Investigation of iterative RHEED calculations

Some new iterative methods for calculating RHEED intensities are investigated. In general, the convergence properties of iterative RHEED calculations are dependent on diffraction conditions. The convergence can be poor at the surface resonance condition and further convergence difficulties, of a different nature, occur when the methods are used to deal very large supercells. These difficulties are explained and two approaches for overcoming them are reported. One approach involves shifting the eigenvalues of the iteration operator and modifying the Greenʹs function used to construct it. The other is a biconjugate gradient technique. Both methods enable the iterative scheme to be made convergent and their advantages and disadvantages are discussed. The methods are very fast and the computer time scales with the number of beams, Nb, like Nblog(Nb). Use of these methods allows calculations for supercell dimensions exceeding 100×100 and beam set sizes exceeding 105 beams, a beam set size about two orders of magnitude larger than possible with a conventional RHEED program. Examples of applications to various model structures on the Si(0 0 1) surface are given.