Self-consistent calculation of the bandgap and screening at Si(111)2 × 1

We perform a model calculation for the static electronic screening at the surface of Si(111)2 × 1, including local field and exchange effects. The latter are shown to be important in order to explain the large dielectric constant of the surface layer, which is found experimentally. The screened Coulomb interaction obtained in this way is used to calculate the quasi-particle correction to the LDA bandgap at the surface, on the basis of the same model. We find that for a gap of E_g = 0.65 eV, the theory is self-consistent and in agreement with experiment.