Photoelectron diffraction is the name given to the phenomenon resulting from the coherent interference of the directly emitted component of an electron wavefield, emerging from an atom as a result of core level photoemission, with other components elastically scattered by surrounding atoms. Experimental characterization of this effect provides information which can be used to provide quantitative determinations of the structure of surfaces, and particularly of adsorbed species on surfaces, in an element-specific fashion. Since the initial. Demonstration of the phenomenon in the late 1970s, an extensive methodology for surface structure determination has been developed. In this review the background physics of the process, and the development of the technique is described. A brief discussion of the high energy forward scattering version of the technique (X-ray photoelectron diffraction-XPD), which utilizes zero-order diffraction effects, is included, but the most of the review is concerned with the lower energy backscattering method more relevant to the determination of detailed adsorption sites on surfaces. In addition to the general theoretical, experimental and methodology background, a number of the more recent developments are described including use of 'direct inversion' methods for (approximate) structure determination, including a survey of photoelectron holography, and the realization of chemical shift photoelectron diffraction to allow structure determinations of surfaces including atoms of one element in more than one inequivalent site. All of the developments are illustrated with specific examples, mainly of molecular and atomic adsorbates on metal surfaces.

https://iopscience.iop.org/article/10.1088/0034-4885/57/10/003/pdf

Adsorbate structure determination on surfaces using photoelectron diffraction

Consequences of a finite energy resolution for photoelectron diffraction spectra

An exact formula for the expansion of an outgoing spherical electron wave around another centre is presented from which new approximation for spherical-wave scattering are derived. These expressions allow a considerably higher accuracy in high-speed numerical multiple-scattering calculations than methods existing hitherto. This is demonstrated for tungsten in the energy range from 50 to 5000 eV. The improvements of the given formulae over earlier approaches are greater the higher the energy. In particular the errors in the forward scattering direction are very small.

https://iopscience.iop.org/article/10.1088/0953-8984/2/6/002/pdf

A new spherical-wave approximation for photoelectron diffraction, EXAFS and MEED

Approximations for photoelectron scattering

The study of the local atomic structure by means of X-ray photoelectron diffraction

In order to improve the calculations of ARPES, ARAES, and EXAFS a new approximation in the multiple-scattering theory for the excited electrons is introduced, which is called reduced angular momentum expansion (RAME). In the RAME the incoming waves are approximated in the range of the scattering potential by a limited set of spherical waves with low angular momenta. This is a much better description than the plane wave approximation in the often used small scattering-centre approximation. The RAME possesses a high accuracy for energies down to 40 eV and needs a substantially lower numerical effort than the full angular momentum expansion. For higher energies it can be further simplified and it modified small-scattering-centre approximation is obtained, which takes into account the curvature of the waves by means of effective scattering amplitudes.



Um die Berechnung von ARPES, ARAES und EXAFS zu verbessern, wird eine neue Naherung in die Vielfachstreutheorie fur die angeregten Elektronen eingefuhrt, die als reduzierte Drehimpulsentwicklung (RAME) bezeichnet werden soll. In der RAME werden die einfallenden Wellen im Bereich des Streupotentials durch einen beschrankten Satz von Kugelwellen mit niedrigen Drehimpulsquantenzahlen approximiert. Das ist eine weitaus bessere Beschreibung als die Approximation durch eine ebene Welle in der oft verwendeten Naherung kleiner Streuzentren. Die RAME besitzt eine hohe Genauigkeit fur Energien bis hinab zu 40 eV und benotigt wesentlich weniger Rechenaufwand als eine vollstandige Drehimpulsentwicklung. Bei hoheren Energien kann sie weiter vereinfacht werden, und man erhalt eine modifizierte Naherung kleiner Streuzentren, die die Krummung der Wellenfronten durch effektive Streuamplituden berucksichtigt.

V. Fritzsche

Papers

A reduced angular momentum expansion in the multiple‐scattering theory