Substrate orientation effects on the Stranski–Krastanov growth mode

Within the framework of the continuum elasticity theory, we have investigated the substrate orientation effects on the Stranski–Krastanov growth mode in Ge/Si heterostructures. To do this, we have estimated the transition thickness and accumulated stress in Ge/Si(111) low-dimensional systems and we have compared these with the values obtained previously for Ge/Si(001) heterostructures. The systems under investigation are pseudomorphic structures with a coherent behaviour at the substrate/film interface. For the dependence of the lattice parameter on the height, a sigmoidal-type function with appropriate constraints is considered. To evaluate the transition thickness, a minimization of the total free energy density with respect to the slope is made. Two different regimes for the accumulated stress are obtained in the range of investigated coverage. These regimes are directly related to the two stages of the Stranski–Krastanov mode. Although increasing Miller indices in the substrate induces a delay in the 2D–3D phase transition with a greater wetting layer, the relief strain mechanisms seem similar to those of Ge/Si(001) heterostructures. The non-rigid-substrate approximation applied in the Ge/Si(111) system also yields successful results for the transition thickness and compressive stress values, the fraction of strained substrate being roughly double in Ge/Si(111). In GexSi1−x/Si (111) heterostructures, the transition thickness is inversely proportional to the Ge composition and the compressive stresses are smaller for decreasing misfit strain. This feature is similar to that of the GexSi1−x/Si (001) system.