Alloyed mercury cadmium chalcogenide semiconductors are promising materials for photoemission and photodetector applications in the near- to far-infrared regions of the electromagnetic spectrum, with ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{Te}$ already used widely in focal plane arrays in the mid- to far-infrared. While ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{S}$ and ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{Se}$ alloys are also promising for these applications, especially in their nanocrystalline forms, characterization of their optical properties has been limited. Using density functional theory, we calculate the electronic structure, effective masses, Luttinger parameters, and optical response functions of zinc blende CdS, HgS, CdSe, and HgSe. We further predict the dielectric function of ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{S}$ and ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{Se}$ alloys in thermodynamic equilibrium at 300 K for compositions between $x=0$ to $x=1$ using a cluster expansion approach with the generalized quasichemical approximation. We find that spin-orbit coupling increases the band gap by up to 0.1 eV, and the use of a hybrid functional increases the alloy band gaps up to 1 eV. We map the $E_1$ and $E_2$ optical critical point peaks and derive the nonlinear relationship between peak energy and composition, resulting in bowing parameters that are distinct from those of the band edges. These findings can serve as a reference for identifying mercury cadmium chalcogenide alloy composition from optical spectroscopic measurements in the visible and ultraviolet spectra.

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• Dielectric properties
• Alloys
• II-VI semiconductors
• Bethe-Salpeter equation
• Cluster expansion
• GGA
• Hybrid functionals