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Ratio between the planar average of [see Eq. (4)] in slabs of different thicknesses and in bulk Si. The position of the slabs was aligned on a common surface. The position of the outermost Si atoms corresponds to the first dip and are indicated for the thinnest slab (four Si layers). The rapid decrease of at the surface is independent of the thickness of the slab.
Size and shape dependences of the average value of the local dielectric response in the core of Si slabs and rods. Rods show a much reduced screening compared to slabs of similar thickness. The influence of surface reconstruction is apparent in the comparison between values obtained for rods with reconstructed surfaces (green line) and unreconstructed surfaces (red line). A similar effect is observed also for slabs [see black and blue lines, corresponding to reconstructed and ideally terminated slabs, respectively]. All of the surfaces considered here are hydrogen terminated.
Planar average of in units of bulk for a 001 nanowire with canted (top) and reconstructed surfaces (bottom), respectively. In order to represent variations with respect to bulk values, we adopted the following color scheme: red corresponds to 115% of bulk value or higher; yellow to bulk average , green to variations between 50% and 85% and blue to lower than 50% of the bulk average. This figure shows that the “skin depth” as defined in Ref. 10 is roughly four to five layers. The large red spots in the right hand side of the bottom panel correspond to the presence of groups and to steps and are the result of the atomic rugosity of the surface.
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