The Simulated Annealing Global Search Algorithm Applied to the Crystallography of Surfaces by LEED

Surface structure determination by Low Energy Electron Diffraction (LEED) is based on a comparison between experimentally measured and theoretically calculated intensity versus energy I(V) curves for the diffracted beams. The level of agreement between these, for different structural models, is quantified using a correlation function, the so-called R factor. Minimizing this factor allows one to choose the best structure for which the theoretical simulations are computed. Surface structure determination thus requires an exhaustive search of structural parameter space in order to minimize the R factor. This minimization is usually performed by the use of directed search methods, although they have serious limitations, most notably their inability to distinguish between false and real structures corresponding to local and global R factor minima. In this work we present the implementation of a global search method based on the simulated annealing algorithm, as suggested earlier by Rous, using the Van Hove and Tong standard LEED code and the results of its application to the determination of the structure of the Ag(111) and CdTe(110) surfaces. Two different R factors, RP and R1, have been employed in the structural searches, and the statistical topographies of these two factors were studied. We have also implemented a variation of the simulated annealing algorithm (Fast Simulated Annealing) and applied it to these same two systems. Some preliminary results obtained with this algorithm were used to compare its performance with the original algorithm proposed by Rous.