Electronic Structure and Optical Properties of Amorphous Ge and Si

The amorphous density of states for an assembly of atoms with short-range order has been obtained from a phenomenological model in which the density of states of the corresponding crystal with different nearest-neighbor distances (± 5% of crystalline value, $r_0$) are averaged by introducing a suitable weighting function of the form $\exp [-(\frac{1}{2{\sigma }^2}\left){(r_0-r)}^2\right]$, $\sigma$ being the Gaussian spread. The pseudopotential formalism is employed in the calculation. The nondirect transition model of Tauc and energy-dependent matrix elements have been used to evaluate the imaginary part of the dielectric constant, ${\epsilon }_2\left(\omega \right)$. The density of states and ${\epsilon }_2\left(\omega \right)$ of amorphous Ge and Si are reported in this paper.