Correlation of electron self-energy with geometric structure in low-energy electron diffraction

In low-energy electron diffraction (LEED) studies of surface geometries where the energy dependence of the intensities is analyzed, the in-plane lattice parameter of the surface is usually set to a value determined by x-ray diffraction for the bulk crystal. In cases where it is not known, for instance in films that are incommensurate with the substrate, it is desirable to fit the in-plane lattice parameters in the same analysis as the perpendicular interlayer spacings. We show that this is not possible in a conventional LEED I(E) analysis because the inner potential, which is typically treated as an adjustable parameter, is correlated with the geometrical structure. Therefore, without having prior knowledge of the inner potential, it is not possible to determine the complete surface structure simply from LEED I(E) spectra, and the in-plane lattice parameter must be determined independently before the I(E) analysis is performed. This can be accomplished by establishing a more precise experimental geometry. Further, it is shown that the convention of omitting the energy dependency of the real part of the inner potential means geometrical LEED results cannot be trusted beyond a precision of approximately 0.01 Å.