Atomic bonding in amorphous hydrogenated silicon carbide alloys: A statistical thermodynamic approach

The free-energy model (FEM) previously developed for predicting the bonding in amorphous covalent alloys has been extended to include tetrahedra, the fundamental structural units in the a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{C}}_{\mathit{y}}$ ${\mathrm{H}}_{\mathit{z}}$ alloys under consideration. It is proven that the tetrahedron probabilities P(i) can be obtained by randomly distributing, according to statistics, the bonds predicted by the FEM among the possible Si- and C-centered tetrahedra. The short-range order present in these alloys therefore corresponds, in general, to partial chemical ordering (CO) with a homogeneous dispersion of the bonds among the available tetrahedra. The nature of the CO predicted for these a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{C}}_{\mathit{y}}$ ${\mathrm{H}}_{\mathit{z}}$ alloys is shown to vary with alloy composition. For example, Si-C bonds are favored over Si-Si and C-C bonds in stoichiometric alloys, Si-Si and C-H bonds are favored over Si-C and Si-H bonds in Si-rich alloys, while Si-C and C-H bonds are favored over C-C and Si-H bonds in C-rich alloys. Detailed predictions are presented for the bond fractions, tetrahedron probabilities, and tetrahedral and polymeric volume fractions in a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{C}}_{1\mathrm{-}\mathit{x}}$ alloys and also in a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{C}}_{\mathit{y}}$ ${\mathrm{H}}_{\mathit{z}}$ alloys with both high H content and lower H content. In the high-H-content alloys, C is predicted to be present primarily in ${\mathrm{CH}}_2$ and ${\mathrm{CH}}_3$ units, in good agreement with experiment, and a significant polymeric component is predicted to be present. In the lower-H-content alloys, on the other hand, more Si-C bonds and a smaller polymeric component are predicted. It is therefore demonstrated that the H content plays a dominant role in controlling the optical and electronic properties of these technologically important alloys. The simplest way of improving the usefulness of these alloys is to lower the H content, thereby promoting the random bonding of C and H atoms in the amorphous Si network.