Properties of grazing-angle X-ray standing waves and their application to an arsenic-deposited Si(111) 1 × 1 surface

Grazing-angle diffraction of X-rays by crystal planes normal to a surface generates dynamical (lattice-modulated) standing waves, which are used in this paper to determine the in-plane structure of arsenic adatoms on an Si (111) surface of the 1 × 1 structure. The X-ray field, formed by the interference of the incident, specular-reflected and Bragg-diffracted beams above the surface, has two components with and without intensity modulation in the direction of the reciprocal-lattice vector parallel to the surface. The two components behave differently as a function of X-ray glancing incidence angle on the surface in the vicinity of the critical angle for total external reflection. This property has been exploited to determine the ordering of the As atoms accurately using X-ray fluorescence signals observed from a sample in ultra-high vacuum at a synchrotron source. The data show highly ordered As atoms occupying the threefold-coordinated sites on the bulk-like Si (111) surface. Displaced arsenic positions are not supported by the observation. The conclusion is fairly insensitive to the vertical height of the overlayer atoms used in the analysis, in accordance with the slow variation of the field profile along the surface normal. The grazing-angle X-ray standing-wave method allows model-independent determination of the registry of foreign atoms at a crystal surface with a positional accuracy of a few hundredths of an Å.