Role of strain energy in the stabilization of the 7×7 structure in the adatom model of the Si(111) surface

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Abstract
The strain energy of the adatom model of the (2n-1)×(2n-1), 2n×2n, n √3 ×n √3, and 2×2n structures of the Si(111) surface is calculated by taking two- and three-body interactions between Si atoms in two cases with and without adatoms at the corner of the unit cell (n=1,2,. . .). One of the 5×5, 7×7, 9×9, 11×11, and 2 √3 ×2 √3 structures appears, depending on the relative magnitudes of the strain energy, the bond-breaking energy, and the Coulomb energy between dangling electrons. The 7×7 structure is stable when the ratio of force constants of bending and stretching interactions is about 0.4, which is 1.4 times as large as that of the bulk, and when the bond-breaking energy is about 2.3 eV, which is 1.2 times as large as that of the bulk.