Supercell RHEED calculations

Efficient calculational techniques for reflection high energy electron diff raction (RHEED) are reported for surfaces with large periodic supercells. A fast Fourier transform approach enables the computer time scaling of a con ventional RHEED calculation to be reduced to n(2)log(n), where n is the num ber of diffracted beams used in the calculation. The special technique need ed to implement this for arbitrary incident azimuths with symmetry optimiza tion is detailed. A Green's function method is also introduced which is par ticularly suitable for calculations for imperfect surfaces. This combines t he conventional approach to RHEED for dealing with substrate diffraction wi th a Green's function treatment for an imperfect surface of supercells and has nlog(n) time scaling. Techniques for matching the results of the conven tional and Green's function treatments at the substrate-surface interface a re given. In addition, numerical procedures for solving the resulting equat ions are described and a selection of illustrative results is presented.