Refractive-Index Behavior of Amorphous Semiconductors and Glasses

TLDR

Refractive‑index behavior of optical glasses and amorphous semiconductors is analyzed using the same oscillator framework previously applied to single‑crystal data, with coordination number identified as the key parameter. The study finds that tetrahedrally bonded materials retain similar refractive‑index behavior despite loss of long‑range order, that adding high‑coordination oxides in mixed‑oxide glasses raises cation coordination and strengthens interband transitions, and that in amorphous forms of 2D and 1D crystal‑derived semiconductors the loss of layer or chain coupling reduces lone‑pair to conduction‑band oscillator strength and lowers dispersion energy.

Abstract

The refractive-index behavior (magnitude and dispersion) of a variety of optical glasses and amorphous semiconductors is discussed within the same oscillator framework applied earlier to single-crystal refractive-index data. Apart from density differences associated with voids and inefficient packing of disordered atoms, the main quantity of interest turns out to be coordination number as found earlier for single crystals. In tetrahedrally bonded materials (Si${\mathrm{O}}_{2}$, Si, Ge, GaP, GaAs, $\mathrm{Si}{\mathrm{O}}_{x}$) the refractive-index behavior, as measured by the dispersion energy ${E}_{d}$, is not significantly affected by loss of long-range order, lending considerable support to the view that the particular combination of moments of the ${\ensuremath{\epsilon}}_{2}$ spectrum that determines this oscillator-strength parameter is related solely to short-range interactions. In mixed-oxide glasses the data suggest that admixtures of high-coordination oxides (e.g., BaO or ${\mathrm{La}}_{2}$${\mathrm{O}}_{3}$) increase the average cation coordination number above 4 and correspondingly increase the strengths of interband optical transitions. Finally, in semiconductors derived from two-dimensional crystals (${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$) and one-dimensional crystals (Se and Te) it is found that layer-layer and chain-chain coupling, respectively, increase the effective crystalline coordination number above the nearest-neighbor value and that these interactions are largely lost in the amorphous forms. The primary optical effect is a reduction in oscillator strength of lone-pair to conduction-band transitions and a corresponding decrease in ${E}_{d}$.