Quantitative computation of RHEED patterns

This thesis is concerned with the general problem of performing quantitative RHEED computations for both flat and rough surfaces using the multislice method. Modifications to the RHEED multislice method which make it into a practical technique for performing RHEED computations are described. Computation of convergent-beam RHEED patterns using the RHEED multislice method is demonstrated by application to the case of MgO (001). Computed patterns are compared (based on the overall pattern geometry) to energy-filtered Tanaka and convergent-beam patterns recorded in a transmission electron microscope. The validity of the RHEED multislice method for convergent-beam computations is demonstrated by the level of agreement achieved. The application of the RHEED multislice method combined with the edge patching algorithm to the computation of RHEED streaks from rough surfaces is demonstrated by applying it to the case of rough Fe (001) surfaces. The computations are done using the column approximation and by neglecting the scattering from steps parallel to the incident beam. The computations are set up using STM images of the surfaces from which the experimental RHEED patterns were recorded. The shapes of the diffuse parts of the computed and experimental streaks agree well. There is a discrepancy between experiment and theory in the magnitudes of the flat surface spot position peaks relative to the diffuse parts of the streaks. The shapes of the diffuse parts of the computed streaks are shown to be insensitive to the computational and potential parameters. The magnitudes of the flat surface spot position peaks are at least weakly dependent on the potential parameters and the long range height variations of the surface. This agreement conclusively demonstrates that the RHEED multislice method can be used to perform quantitative computations of RHEED streaks from real rough surfaces. An approximation method (the patchwork approximation) for doing RHEED computations, exact in the limit of large terraces, is developed and tested by comparison to full computations.