Lateral and vertical ordering of PbSe self-assembled quantum dots in PbSe/PbEuTe superlattices

The shape and the positions of self-organized PbSe quantum dots embedded in PbEuTe are studied by means of grazing-incidence small angle x-ray scattering and x-ray diffraction. Using a detailed numerical analysis of the measured x-ray data, we have determined a truncated pyramidal shape of the free-standing dots. The type of the lateral dot ordering depends substantially on the period of the PbSe/PbEuTe superlattice. In the case of smaller periods, the lateral ordering of the dots obeys a short-range order model and we have determined the statistical properties of the dot arrangement. For intermediate spacer thicknesses the dots form a hexagonal lattice. For larger periods, the dots are completely uncorrelated and their distribution can be described as a two-dimensional ideal gas. From coplanar x-ray diffraction we have determined additionally the vertical correlation of the dot positions changes from a mere vertical correlation for small superlattice periods, to a distorted trigonal lattice for the intermediate periods. For the largest period, no vertical correlation of dot positions is observed.