Electron attenuation anisotropy at crystal surfaces from LEED

Dynamical theory of electron scattering is used to describe the electron transport in the surface regions of crystals. The angle resolved attenuation length of electrons is derived from the transmitted LEED electron current decay. Electron attenuation length energy dependence and anisotropy in polar angle are found for crystalline Cu(1 1 1) for two high symmetry azimuths. Pronounced anisotropy in polar angle distributions of attenuation lengths is found to be in qualitative agreement with the results obtained from the photoelectron diffraction. Comparison with the attenuation lengths obtained from semiclassical simulations for amorphous copper is given. This comparison demonstrates that simple transfers of the smoothly behaving surface sensitivity from amorphous materials oversimplifies the electron attenuation process and can lead to incorrect results in quantitative analyses of crystalline surfaces.