Tetrahedron model for the dielectric function of amorphous silicon-carbon alloys

Abstract

A Si- and C-centered tetrahedron model is developed for the determination of the optical dielectric function ε=${\epsilon }_1$+i${\epsilon }_2$ of amorphous silicon-carbon (a-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{C}}_{\mathrm{x}}$) alloys. The Phillips–Van Vechten–Levine dielectric model, along with the scaling procedure of Aspnes and Theeten, is used to obtain predictions for ${\epsilon }_1$ and ${\epsilon }_2$ for the individual Si-${\mathrm{Si}}_{4\mathrm{-}\nu }$ ${\mathrm{C}}_{\nu }$ and C-${\mathrm{Si}}_{4\mathrm{-}\nu }$ ${\mathrm{C}}_{\nu }$ (ν=0–4) tetrahedra. The tetrahedron model then uses these tetrahedra as the components in the Bruggemann effective-medium approximation to obtain predictions for ${\epsilon }_1$ and ${\epsilon }_2$ for the a-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{C}}_{\mathrm{x}}$ alloys. These predictions for ${\epsilon }_1$ and ${\epsilon }_2$, and for the optical energy-gap parameter $E_{\mathrm{opt}}$, are obtained for three different types of chemical ordering in the films: (1) no chemical ordering, (2) complete chemical ordering with homogeneous dispersion, and (3) complete chemical ordering with phase separation. The predictions of this model are presented in detail in this paper and are compared with experimental results for ${\epsilon }_1$, ${\epsilon }_2$, and $E_{\mathrm{opt}}$ for a series of a-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{C}}_{\mathrm{x}}$:H alloys in the following paper.