Electronic density of states of amorphous Si and Ge: Application of a molecular-liquid model

The electronic structures of $a$-Si and $a$-Ge have been investigated by introducing the molecular-liquid model (MLM). The theoretical structure factors have been expressed in terms of three simple parameters—nearest-neighbor distance, packing density, and coordination number. For the electronic density of states (EDS), nonlocal energy-dependent pseudopotentials have been considered to second order in perturbation theory. When compared with the experimental structure factors, the MLM structure factors agree well for the momentum transfer in the region of $0<k<\mathrm{}4\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, but there is some departure for higher values of $k$. The calculated energy values exhibit a number of new features in the $E_2$ vs $k$ curves that were not noticed previously with local-pseudopotential and on-Fermi-surface approximation. The EDS, however, show remarkably good agreement with recent theoretical and experimental results.