Quaternary alloy ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x{\mathrm{S}}_y{\mathrm{Se}}_{1-y}$

The band-gap energy of II-VI compound semiconductors was simply calculated using a modified dielectric theory. The calculated band-gap energies of MgS and MgSe were 4.62 and 3.67 eV. From the extrapolation of the band-gap energies of ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x\mathrm{Se}$ and ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x\mathrm{S},$ the band-gap energies of MgSe and MgS of zinc blende at room temperature were determined to be 3.59 and $4.45\pm 0.2\mathrm{eV},$ almost the same as the value calculated using the modified dielectric theory. The bowing parameter of the ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x\mathrm{Se}$ ternary alloy was experimentally obtained as 0 eV, which can be explained in terms of the modified dielectric theory. The lattice constant of the quaternary alloy ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x{\mathrm{S}}_y{\mathrm{Se}}_{1-y}$ can be expressed by Vegard’s law [Z. Phys. 5, 17 (1921)]. The band-gap energy of ${\mathrm{Zn}}_{1-x}{\mathrm{Mg}}_x{\mathrm{S}}_y{\mathrm{Se}}_{1-y}$ can be expressed by the parabolic function of the composition considering the bowing parameter, where we use of 4.65, 3.59, 3.68, and 2.69 eV as the band-gap energies of MgS, MgSe, ZnS, and ZnSe, respectively.