Strain and shape in self-assembled quantum dots studied by X-ray grazing incidence diffraction

We have developed a method to determine the relationship between strain and lateral size of coherent self-organized quantum dots. In our approach, X-ray grazing incidence diffraction is used to collect information on strain and shape effects in the vicinity of a prominent surface reflection. We demonstrate that for highly strained nano-scale islands it is possible to separate strain-induced and form factor-induced scattering without comparing different reflections. Experimental data from InAs on GaAs(100) quantum dots is discussed with respect to this model. Reciprocal space mapping around the (220) surface reflection shows a linear relationship between relaxation from the substrate lattice parameter and the outer perimeter of the dot. In addition, the functional form of the gradient of relaxation is found to be non-monotonous and rapidly increasing towards the tip of the dot.