Theory of angle-resolved photoemission extended fine structure

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Abstract
We present a theory for photoelectron scattering in the 100–1000 eV energy range designed to simulate experimental measurements of angle-resolved photoemission extended fine structure (ARPEFS) from ordered surfaces. The zero-order problem of photoabsorption in the solid is treated first, followed by a scattering problem which incorporates the scattering ion cores in a perturbation series (cluster expansion). The dynamics of core-hole relaxation are discussed, but the dynamical effects are shown to be small. The Taylor-series magnetic-quantum-number expansion is used for the curved-wave, multiple-scattering equations. We argue that a velocity-dependent surface barrier gives primarily an inner potential shift, with no clear evidence for surface electron refraction. Analytic formulas for aperture integration are derived and thermal averaging in a correlated Debye model is extended to multiple scattering. Reasonable values for nonstructural parameters in the theory are shown to give very good simulations of the experimental ARPEFS measurements from c(2×2)S/Ni(001) in contrast to previous theoretical calculations. We find, in agreement with full multiple-scattering calculations, that forward focusing is a fundamental feature of ARPEFS and that curved-wave corrections are essential for quantitative results. Since the scattering path-length difference is not appreciably altered by forward scattering, the ARPEFS oscillation frequency is equal to the geometrical path-length difference plus a small potential phase shift, but the amplitude and constant phase of the oscillations cannot be predicted by theories based upon single-scattering or plane-wave approximations.