Investigation of iterative RHEED calculations

Some new iterative methods for calculating RHEED intensities are investigat ed. 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 dif ferent nature, occur when the methods are used to deal very large supercell s. These difficulties are explained and two approaches for overcoming them are reported. One approach involves shifting the eigenvalues of the iterati on operator and modifying the Green's function used to construct it. The ot her is a biconjugate gradient technique. Both methods enable the iterative scheme to be made convergent and their advantages and disadvantages are dis cussed, The methods are very fast and the computer time scales with the num ber of beams, N-b, like N-b log(N-b). Use of these methods allows calculati ons for supercell dimensions exceeding 100 x 100 and beam set sizes exceedi ng 10(5) beams, a beam set size about two orders of magnitude larger than p ossible with a conventional RHEED program. Examples of applications to vari ous model structures on the Si(001) surface are given. (C) 2001 Elsevier Sc ience B.V. All rights reserved.