Spin Splitting and the Ultraviolet Absorption of Ge

The spin-split energy bands of germanium are computed throughout the entire Brillouin zone. A combined orthogonalized-plane-wave and pseudopotential approach is employed. A parametrization for the spin is given which we believe to be accurate to about 10% for both the valence and the conduction band, and which includes most of the $2p-3p$ core interference effects. A highly refined zone sampling is used to get the fine details of the optical spectrum. The resulting line shape is excellent for the 2.1-2.3-eV doublet. The structure near 5.0 eV is much improved over the spin-free results. In addition, a new, but quite weak, multiplet is found near 3 eV and is associated with the ${\Gamma }_{{25}^{\prime }}\to {\Gamma }_{15}$ transitions.