to the plasmon energy.