Abstract: Transform-deconvolution analysis of LEED: The structures of some clean metal surfaces
Authors: Adams David L. , Landman Uzi 
Published: July 2002

In recent papers1–5 we have described a direct approach to surface structure determination from analysis of low-energy electron diffraction (LEED). The method is based on Fourier transformation of experimental LEED intensities followed by deconvolution of structural and nonstructural features of the transform. Within a single scattering approximation we have shown that the Fourier transform consists of a convolution product of a periodic set(s) of delta functions (related to the surface structure) with the Fourier transform(s) of the truncated scattering factor(s).1,2 Application of the analysis to experimental data for Al(100), which contains extra features attributable to multiple scattering processes, led to the conclusion that the effect of multiple scattering was to introduce ’’noise’’ into the deconvolution result without seriously influencing the structural content (’’signal’’).2–4 This conclusion was supported by the result of analytical Fourier transformation of an expression for dynamic LEED intensities.5
The new results6,7 reported in this paper are concerned with the development of an improved procedure for analysis of experimental data exhibiting strong multiple scattering features and the application of the procedure to the investigation of the surface-interlayer spacing for Al(100), Ni(100), Cu(100),6 and Al(111).7
The basic difficulty in the application of the transform deconvolution method to experimental data analysis is that, in general, a unique solution to the deconvolution problem cannot be achieved. This difficulty is exacerbated by the occurrence of multiple scattering which effectively alters the single scattering factors used in the deconvolution. It will be demonstrated, however, that the deconvolution algorithm can be constrained to produce physically reasonable solutions.6,7
The hypothesis is made, to be substantiated by analysis of experimental data, that the best approximation to the correct surface structure corresponds to the deconvolution with maximum signal-to-noise. Accordingly, the algorithm involves an optimization procedure to determine the best values of two adjustable parameters, namely, the inner potential V0 and the effective surface Debye temperature ϑD yielding maximum signal-to-noise.
The output of the procedure, in addition to V0 and ϑD, is the interlayer spacing d and an estimate of the layer attenuation exponent μ. Comparison of the output, optimum values of V0, ϑD, and μ, with values expected from other considerations, including the results of model calculations for the systems in question, provides additional grounds for confidence in the determined structural parameter d. The results of application of the procedure described above to experimental LEED data for Al(100), Al(111), Ni(100), and Cu(100) will be presented.6,7 For the (100) surfaces, analysis of specular beam intensity spectra for a number of incidence and azimuthal angles indicates that the surface-interlayer spacing is equal to the corresponding bulk spacing to within ±1%. For Al(111) a contraction of the surface-interlayer spacing of ∠3% is indicated.7