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.