Size dependence of strain relaxation and lateral quantization in deep etched ${\mathrm{Cd}}_x{\mathrm{Zn}}_{1-x}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ quantum wires

A systematic experimental and theoretical analysis of the lateral size and composition dependence of strain release and lateral quantization in etched ${\mathrm{Cd}}_x{\mathrm{Zn}}_{1-x}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}\mathrm{e}$ quantum wires is presented. Wires with lateral structure sizes down to 14 nm were realized by electron beam lithography and wet chemical etching and characterized by photoluminescence (PL) and Raman spectroscopy. For wide wires ($L_x>40\mathrm{}\hspace{0.5em}\mathrm{nm}$), the strain relaxation results in a redshift of both the energy of the PL signal and the ${\mathrm{Cd}}_x{\mathrm{Zn}}_{1-x}\mathrm{Se}$ LO phonon frequency in the wire region. To model the strain release, theoretical calculations have been performed, minimizing the elasticity energy in the wire cross section. A size-dependent strain release, strongly inhomogeneous across the wire cross section, is obtained. This results in a size- and composition-dependent band-gap shift, which is found to be in good agreement with the experimental data. In narrow wires ($L_x<30\mathrm{}\hspace{0.5em}\mathrm{nm}$), the Raman data indicate a saturation of the strain release. As a consequence, clear lateral quantization effects due to the quasi-one-dimensional carrier confinement are observed in the PL spectrum, resulting in a blueshift of the PL signal with decreasing wire width.