On the lattice parameter profiles in the Stranski-Krastanov growth mode

Within the framework of the elasticity continuum theory in the linear approximation we have obtained the lattice parameter profiles for Ge/Si(001) and InAs/GaAs(001) quantum dots. In our model we assume that a small fraction of the substrate participates in heterostructure relaxation in the non-rigid approximation. Minimization of the free energy by the Euler-Lagrange method allow us to predict the evolution of the lattice parameter with the film coverage. A sigmoidal-like law for the lattice parameter profile is reached in the rigid and non-rigid substrate approximations. These results agree with x-ray diffraction measurements in the grazing schemes. As the aspect ratio changes, we observed a slight dependence of the lattice parameter slope, which can explain how the relaxation mechanism can affect the formation of quantum dots as the height to lateral dimensions are modified. From the results, we have deduced that the aspect ratio and the misfit strain significantly affect the relaxation processes, since they define changes in the lattice parameter as the height coverage increases.