Surface States

Abstract

Various techniques have been developed for computing electronic surface band structures of three-dimensional semiconductors. They use either the local-density functional approximation and first-principle pseudopotentials or an (s,p, s*) set of tight-binding parameters¹. Such theoretical calculations, as detailed and realistic they may be, are nevertheless individual case studies. Here, more conceptual approaches shall be considered. A linear, one-dimensional lattice will be treated by using both the nearly free electron and a tight-binding approximation. First, however, the complex band structure of semiconductors will be considered. Adatoms on semiconductor surfaces are forming chemical bonds with substrate atoms. Sparsely distributed adatoms will predominantly interact only with their nearest neighbors. Then adatom-substrate bonds may be treated in analogy to isolated, heteropolar molecules. The energy levels of such surface-molecules will be obtained by using a simple tight-binding approach. Covalent bonds are partly ionic. Therefore, adatoms will induce surface dipoles in addition to surface states. As with small molecules, the chemical trends of the adatom-induced surface dipoles may be predicted from the difference of the adatom and substrate electronegativities.