n-Beam dynamical diffraction of high-energy electrons at glancing incidence. General theory and computational methods

The n-beam dynamical theory of high-energy electrons is currently used in transmission (Laue case) for accurate determination of the Fourier components of the crystal potential. The same theory is expected to provide information about the surface potential when used to interpret diffraction patterns in reflection at glancing incidence (Bragg case). Some peculiar aspects are elucidated in detail, insofar that they are different from the transmission case, particularly the boundary conditions. Inelastic scattering effects are introduced by means of a complex potential. Changes of the Fourier components of the potential near the surface are considered, and a model has been developed which incorporates these changes into the theory. A slice treatment developed in the frame of Bethe's theory is presented.