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 < 100 > directions, with an array lattice constant of about 500 nm.