A theory of rheed

Elastic Reflection High Energy Electron Diffraction (RHEED) by solid surfaces is studied theoretically. First, the problem of finding the electron reflection and transmission coefficients of a crystal slab is formally solved. Following this, it is shown how the formal solution may be used in a practical computation of the diffracted beam intensities. These two results are applied to a study of high energy (20 keV) electron diffraction by the Ag(001) surface. Rocking curves are computed to illustrate the dependence of the reflection coefficients on the glancing angle of the incident beam, the incident beam azimuth being in the [110] direction. The curves are shown to have several features in common with a typical set of LEED I-V plots: primary Bragg peaks, secondary Bragg peaks and resonance peaks are all present. The dependence of the reflection coefficients on the deviation of the incident beam azimuth from the [110] direction is also described. Additional computations are made to illustrate the sensitivity of the RHEED pattern to the details of the surface structure: the relative heights of the peaks in the rocking curves are shown to be quite sensitive to the spacing of the topmost atomic layers.