Interaction energy between dipole lines applied on symmetric (2 × 1) reconstructed Si(001)

To study Si(001) vicinals, a periodic array of lines of dipole forces f = (0, fy, fz) is applied on symmetric (2 × 1) reconstructed Si(001), the lines being directed towards x. The elastic relaxation at T = 0 K by using the MEAM potential gives surface deformations and line-line interaction energies. The results compared with the Marchenko-Parshin (MP) improved by adding an extra contraction contribution due to surface stress. Two cases are studied: f perpendicular to dimer axis and f parallel to dimer axis. Otherwise, f is either (0, fy, 0) or (0, 0, fz) for better identification. As predicted by the improved MP model with small λ, surface deformations vary as Λf(1 − λf) / y2 where Λ is deduced from elastic constants, y is the surface position from the dipole line and λ, present only for f = fy, reflects the extra contraction of the terrace due to surface stress. For f perpendicular to dimer axis, Λ can be deduced from bulk elastic constants (Λb), i.e. equal to between 0.7 and 0.8Λb. λ (present only for f = (0, fy, 0)) is low and at least ten times smaller than this predicted by the improved MP model. This results from the reconstructed nature of Si(001). From surface deformations, this model correctly reproduces interaction energies between dipole lines. For f parallel to dimer axis, λ is non-existent, regardless of the direction of f. The constant Λ cannot be deduced from Λb. In respect to Λb and for (0, fy, 0) and (0, 0, fz), respectively, different Λ's are equal to 1.5 and 1.0 for surface deformations and 2.7 and 1.5 for line-line interaction energies.