Tetrahedron model for the optical dielectric function of hydrogenated amorphous silicon nitride alloys

A microstructural model based on Si-centered tetrahedra is proposed for hydrogenated amorphous silicon nitride (a-Siₓ{N}yHz) alloys. The dependence of the optical dielectric function {ε}=ε₁+iε₂ of the a-Siₓ{N}yHz alloys on stoichiometry ([N]/[Si] ratio) and hydrogen content has been determined for (1) Si-rich a-Siₓ{N}_{1{{-}}x}$ alloys (containing no hydrogen), using five tetrahedra, Si-${Si}_{4{{-}}i}Nᵢ (i=0--4) and (2) N-rich a-Siₓ{N}_{y{{-}}z}$(NH${)}z$ alloys, again using five tetrahedra, Si-${N}_{4{{-}}i}$(NH${)}ᵢ(i=0--4). Specific alloys of interest for which ε has been predicted using the Bruggemann effective-medium approximation include a-{Si}₃N₄ and a-Si(NH)₂, amorphous silicon diimide. The predictions of the model for {ε}, the optical energy gap Eₒₚₜ, and the index of refraction n have been obtained considering both random bonding and phase separation in the alloys. These predictions are compared here with previous experimental results, while a more comprehensive comparison with experiment for some N-rich a-Siₓ{N}yHz films is presented in the following paper.