X-ray photoelectron diffraction at high angular resolution
Physical Review B (Condensed Matter)
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
... 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  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. XPD cluster picture and dynamical electron scattering from lattice planes showed that the latter is more appropriate for very high energies. Hence, for the present study of hard x-ray photoelectron diffraction (hXPD) the dynamical scattering approach for bulk crystals is expected to be the more efficient theoretical description. By exploiting exchange scattering and multiplet splittings, even antiferromagnetic short-range order has been probed by XPD [17, 18] . Experimentally, XPD is studied using angular-resolved photoelectron spectroscopy. Large polar angular ranges of typically 0°-60°can be observed, mostly by rotating the sample about its surface normal (e.g. [8, 10, 11] ). But also display-type electron analysers were developed    which give direct 2D full-field angular distributions in a wide angular range     . One main emphasis was to observe the pronounced forward scattering along atom rows in off-normal directions [4, 8] , hence the trend to observe a maximum polar angular range. Typical angular resolutions in both angular-scanning and display-type recording modes are ∼1°, but in some cases higher resolutions (<1°FWHM) have been reached    . Here we present the first study of XPD using the new technique of momentum microscopy. In this type of photoelectron analyser, a cathode-lens (usually with an electrostatic extractor field) yields a reciprocal image in its backfocal plane (BFP), which is magnified on the image detector. This recording mode bears several essential differences in comparison with previous approaches: The diffractograms are observed in reciprocal space (i.e. on a momentum scale) instead of real-space polar coordinates. The k-field of view in the present study is up to ∼14 Å −1 at 7 keV, corresponding to a small polar angular range of 0°-9°. The k-resolution of ∼0.03 Å −1 corresponds to an angular resolution of 0.03°. For the small angular range, full-field imaging works without sample rotation, similar to the display-type solutions. Larger off-normal observation angles are accessible by rotation of the sample using a mode with zero extractor field. The real-space observation mode (PEEM mode) facilitates checking of surface quality and easy selection of desired sample areas. The aim of this first detailed momentum-microscopy XPD study was to explore the so far inaccessible regime of high-resolution, small-angle hXPD and to compare the measured diffractograms with state-of-the-art dynamical calculations using the Bloch-wave approach [7, 29] . We stress the complementarity of the present results with XPD work on much larger angular scales. High-resolution k-space mapping offers an increased sensitivity to the effects of long-range order, which can be revealed in the fine structure of bulk diffraction features. Wide-angular-range investigations are focussed on the local order around the photoemitter sites (even without long-range order), as manifested e.g. by the forward-focussing directions toward neighbour sites.