Direct determination of crystal and surface structures in THEED

Abstract Tensor theory of transmission high-energy electron diffraction (THEED) has been formulated based on a standard first-order perturbation theory. The theory has been applied to both a thin crystal film with perfect bulk structure and a crystal slab having its surface layer reconstructed, and has been combined with a direct scheme which reduces the complicated problem of crystal and surface structure determination to a linear least-squares problem. The crystal or surface structure can be obtained either by directly inverting and n × n matrix of the linear least-squares problem, where n is the number of parameters to be determined, or, in the case when the problem is under-determined, using a singular value decomposition method. The scheme allows the variances associated with the estimate of the unknown parameters to be readily obtained and thus assessment of the reliability of the determined parameters, and can be applied to many other cases where a perturbation treatment applies.