Momentum-transfer model of valence-band photoelectron diffraction

Abstract

AbstractRecent instrumental progress of valence-band photoemission in the X-ray range allows uncovering bulk- and surface-related electronic properties. Four-dimensional recording of energy and momentum-vector gives access to the complete spectral-density function. Systematic measurements for a number of transition metals between 15 eV-6 keV reveal unexpected strong intensity modulations due to photoelectron diffraction. Here, we present a graphical model that illustrates the role of momentum-conservation in Fermi’s Golden-Rule in an intuitive way. Intensity enhancement or reduction by factors >5 are confined to small energy- and momentum-intervals (widths 0.03 Å−1 and 200 meV). Laue-type diffraction involves the photon momentum and is intrinsic in the photoemission process, in accordance with Pendry’s final-state-model. At higher energies, Kikuchi-diffraction imprints additional modulations on valence-band-patterns and quasi-elastic background. The absence of photon-momentum transfer uncovers the extrinsic nature of Kikuchi-diffraction. For Re at 30 K and 3.4 keV the relative weight of the Kikuchi-branch is comparable to the Laue-branch, whereas at 6 keV the Kikuchi-branch prevails.