ANALYTICAL TREATMENT OF SURFACE RESONANCE DIFFRACTION OF HIGH-ENERGY ELECTRONS

The surface resonance RHEED problem is solved exactly using the tight-binding model for the case of the off-Bragg orientation of the incident beam. Explicit expressions are obtained for the wave function and for the resonance part of the surface reflectivity. It is shown that the dominant contribution to the reflectivity results from a process involving at least several states each localized in the potential of adjacent atomic planes parallel to the surface, and in the crystal bulk the wave function of the scattering problem belongs to the continuum of Bloch states. The analytical solution found provides an accurate approximation to the results of numerical integration of the relevant equations of the theory of RHEED, and demonstrates that no concept of a surface state is required for interpretation of the angular dependence of the reflectivity of a clean crystal surface in the vicinity of the resonance condition.