Diffraction analysis of a disordered surface, modelled on a probability distribution of reconstructed blocks: Bi/Si(001)-(2xn), n = 6.45

Bismuth adsorbs on the Si(001)-(1 x 2) surface in the form of rows of dimers. Missing-dimer lines (MDLs) are created perpendicularly every n units, leading to (2 x n) periodicity. Depending on the coverage, n can vary from 12 to 5. We investigated by grazing incidence x-ray diffraction the (2 x n) structure, with n = 6.45. The disorder in the MDL periodicity, as well as the defects along the MDL, reduce considerably the correlation length of the reconstructed domains. As a consequence, the integrated intensity of each reflection must be corrected, evaluating the trace of the resolution function across the diffraction node. The structural refinement, based on the as-derived intensities, provides the Bi dimer bond length (3.11 Angstrom) the Si atom positions (bulklike), and the height of the Pi plane with respect to Si (1.88 Angstrom). In addition, we give evidence that the dimers are displaced along the row from ideal positions towards the MDL (from 0.15 to 0.50 Angstrom). Last, the diffraction profiles are calculated, on the basis of a probability distribution of (2 x n) cells (n = 6, 7, 1), using the phase-matrix method. The average positions of the fractional peaks are related to the concentration of each type of cell. The width and the intensity of the second order peaks, compared to those of the first order peaks, allow us to account for the aggregation tendency.