Low-energy electron diffraction from Cu(111): Subthreshold effect and energy-dependent inner potential; surface relaxation and metric distances between spectra

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Abstract
In the present low-energy electron-diffraction (LEED) study of the copper (111) surface the inner potential and the surface relaxation are determined independently from the subthreshold effect and from Bragg-type diffraction. A "subthreshold effect" is a narrow LEED intensity structure occurring at a setting where new beams have an emergence threshold in the metal: a "subthreshold." We reconsider the absorption of electrons with regard to its spatial distribution in the crystal and design a phenomenological model comprising two parameters which are adjusted to the absorptive scattering cross section of the ion cores and that of the interstitial region. The two-parameter model for the interlayer attenuation indicates the existence of a transparent scattering channel "pseudoparallel" to the surface for beams emerging in the crystal. The channeling extends over all layers penetrated by the LEED electrons, giving the subthreshold effect a peak width of about 2 eV. Each observable subthreshold effect fixes a point on the energy-dependent inner potential; for the copper (111) surface we are able to measure the inner potential at 19.5-, 73.6-, and 109-eV incidence energy. A local excited-state potential of the Hedin-Lundqvist type produces for the copper (111) surface an inner-potential curve that agrees well with the measured points. From LEED spectra for the 00, 10, and 01 beams from the copper (111) surface in the energy range 16-190 eV we infer a top-layer spacing contracted (0.7 ± 0.5)% relative to the layer spacing in the bulk. The theoretical and experimental spectra are compared by means of metric distances, which are stable with respect to noise in the data and give a linear response to small variations of the structural parameters.