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.

A theory of rheed

The image contrast of surface steps in reflection electron microscopy

Surface imaging using diffracted electrons

Bragg diffraction imaging of defects at crystal surfaces

Direct calculation of the dynamical reflectivity matrix for RHEED

The n-beam dynamical theory of high-energy electrons is currently used in transmission (Laue case) for accurate determination of the Fourier components of the crystal potential. The same theory is expected to provide information about the surface potential when used to interpret diffraction patterns in reflection at glancing incidence (Bragg case). Some peculiar aspects are elucidated in detail, insofar that they are different from the transmission case, particularly the boundary conditions. Inelastic scattering effects are introduced by means of a complex potential. Changes of the Fourier components of the potential near the surface are considered, and a model has been developed which incorporates these changes into the theory. A slice treatment developed in the frame of Bethe's theory is presented.

R. Colella

Papers

n-Beam dynamical diffraction of high-energy electrons at glancing incidence. General theory and computational methods