  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.
