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Rocking curves for the 2nd to 7th order reflections of the systematic set from the (111) planes of a highly perfect silicon single crystal have been obtained in an ultra-high-vacuum reflection electron diffraction camera operated at 40 keV. These have been compared with the profiles computed with an n-beam dynamic high-energy electron diffraction theory adapted to the Bragg case at glancing incidence. It is shown that, for the 333 reflection, six nodes of the hhh row from 111 up to 444 are adequate to take into account the systematic multiple beam interference effects. The calculated widths are found to agree with the observed widths within the experimental error for all reflections. The peak reflectivities computed initially for a perfect semi-infinite crystal are systematically higher than the experimental values, by a factor of 7 for the 222 node, decreasing to near agreement for the 777 node. Possible reasons for such discrepancies are discussed. Neither inelastic scattering effects nor reasonable changes in the silicon lattice potential near the surface can bring the observed and calculated intensities into agreement. The discrepancy can be considerably reduced for all orders of reflection, however, when the non-flat nature of the surface is considered.
Colella et al. (Sat,) studied this question.