Strain-induced structure transformations on Si(111) and Ge(111) surfaces: a combined density-functional and scanning...

Si(111) and Ge(111) surface formation energies were calculated using density functional theory for various biaxial strain states ranging from -0.04 to 0.04, and for a wide set of experimentally observed surface reconstructions: 3 × 3, 5 × 5, 7 × 7 dimer-adatom-stacking fault reconstructions and c(2 × 8), 2 × 2, and √3×√3 adatoms based surfaces. The calculations are compared with scanning tunneling microscopy data obtained on stepped Si(111) surfaces and on Ge islands grown on a Si(111) substrate. It is shown that the surface structure transformations observed in these strained systems are accounted for by a phase diagram that relates the equilibrium surface structure to the applied strain. The calculated formation energy of the unstrained Si(111)-9 × 9 dimer-adatom-stacking fault surface is reported for the first time and it is higher than corresponding energies of Si(111)-5 × 5 and Si(111)-7 × 7 dimer-adatom-stacking fault surfaces as expected. We predict that the Si(111) surface should adopt a c(2 × 8) reconstruction when tensile strain is above 0.03.