Gierer, M.; Iglesias, A.; Moritz, Wolfgang
Determination of domain size distributions from LEED beam profiles: An optimization scheme based on the maximum entropy method.
In: Surface Science, Vol. 490, Nr. 1-2: S. 175-195
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An optimization scheme based on the maximum entropy method (MEM) is derived for the analysis of spot profiles which are measured using the spot profile analysis low energy electron diffraction (SPALEED) method. The profiles of the spots in the diffraction pattern contain information about the distribution of terrace lengths, step heights and island diameters in the surface region. For one-dimensionally disordered structures, the spot profiles for given domain length distributions can be calculated using the domain matrix method (DMM). It is shown that the reverse calculation, namely the direct determination of the domain size distributions from spot profile intensities, can be performed by combining the DMM with the MEM. An iteration scheme is developed which reveals smooth, positive domain length distributions directly from the experimental data. In principle, the scheme is not restricted to SPALEED but can be applied also to the analysis of profiles measured with surface X-ray diffraction or He beam diffraction. Model calculations for stepped surfaces demonstrate that it is possible to extract both step height distributions and terrace lengths from the spot profiles. The iteration scheme is applied to the analysis of the domain structure of the disordered (3×2) phase of Ge(113).