Single-crystal films of (001)${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathit{A}}_{\mathit{x}}$Se (A=Mn, Fe, Co) (0≤x<0.14) grown by molecular-beam epitaxy on (001)GaAs have been studied by spectroscopic ellipsometry in the 3.5–5.5 eV photon-energy range. Using fits of the ${\mathit{E}}_1$ and ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ peaks with a standard analytic expression, we find that the linewidths increase with x for all samples, the energies increase with x for ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se and ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se, and the energies decrease with x for ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se. A model describing the effects of the sp-d exchange interaction on the L point band-gap energy is developed and applied. We find that the strength of the energy correction due to this interaction, which is proportional to the product of the square of the exchange integrals and the magnetic susceptibility of the material, is largest in Mn-doped and smallest in Co-doped ZnSe. While the sp-d exchange interaction model is consistent with the composition dependence of the ${\mathit{E}}_1$ and ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ band-gap energies in ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se, it does not describe the behavior observed in ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se and ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se. We show that an sp-d hybridization model, which includes the location of the energy levels of the magnetic impurity d levels, can account for the composition dependence of ${\mathit{E}}_1$ and ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ band-gap energies of all three materials.

• Received 12 May 1993

DOI:https://doi.org/10.1103/PhysRevB.49.1732