Wire-width dependence of the LO-phonon splitting and photoluminescence energy in ${\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}/\mathrm{C}\mathrm{d}}_{0.35}{\mathrm{Zn}}_{0.65}\mathrm{Se}$ quantum wires

${\mathrm{Cd}}_x{\mathrm{Zn}}_{1-x}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ quantum wires with lateral widths down to 13 nm were fabricated by electron-beam lithography and wet chemical etching. In order to study the wire-width dependence of both the LO-phonon splitting between the barrier and the wire regions and the emission energy, micro resonance Raman spectroscopy and photoluminescence (PL) measurements have been performed. Reducing the wire width down to about 30 nm, we found an increasing splitting between the ZnSe phonon of the barrier layers and the ZnSe-like phonon of the ${\mathrm{Cd}}_x{\mathrm{Zn}}_{1-x}\mathrm{Se}$ wire regions as well as an increasing redshift of the PL energy. This behavior is due to the strain relaxation of the deeply etched, biaxially strained wires. By calculating the size dependence of the strain distribution and the LO-phonon wave numbers, good agreement between experiment and theory is obtained. Decreasing the wire size further down to the sub-20-nm range, the LO splitting is found to be almost independent of the wire width, indicating no further change of the strain relaxation. In this range, the PL spectrum shows a blueshift with decreasing wire size due to lateral carrier confinement.