Free-energy model for bonding in amorphous covalent alloys

A free-energy model (FEM) for bonding in amorphous covalent alloys is developed and applied to the ternary a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{N}}_{\mathit{y}}$ ${\mathrm{H}}_{\mathit{z}}$ alloy system. The Gibbs free energy of mixing ${\mathit{G}}_{\mathit{M}}$=${\mathit{H}}_{\mathit{M}}$-${\mathit{TS}}_{\mathit{M}}$ is obtained with use of the quasichemical approach to the thermodynamics of regular solutions. The enthalpy of mixing, ${\mathit{H}}_{\mathit{M}}$, is expressed in terms of the nearest-neighbor bond energies, while the entropy of mixing, ${\mathit{S}}_{\mathit{M}}$, is given by the number of possible bonding configurations in Si-centered tetrahedra. Chemical ordering (CO) in these alloys is shown to correspond to the preference for Si-N and Si-H bonds at the expense of Si-Si and N-H bonds. The predictions of the FEM are shown to be in good agreement with experimentally determined bond concentrations in a-${\mathrm{Si}}_{\mathit{x}}$ ${\mathrm{N}}_{\mathit{y}}$ ${\mathrm{H}}_{\mathit{z}}$ alloy films where, in general, neither the CO (T=0 K) nor random-bonding limits are valid.