Total energy minimization for surfaces of covalent semiconductors C, Si, Ge, and α-Sn: I. (111)2×1 surfaces

Abstract

A semi-empirical tight-binding approach to the total energy of a surface system is presented. The resulting energy functional includes the electron-electron and ion-ion interaction in a reasonable way. It incorporates a self-consistent treatment of energies and charge transfers and is therefore capable of handling complex surface reconstruction geometries. The energy gain due to reconstruction and the resulting equilibrium surface geometry follow from the minimization of the total energy functional with respect to the atomic coordinates. The method is applied to the (111)2×1 surfaces of diamond, silicon, germanium, and α-Sn. Three reconstruction models are studied: the Haneman buckling model, the Pandey π-bonded chain geometry, and the Chadi molecule structure. Among the models suggested for the 2×1 reconstructed (111) surfaces the π-bonded chain model has to be favoured from the energetical point of view. The energy minimization in the framework of the buckling model only yields the ideal bulk-terminated surface structure. The molecule reconstruction does not give rise to any positive energy gain. For the π-bonded chain model the deepest energy is found for slightly buckled but undimerized chains. Chemical trends are discussed. The minimum-energy equilibrium geometrical structures obtained for this model are compared with atomic configurations extracted from other total energy calculations, medium-energy ion scattering and dynamical LEED. Overall agreement is stated. However there are also characteristic differences with respect to the magnitude of the tilts in the individual atomic layers, the relaxation of these layers and the strain resulting in these geometries. The atomic structures obtained experimentally are tested by means of the presented total energy functional.