High resolution x-ray diffraction from multilayered self-assembled Ge-dots

We have studied multilayers of self-assembled Ge-rich dots embedded in silicon grown by molecular-beam epitaxy using high resolution x-ray reciprocal space mapping and reflectivity. The Si spacer thicknesses between the dot arrays were in the range of 10–40 nm, the typical dot size was about 150 nm for the diameter and 7 nm for the height. The measured reciprocal space maps were simulated using statistical kinematical x-ray-diffraction theory, and a good agreement between experimental and simulated data has been achieved. From the measurements, the in-plane strain in the dot lattice was determined. We derived the degree of the vertical correlation of the dot positions (``stacking'') and a lateral ordering of the dots in a square array with main axes parallel to the directions, with an array lattice constant of about 500 nm.