Strain-induced structure transformations on Si(111) and Ge(111) surfaces: a combined density-functional and scannning tunnneling microscopy report

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: 3x3, 5x5, 7x7 dimer-adatom-stacking fault reconstructions and c(2x8), 2x2 and \sqrt{3}x\sqrt{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)-9x9 dimer-adatom-stacking fault surface is reported for the first time and it is higher than corresponding energies of Si(111)-5x5 and Si(111)-7x7 dimer-adatom-stacking fault surfaces as expected. We predict that the Si(111) surface should adopt a c(2x8) reconstruction when tensile strain is above 0.03.