# Low-energy-electron-diffraction spectra from [001] surfaces of face-centered cubic metals: Theory and experiment

## Abstract

Extensive calculations of low-energy-electron-diffraction (LEED) spectra on face-centered cubic metals have been made with the layer-Korringa-Kohn-Rostocker (layer-KKR) method which treats multiple scattering within layers by the KKR method of band theory and multiple scattering between layers by matrix methods based on a beam representation of the wave field. The theory of the method is compactly and simply formulated using matrix notation. Calculations made with zero absorption in the material exhibit the close relationship in the structures of the curves for energy bands, reflected-flux spectra and transmitted-flux spectra, when plotted on a common energy scale. A check on the accuracy of the method is provided by the close agreement of the energy bands with independent calculations by standard methods. Calculations made with absorption for Al {001}, Cu {001}, and Ag {001} using 29 beams and 8 phase shifts for incident electrons up to 150 eV and for Al {001} at angles of incidence up to 25° are compared with experiment. A correction for lattice motion is introduced and several ways of matching waves at the surface are discussed. Detailed spectra at various angles show close correspondence between theory and experiment in relative peak positions, widths, and shapes and permit discrimination among crystal potentials. Estimates of inner potentials by comparison of measured and calculated spectra appear to provide information on the energy dependence of the effective one-electron potential in real crystal. © 1972 The American Physical Society.