Non-Muffin-Tin Energy Bands for Silicon by the Korringa-Kohn-Rostoker Method

A method is proposed for removing the "muffin-tin" restriction from the Green's function or the Korringa-Kohn-Rostoker method of band calculation and, more generally, from multiple-scattering theory as formulated by Beeby and Edwards. The method is applied to a model for crystalline silicon involving a single parameter which is adjusted to reproduce the experimental indirect gap. The numerical results are in good agreement with a large number of experiments and in particular support the view that the $\Delta$ axis is important to the reflectivity peak at 3.4 eV. (The energy separation ${\Gamma }_{15}-{{\Gamma }_{25}}^{\prime }$ is found to be 3.04 eV.)