We use the many-beam dynamical theory of electron diffraction for the calculation of x-ray photoelectron diffraction $\left(\mathrm{XPD}\right)$ 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 $\mathrm{XPD}$ 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 $\mathrm{XPD}$ 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

• Received 8 December 2003

DOI:https://doi.org/10.1103/PhysRevB.69.245417