Determining angles of incidence and heights of quantum dot faces by analyzing X-ray diffuse and specular scattering

Scattering of X rays by structures with multilayer ensembles of quantum dots MBE-grown in the In(Ga)As-GaAs system is studied by high-resolution grazing X-ray reflectometry. The peaks of the diffuse scattering intensity are discovered for the first time in structures with both vertically uncorrelated and vertically correlated quantum dots. It is shown that the position of the peak is totally determined by angle of inclination of the quantum dot pyramidal faces (the so-called blaze condition for diffraction gratings), which was theoretically predicted earlier. Comparison with the results of scattering simulation carried out by the technique of boundary integral equations indicates that a simple geometrical condition allows one to exactly determine the value of from the position of the intensity peak, the shape of which depends on many parameters. As follows from the theory and experiment, the width and height of the peaks for samples with vertically correlated quantum dots are larger than for those with uncorrelated dots. The roughness and interdiffusion of interfaces and the height of quantum dots are found from the position and amplitude of Bragg peaks. Thus, the conventional application of high-resolution grazing X-ray reflectometry is extended in this work to determination of the quantum dot geometry.