Stranski-Krastanov growth mode in Ge/Si(001) self-assembled quantum dots

Within the framework of the continuum elasticity theory, we have characterized the Stranski-Krastanov mode in Ge/Si(001) self-assembled quantum dots by means of the transition thickness and the accumulated stress. The systems under investigation are pseudomorphic structures with a coherent behavior at the substrate/film interface. For the dependence of the lattice parameter with 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, characterized by a second-order transition where the slope is the order parameter. The non-rigid substrate approximation is applied in our systems yielding transition thickness and compressive stress values which are in good agreement with the experimental ones. From these results, it can be deduced that the substrate is affected by relaxation phenomenon in the Stranski-Krastanov mode. In GexSi1-x/Si(001) heterostructures, the transition thickness is inversely proportional to the Ge composition and the compressive stresses are smaller for decreasing misfit strain. (C) 2003 Elsevier Science B.V. All rights reserved.