Dynamic effective charge and surface reconstruction on Si(111)

The previously developed soft-mode theory of surface reconstruction is applied to the (111) surface of silicon. It is shown that the mutual interaction of surface dynamic effective charges can cause the ideal equilibrium configuration of the surface atoms to be unstable, thus leading to reconstruction. This instability is studied in detail using lattice-dynamical methods and it is found that dynamic effective charges on the order of $0.5e$ can lead to the 2 × 1 reconstruction observed experimentally. The directions in which the atoms displace due to the instability are shown and a new atomic configuration for the reconstructed surface is thereby predicted. The results are found to be nearly independent of the details of surface relaxation, of the distribution of the dynamic effective charges, and of the supposed weakening of the short-range forces in the surface region.