Resonance Effects in Diffraction of Low-Energy Electrons by Crystals

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Abstract
Resonance minima in specular reflectivity of low-energy electrons by crystals explained in terms of the coupling of an incident wave and a wave which is bound inside the crystal only in the direction normal to the surface but travels parallel to the surface with a momentum larger than the parallel component of the incident momentum and propagates into vacuum. The theory is formulated on the basis of a set of coupled one-dimensional differential equations which are obtained from the Schroedinger equation by the two-dimensional Fourier transform of the potential. The minima are caused by transitions of incident electrons not only to penetrating bound states but also to localized bound states which are analogous to Tamm-Shockley surface states in semiconductor surface physics. Numerical calculations are made for model cases. The effects of inelastic processes are wholly neglected.