Growth temperature and coverage dependence of vertical and lateral ordering in self-assembled PbSe quantum-dot superlattices

Self-organized three-dimensional ordering in ${\mathrm{P}\mathrm{b}\mathrm{S}\mathrm{e}/\mathrm{P}\mathrm{b}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ quantum dot superlattices is investigated as a function of growth temperature and PbSe dot layer thickness. It is found that in both cases the vertical and lateral dot correlation is significantly influenced by the changes in dot size that are induced by the changes in growth conditions. For the variation of PbSe coverage, an fcc-like vertical dot stacking occurs only for PbSe thicknesses between four and six monolayers when the growth temperature is fixed at 360 °C. For smaller PbSe thicknesses, no vertical or lateral correlations are observed, whereas for larger thicknesses the dots are vertically aligned along the growth direction. On the other hand, for a constant five-monolayer PbSe layer thickness an fcc-like dot stacking is only observed for growth temperatures between 360 and 380 °C. At lower temperatures no vertical or lateral correlations are formed, whereas at higher temperature the dots are vertically aligned. The transitions between the different ordering regimes are in good agreement with the results of a model that describes the interlayer dot interactions as a function of the PbSe dot size.