Unified computation scheme of low-energy electron diffraction—the combined-space method

A new microscopic method for the evaluation of reflected elastic intensities of low-energy electron diffraction from crystal surfaces is developed. This method divides layers of a crystal into subgroups. Layers having small interlayer separations with their neighbors form a subgroup and are solved in the $L$-space representation using iterations, matrix inversions, or a combination of both. Results of each subgroup are transformed to the $K$-space representation. Multiple scattering between subgroups and other crystal layers separated by larger interlayer spacings are solved in $K$ space. The scheme is particularly useful in analyzing surface structures where coplanar or near coplanar layers are mixed together with other layers having larger separation distances. Some examples of these are the chemisorption of hydrogen and small gas atoms on open crystal faces, the surface structures of reconstructed and unreconstructed semiconductors and layer compounds, and the reconstructed faces of some transition metals, etc.