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High-resolution full-field imaging of ( k _x , k _y ) photoelectron distributions ( k -resolution 0.03 Å ^−1 , angular resolution 0.03° at 6.7 keV) in a large field of view (up to 16 Å ^−1 dia.) allows to observe fine details in Kikuchi-type diffractograms. Alongside with the element specificity via core-level spectra, this method opens a new avenue to structural analysis using hard x-ray photoelectron diffraction (hXPD). Here we present a theoretical study of the emitter-site specificity by simulating hXPD patterns for arbitrary positions of emitter atoms in the unit cell. Using the Bloch wave approach to photoelectron diffraction from lattice planes, the diffraction patterns from a number of positions in the unit cell can be obtained simultaneously exploiting the reciprocity theorem. Simulations for dopant atoms and dopant multimers (dimers, trimers, clusters) in the Si lattice at various positions in the unit cell reveal a strong site-sensitivity in terms of dramatic changes in the diffraction patterns with emitter-atom position. The results are compared with measurements for Si hyperdoped with Te.

Photoemission-intensity distributions I _RCP/LCP ( E _B , k ) measured for right- and left-circularly polarized soft x-rays revealed a large circular dichroism in angular distribution ( CDAD) in the 4D parameter space ( E _B binding energy, k momentum vector). Full-field k -imaging combined with time-of-flight energy recording at a high-brilliance soft x-ray beamline allowed mapping the CDAD in the bulk Brillouin zone of tungsten and the entire d -band complex within a few hours. CDAD -asymmetries are very high (up to 90%), persist throughout the whole photon-energy range (300–1300 eV) and show a pronounced dependence on momentum k and binding energy E _B , visualized as movies or sequences of cuts through the 4D object. One-step photoemission calculations for the same photon energies show fair agreement with the measured results. In addition to the requirement of a ‘handed’ experimental geometry, known from previous experiments on adsorbates and surface states, we find an anti-symmetric behavior of the CDAD with respect to two bulk mirror planes. A new symmetry condition along the perpendicular momentum k _z makes CDAD a valuable tool for an unambiguous identification of high-symmetry planes in direct transitions in the periodic zone scheme. Technically, the method provides a circular polarimeter for soft, tender and hard x-rays.

Hard x-ray photoelectron diffraction (hXPD) patterns recorded with a momentum microscope with high k -resolution (0.025 Å ^−1 equivalent to an angular resolution of 0.034° at 7 keV) reveal unprecedented rich fine structure. We have studied hXPD of the C 1s core level in the prototypical low-Z material Graphite at 20 photon energies between 2.8 and 7.3 keV. Sharp bright and dark lines shift with energy; regions of Kikuchi band crossings near zone axis exhibit a filigree structure which varies rapidly with energy. Calculations based on the Bloch wave approach to electron diffraction from lattice planes show excellent agreement with the experimental results throughout the entire energy range. The main Kikuchi bands in the [001] zone axis appear fixed on the momentum scale with a width of the corresponding reciprocal lattice vector, allowing to reconstruct the size of the projected Brillouin zone. The newly developed high-energy k -microscope allows full-field imaging of ( k _x , k _y )-distributions in large k -fields (up to >22 Å ^−1 dia.) and time-of-flight energy recording.

Photoelectron spectroscopy, especially at pulsed sources, is ultimately limited by the Coulomb interaction in the electron cloud, changing energy and angular distribution of the photoelectrons. A detailed understanding of this phenomenon is crucial for future pump–probe photoemission studies at (x-ray) free electron lasers and high-harmonic photon sources. Measurements have been performed for Ir(111) at h ν = 1000 eV with photon flux densities between ∼10 ^2 and 10 ^4 photons per pulse and μ m ^2 (beamline P04/PETRA III, DESY Hamburg), revealing space-charge induced energy shifts of up to 10 eV. In order to correct the essential part of the energy shift and restore the electron distributions close to the Fermi energy, we developed a semi-analytical theory for the space-charge effect in cathode-lens instruments (momentum microscopes, photoemission electron microscopes). The theory predicts a Lorentzian profile of energy isosurfaces and allows us to quantify the charge cloud from measured energy profiles. The correction is essential for the determination of the Fermi surface, as we demonstrate by means of ‘ k -space movies’ for the prototypical high-Z material tungsten. In an energy interval of about 1 eV below the Fermi edge, the bandstructure can be restored up to substantial shifts of ∼7 eV. Scattered photoelectrons strongly enhance the inelastic background in the region several eV below E _F , proving that the majority of scattering events involves a slow electron. The correction yields a gain of two orders of magnitude in usable intensity compared with the uncorrected case (assuming a tolerable shift of 250 meV). The results are particularly important for future experiments at SASE-type free electron lasers, since the correction also works for strongly fluctuating (but known) pulse intensities.