Phase diagram of growth mode for the SiGe/Si heterostructure system with misfit dislocations

The strain, surface and interface energies of the SiGe/Si (SiGe grown on Si) heterostructure system with and without misfit dislocations were calculated for the Frank–van der Merwe (FM), Stranski–Krastanov (SK) and Volmer–Weber (VW) growth modes essentially based on the three kinds of fundamental and simple structures. The free energies for each growth mode were derived from these energies, and it was determined as a function of the composition and layer thickness of SiGe on Si. By comparison of the free energies, the phase diagrams of the FM, SK and VW growth modes for the SiGe/Si system were determined. The (1 1 1) and (1 0 0) reconstructed surfaces were selected for this calculation. From the phase diagrams, it was found for the growth of SiGe on Si that the layer-by-layer growth such as the FM mode was easy to be obtained when the Ge composition is small, and the island growth on a wetting layer such as the SK mode was easy to be obtained when the Ge composition is large. The VW mode is energetically stable in the Ge-rich compositional range, but it is difficult for the VW mode to appear in the actual growth of SiGe on Si because the VW region is right above the SK region. The regions of the SK and VW modes for the (1 1 1) heterostructure are larger than those for the (1 0 0) one because the strain energy of the (1 1 1) face is larger than that of the (1 0 0) face. The regions of the SK and VW modes for the heterostructure with misfit dislocations are narrower than those for the one without misfit dislocations because the strain energy is much released by misfit dislocations. The phase diagrams roughly explain the behavior of the FM and SK growth modes of SiGe on Si.