Compositional dependence of the band gap of (CuIn$_{5}$S$_{8}$)$_{1-x}$ $\cdot$ (FeIn$_{2}$S$_{4}$)$_{x}$ alloys

The transmittance spectra of single-crystal CuIn$_{5}$S$_{8}$ and FeIn$_{2}$S$_{4}$ ternary compounds and (CuIn$_{5}$S$_{8}$)$_{1-x}$ $\cdot$ (FeIn$_{2}$S$_{4}$)$_{x}$ alloys grown by planar crystallization of the melt are studied in the region of the fundamental-absorption edge. From the experimentally recorded spectra, the band gap of the compounds and their alloys is determined, and the compositional dependence of the band gap is constructed. It is established that the band gap nonlinearly varies with the composition parameter $x$ (with a maximum at the average content $x$) and can be described by a quadratic dependence.