P.M. Len

DIFFRACTION AND HOLOGRAPHY WITH PHOTOELECTRONS AND FLUORESCENT X-RAYS

Abstract We consider studies of the atomic and magnetic structure near surfaces by photoelectron diffraction and by the holographic inversion of both photoelectron diffraction data and diffraction data involving the emission of fluorescent x-rays. The current status of photoelectron diffraction studies of surfaces, interfaces, and other nanostructures is first briefly reviewed, and then several recent developments and proposals for future areas of application are discussed. The application of full-solid-angle diffraction data, together with simultaneous characterization by low energy electron diffraction and scanning tunneling microscopy, to the epitaxial growth of oxides and metals is considered. Several new avenues that are being opened up by third-generation synchrotron radiation sources are also discussed. These include site-resolved photoelectron diffraction from surface and interface atoms, the possibility of time-resolved measurements of surface reactions with chemical-state resolution, and circular dichroism in photoelectron angular distributions from both non-magnetic and magnetic systems. The addition of spin to the photoelectron diffraction measurement is also considered as a method for studying short-range magnetic order, including the measurement of surface magnetic phase transitions. This spin sensitivity can be achieved through either core-level multiplet splittings or circular-polarized excitation of spin-orbit-split levels. The direct imaging of short-range atomic structure by both photoelectron holography and two distinct types of x-ray holography involving fluorescent emission is also discussed. Both photoelectron and x-ray holography have demonstrated the ability to directly determine at least approximate atomic structures in three dimensions. Photoelectron holography with spin resolution may make it possible also to study short-range magnetic order in a holographic fashion. Although much more recent in its first experimental demonstrations, x-ray fluorescence holography should permit deriving more accurate atomic images for a variety of materials, including both surface and bulk regions.

Photoelectron diffraction and holography: Present status and future prospects

Abstract Photoelectron diffraction and photoelectron holography, a newly developed variant of it, can provide a rich range of information concerning surface structure. These methods are sensitive to atomic type, chemical state, and spin state. The theoretical prediction of diffraction patterns is also well developed at both the single scattering and multiple scattering levels, and quantitative fits of experiment to theory can lead to structures with accuracies in the ±0.03 A range. Direct structural information can also be derived from forward scattering in scanned-angle measurements at higher energies, from path length differences contained in scanned-energy data at lower energies, and from holographic inversions of data sets spanning some region in angle and energy space. Diffraction can also affect average photoelectron emission depths. Circular dichroism in core-level emission can be fruitfully interpreted in terms of photoelectron diffraction theory, as can measurements with spin-resolved core-spectra, and studies of surface magnetic structures and phase transitions should be possible with these methods. Synchrotron radiation is a key element of fully utilizing these techniques.

PHOTOELECTRON DIFFRACTION: SPACE, TIME, AND SPIN DEPENDENCE OF SURFACE STRUCTURES

The current status of photoelectron-diffraction studies of surface structures is briefly reviewed, and several recent developments and proposals for future areas of application are then discussed. The application of full-solid-angle diffraction data, together with simultaneous characterization by low-energy electron-diffraction and scanning-tunneling microscopy, to epitaxial growth is considered. Several new avenues that are being opened up by third-generation synchrotron-radiation sources are also considered. These include photoelectron diffraction from surface and interface atoms, the possibility of time-resolved measurements, and circular dichroism in photoelectron angular distributions. The addition of spin to the photoelectron-diffraction measurement is also considered, and can be achieved either through core-level multiplet splittings or by circular-polarized excitation of spin–orbit-split levels. This last development should make it possible to study short-range magnetic order, perhaps even in a holographic fashion.

Photoelectron holography: Prospects and limitations of direct methods

Abstract Images of near-surface atoms can be obtained from photoelectron diffraction data by various imaging algorithms, the basic method being: (a) a Fourier transform over k-space involving a path-length difference phase factor. We will also discuss two recently proposed direct methods that compensate for the non-optical atomic scattering of photoelectrons: (b) a Fourier transform of small k-space cones centered on the approximately optical scattering regions of a photoelectron diffraction data set; and (c), a truly quantum mechanical Fourier transform that accounts for the non-optical propagation and atomic scattering of the photoelectrons in the first Born approximation. Atomic images produced by these three methods are compared for photoelectron diffraction patterns calculated from a single scattering Ni trimer, and a large multiple scattering Ni bulk cluster. All three methods are found to comparably resolve backscattering atomic images, while poorly resolving forward and side scattering atomic images.

Optimal atomic imaging by photoelectron holography

Abstract Several recent papers have dealt with the question of whether large-scale photoelectron diffraction data spanning a significant range in both angle and wavenumber can be analyzed as holograms so as to produce directly three-dimensional images of near-surface atomic structure. Data are thus taken over some volume in the photoelectron wavevector k-space, and then transformed to obtained atomic images. In this work, we review four analysis methods proposed to date for deriving atomic positions directly from photoelectron diffraction data and consider the application of them to theoretical diffraction patterns calculated from various single-scattering model clusters. This permits some general conclusions as to domains of applicability and the optimization of k-space sampling so as to minimize data acquisition time, while still assuring atomic images that are free of coarse k-sampling aberrations. We conclude that holographic imaging of atoms does not require exceedingly large photoelectron diffraction data sets, with a few thousand data points being a suitable minimum, and we also comment on the relative merits of the four different imaging algorithms.

Atomic holography with electrons and x-rays

Gabor first proposed holography in 1948 as a means to experimentally record the amplitude and phase of scattered wavefronts, relative to a direct unscattered wave, and to use such a “hologram” to directly image atomic structure. But imaging at atomic resolution has not yet been possible in the way he proposed. Much more recently, Szoke in 1986 noted that photoexcited atoms can emit photoelectron or fluorescent x-ray wavefronts that are scattered by neighboring atoms, thus yielding the direct and scattered wavefronts as detected in the far field that can then be interpreted as holographic in nature. By now, several algorithms for directly reconstructing three-dimensional atomic images from electron holograms have been proposed (e.g. by Barton) and successfully tested against experiment and theory. Very recently, Tegze and Faigel, and Gog et al. have recorded experimental x-ray fluorescence holograms, and these are found to yield atomic images that are more free of the kinds of aberrations caused by the non...

Optimization of k-space sampling in atomic imaging by electron emission holography

Abstract Two limiting-case algorithms have previously been proposed for holographically imaging atoms near surfaces using photoelectron diffraction data and other diffraction data associated with electron emission: (i) a phased sum of Fourier transforms of scanned-angle data taken at several energies from Barton, (ii) and a phased sum of Fourier transforms of scanned-energy data taken along several directions due to Tong et al. We first point out that both methods are equivalent three-dimensional transforms in the wave vector k of the emitted electron, differing only in the way they sample k -space. A continuum of different sampling densities in the direction and magnitude of k exists in such holography, spanning the two limits previously discussed. An additional variant on these methods involves using only a small cone of data in k -space for each transform. Using model diffraction calculations for localized electron emission (e.g., core photoelectron emission) from Cu(001) clusters, we have explored the full range of k -space sampling possible, and find that optimum image quality is expected for choices intermediate between the extreme limits of scanned-angle or scanned-energy. General rules for optimizing image quality for a given data-set range are also discussed, and used to evaluate the sampling choices made in some prior experimental studies.