Calculation of RHEED Intensities for Imperfect Surfaces

RHEED calculation techniques for imperfect surfaces are reviewed and some applications of the calculational methods are described. Systems of interest typically consist of a perfectly ordered substrate which is periodic in three dimensions together with a surface which has imperfections in the form of disorder or steps. Calculational techniques for this type of system include: supercell methods in which the disorder is modeled by considering a large periodic system; perturbation theory in the distorted wave Born approximation where the scattering by the imperfections is taken to be a perturbation but the scattering by the periodic part of the system is treated exactly; the multislice method as used in transmission electron diffraction theory; and a promising new approach based on Green's functions. The validity of perturbation theory is investigated in detail and it is shown to give good agreement with supercell calculations in the case where the potential of the imperfections is weak or where their correlation length is small. This makes perturbation theory very suitable for treating disordered over-layers, but stepped surfaces with a large correlation length require the other methods. These methods are more expensive computationally and some possible ways of reducing the CPU time are considered. Finally, illustrative results are presented to show how the various calculational techniques can be applied to real systems. Particular cases include RHEED intensity oscillations and reflection electron microscope images.