Influence of elastic strains in sublayers on the critical thickness of the Stranski-Krastanow transition for the GeSi/Si(001) system

A novel estimation of the critical thickness of the epitaxial layer in the Stranski-Krastanow (SK) transition is proposed. The transition criterion is based on accumulation of the energy of the effective strain up to a certain critical value. The calculation includes the elastic energy stored in elastically strained layers, takes into account the restriction on the depth of the strained layer still affecting the transition, and a segregation effect described by thermally activated atomic exchange. The equations of growth on the vicinal substrate surface that divide each monolayer into submonolayers parallel to the surface are used. Simulation results are compared with the corresponding experimental data for the heterostructures built of a strained sublayer covered by a spacer layer on which a wetting layer is deposited until the SK transition occurs. The Ge/Si structures of this type are grown by molecular beam epitaxy, and in addition, the experimental results for InAs/GaAs systems, published in the literature, are used. A comparison of experimental and calculated data on the dependence between the critical thickness of the wetting layer and the thickness of the spacer layer shows good agreement for both Ge/Si and InAs/GaAs systems.