# PROPRIÉTÉS DES INTERFACESPROPRIÉTÉS ÉLECTRONIQUES DES SURFACES

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Abstract : Electronic properties of surfaces are studied in the case of ideal surfaces, identical to a bulk plane, as cristallographic arrangement is concerned. The translationnal symmetry is then preserved in the surface plane and the reciprocal lattice is build from a surface elementary cell to take advantage of this symmetry in the study of the electronic states. Before going on this problem, the question arises of the meaning of a one electron approximation in the case of a crystal vacuum interface, where the potential is rapidly varying, the electronic correlation terms are the basic terms to describe the classical image potential, where new excitations are experimentally known surface plasmons. After a short discussion of this problem, the electronic surface properties are studied in a growing complexity order. The case of normal metals is first studied, in the approximation of free electrons, in a square well potential. The surface effect is then completely included in the potential barrier. The model of Bardeen is recalled. The limited heigh. of the barrier, which corresponds to a limited work function, allows electrons to get out the surface by tunnel effect, thus creating an electric dipolar layer. The nearly free electron model takes into account the symmetry of the crystal and allows to interprate the anisotropy of the superficial tension. The introduction of a periodical potential and of his rupture by the surface brings the existence of new electronic surface states, which appear in the band gaps of the bulk band structure. The one dimension model of Garcia and Moliner determines the energy level of the surface state. This result may be generalized to the three dimensionnal case : by selecting a wave vector K in the surface plane, the problem to determine the surface states with a K component in the surface is a one dimensionnal problem. Such a study may be applied to pure covalent semiconductors, but his extension to ionocovalent semiconductors requires a self consistent intervention of ionicity. Case of transition metals. For these metals, the elastic, electric and magnetic properties depend on the filling in the -d- band and they are quite well described by a tight binding model for the -d- band and a free electron model for the -s, p- band. The notion of local density is first defined in the case of a perfect crystal, for -d- electrons : n0E, for states with a given symmetry nEE, nTE

For an infinite perfect crystal, with one atom by cell the density of states of the -d- band is Nn0E, where N is the number of atoms. When a surface is created, the translationnal symmetry perpendicular to the surface is destroyed and the local densities depend on the distance to the surface. The invariance of the Fermi level involves the existence of a self-consistent potential on the next nearer layers of the surface and practically only on the surface layer. The study of the superficial tension and his anisotropy can be done by the moment method with a good accuracy. The phase shift method allows to account for surface states which are sery sensitive to the self-consistent surface potential. Taking into account the degeneracy of the -d- band, this method is complicated and good results are then obtained from the recursive method. This method is presented on a one dimensionnal example and then applied to the three dimensionnal problems. In the last section, the case of atoms adsorbed on an ideal surface of a transition metal is then introduced. Two different cases are then considered according the value of the intra atomic exchange potential term on the adsorbate compare to this term in the metal. The first case contains the transition atoms adsorbed on a transition metal. The binding energy is thus obtained by using the Friedel sum rule and a model including the image of the adsorbed atom. The case of alcaline atoms, which a large charge transfert ; as it is shown the variation of the work function, is then described in a Friedel-Anderson model. The main results concerning the theory of the hydrogen chemisorption on a transition metal are then given and compared with the photo and field emission experimental results.

Author: ** P. Lenglart **

Source: https://hal.archives-ouvertes.fr/