Evolution of hexagonal lateral ordering in strain-symmetrized ${\mathrm{P}\mathrm{b}\mathrm{S}\mathrm{e}/\mathrm{P}\mathrm{b}}_{1\mathrm{-}\mathrm{x}}{\mathrm{Eu}}_{\mathrm{x}}\mathrm{Te}$ quantum-dot superlattices

Lateral ordering and size homogenization of self-organized PbSe quantum dots in strain-symmetrized ${\mathrm{P}\mathrm{b}\mathrm{S}\mathrm{e}/\mathrm{P}\mathrm{b}}_x{\mathrm{Eu}}_{1-x}\mathrm{Te}$ superlattices is studied using atomic force microscopy. For superlattices with the number of superlattice periods varying from $N=1\mathrm{}$ to 100 it is found that a nearly perfect hexagonal two-dimensional (2D) lattice of PbSe dots is formed on the surface already after a few periods. A detailed analysis of the dot arrangement shows that within these superlattices, the in-plane spacing of the dots as well as the dot sizes within each PbSe layer remain essentially constant throughout the whole superlattice growth. This marked different behavior as compared to other self-assembled quantum dot superlattice systems is explained by the special ordering mechanism in our material system that is characterized by the formation of a non-vertical alignment of the PbSe dots in the superlattice stack due to the very high elastic anisotropy of the IV-VI semiconductors. In addition, from in situ reflection high-energy electron diffraction measurements it is found that the critical coverage for PbSe islanding, and thus the material distribution between the wetting layer and the islands are not changed within the stack. Therefore, remarkable homogenous three-dimensionally ordered quantum dot arrays are formed.