Determination of the chemical valence-band offset for ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ multiple-quantum-well structures of high $x$

Six ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ multiple-quantum-well structures with barrier Mn concentrations of $x\approx 0.25$ were studied by reflectivity spectroscopy, photoluminescence excitation spectroscopy, and spin-flip Raman spectroscopy at low temperatures and at magnetic fields up to 7.5 T. The three techniques give complementary information about the excitonic and electronic transitions in the quantum wells and in the barrier layers. In analyzing the spectra we have focused on three quantities whose behavior is sensitive not only to the chemical valence-band offset (VBO) fraction but also to the strain and to the interface quality. These three quantities are the energy splitting between the first light and heavy-hole quantum-well transitions in zero-magnetic field, the energy splitting between the two polarization components of the first heavy-hole quantum-well transition at 3 T and the saturation Raman shift for spin-flip scattering in the conduction band of the quantum well. All three quantities were calculated as functions of well width and compared with the values obtained by experiment to determine the VBO for the ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ system for $x\approx \mathrm{0.25.}$ In our model, we take into account the strain, the exciton binding energy effects and the interface roughness, as well as the enhanced paramagnetism at the interfaces. A consistent description of the experimental data can only be achieved by taking a VBO of $(20\mathrm{}\pm 10)\%,$ combined with a biaxial strain of the structure to a lattice constant $a_L{=(a}_{\mathrm{ZnSe}}{+2a}_{\mathrm{ZnMnSe}})/3\mathrm{}$ and with an interface roughness represented by average Mn concentrations of $0.9x$ and $0.1x$ in the cation monolayers immediately adjacent to the interface between the barrier and the quantum well, respectively.