Low-energy electron diffraction amplitudes

Abstract

The reflection (Bragg) case of the dynamical theory of diffraction is analyzed with a view to applications in low-energy electron diffraction. A theoretical description of diffraction amplitudes is developed for a model consisting of a substrate crystal periodic in three dimensions, with a two-dimensionally periodic selvedge (surface region). The diffraction amplitude is considered as a function of electron energy, which is allowed to take complex values, and the emphasis is placed on the analytic structure of the diffraction amplitude function. A detailed analysis is given for the case of elastic scattering, represented by a real scattering potential. The substrate band structure and the surface-state resonances are included, respectively, as branch points on the real-energy axis and poles on specific unphysical sheets of the amplitude function. A dispersion relation satisfied by the amplitudes of individual diffracted beams or by specific combinations of such amplitudes is derived. The significance of the analysis for models in which inelastic scattering is included phenomenologically by an optical potential is discussed.