Band structure calculations of low energy electron diffraction at crystal surfaces

Abstract

The band structure formulation of the dynamical theory of Low Energy Electron Diffraction as proposed by Heine is considered from the point of view of actual calculations. This formulation is essentially based upon the continuous matching of the incident and reflected electron wavefunctions to the Bloch waves at the solid-vacuum interface. The equivalence to the multiple scattering formulation of McRae is illustrated by a calculation on a model crystal consisting in a semi-infinite cubic array of s-wave scatterers. The choice of this model crystal serves the two purposes of enabling quantitative comparison with the results of McRae and providing reasonable evidence that the method can be successfully applied to real situations. The multiple scattering effects and the surface wave resonance are shown to be accounted for by the formulation, in agreement with the theory of Boudreaux and Heine. In addition, the close correspondence between the band structure and the reflected intensity curves is pointed out. The application of the band structure formulation to real situations involving inelastic effects and pure surface effects is discussed.