Calculation of the Optical Properties of AmorphousSiOxMaterials

The electronic structure and optical behavior of materials of the amorphous series $\mathrm{Si}{\mathrm{O}}_x$ with $0<~x<~2$ are calculated using a quantum chemical cluster approach. These materials are both compositionally and structurally disordered, and exhibit energy gaps ranging from ∼1 eV for Si to ∼9 eV for Si${\mathrm{O}}_2$. Each composition, i.e., value of $x$, is represented here by a number of topologically distinct clusters each containing 8 silicon atoms and $8x$ oxygen atoms. Each silicon is tetrahedrally coordinated with $y$ oxygens and $4-y$ silicons with $0<~y<~4$ and $〈y〉=2x$. We saturate peripheral bonds by a generalization of the periodic boundary conditions appropriate for a regular array. A simple molecular-orbital scheme, the extended Hückel theory, is applied to obtain electronic energy levels for each cluster. Using the indirect constant-matrix-element approximation and taking a weighted average over the various configurations, we obtain the imaginary part of the dielectric constant for a given composition $x$. The calculated results are in rather good semiquantitative agreement with the experimental results of Philipp, including the variation of the energy gap with composition and the general shape of the ${\epsilon }_2$-vs-frequency curves.