Simulation of high energy photoelectron diffraction using many-beam dynamical Kikuchi-band theory

Abstract

We use the many-beam dynamical theory of electron diffraction for the calculation of x-ray photoelectron diffraction ͑XPD͒ patterns of the substrate emission. The reciprocity principle is used to apply a Bloch wave model for the diffraction of an incoming plane wave by a three-dimensional crystal. In this way, many-beam dynamical simulations of XPD in the context of Kikuchi-band theory can be carried out. This extends the results of the two-beam theory used so far and leads to quantitative descriptions of XPD patterns in the picture of photoelectrons reflected by lattice planes. The effects of forward scattering directions, substrate polarity, circular structures due to onedimensional diffraction, and emitter specific extinction of Kikuchi lines can be reproduced by Kikuchi-band theory. The results are compared with single scattering cluster calculations. In this way, the equivalence of the cluster approach and the Kikuchi-band picture can be demonstrated completely in both directions

High-energy photoelectron diffraction: model calculations and future possibilities

“…It was shown that this theory can not only explain the formation of Kikuchi bands but also reproduces features like forward-scattering directions and ring-shaped interference maxima around these directions. Such features can also be explained in the intuitive forward scattering picture of cluster calculations, as has been shown by direct comparison with single scattering cluster (SSC) simulations [21]. These rings are the long-range-order analogues of what have been termed firstorder diffraction fringes in XPD studies of small molecules and chains [1].…”

“…We will only give a short summary of the general approach we apply. More details can be found in Winkelmann et al [21,24].…”

“…Although the full details of our long-range-order dynamical approach have been presented elsewhere [21], we introduce the essentials briefly here. For the description of the photoelectron diffraction process, we assume in the first approximation that the electrons originate isotropically from point sources which are periodically arranged inside a crystal.…”

“…and results in the cross section formula that we have used in our previous simulations for quasi-elastic backscattering of electrons and XPD [21,24]:…”

“…Making use of this view of an effectively three-dimensional crystal that is diffracting the photoelectrons, one of the authors has previously been able to show that the Bloch wave approach of the dynamical theory of electron diffraction is able to provide a practical framework for the simulation of XPD patterns at high kinetic energies [21]. It was shown that this theory can not only explain the formation of Kikuchi bands but also reproduces features like forward-scattering directions and ring-shaped interference maxima around these directions.…”