Substrate orientation effects on the Stranski–Krastanov growth mode

Abstract

Within the framework of the continuum elasticity theory, we have investigated thesubstrate orientation effects on the Stranski–Krastanov growth mode in Ge/Siheterostructures. To do this, we have estimated the transition thickness and accumulatedstress in Ge/Si(111) low-dimensional systems and we have compared these with the valuesobtained previously for Ge/Si(001) heterostructures. The systems under investigationare pseudomorphic structures with a coherent behaviour at the substrate/filminterface. For the dependence of the lattice parameter on the height, a sigmoidal-typefunction with appropriate constraints is considered. To evaluate the transitionthickness, a minimization of the total free energy density with respect to theslope is made. Two different regimes for the accumulated stress are obtainedin the range of investigated coverage. These regimes are directly related to thetwo stages of the Stranski–Krastanov mode. Although increasing Miller indicesin the substrate induces a delay in the 2D–3D phase transition with a greaterwetting 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) systemalso yields successful results for the transition thickness and compressive stressvalues, the fraction of strained substrate being roughly double in Ge/Si(111). InGexSi1−x/Si (111) heterostructures, the transition thickness is inversely proportional to the Ge composition and thecompressive stresses are smaller for decreasing misfit strain. This feature is similar to that of theGexSi1−x/Si (001) system.