Method for the rapid simulation and adaptation of the x-ray spectra of superlattices

摘要

A method of simulation and/or fitting of X-ray scattering patterns comprising X-ray reflection and X-ray diffraction from multilayers with N repeating basic periods of a superlattice comprising a number L of single layers within each basic period, on a substrate, comprises the following steps:a) introducing the scattering matrix (SM) of one basic period of the superlattice, wherein the scattering matrix consists of the product of the scattering matrices of the single layers within the basic period;b) construction of superlattice eigenwaves using diagonalisation of the scattering matrix;c) using the superlattice eigenwaves to obtain an analytical representation of the wavefield and a solution of the boundary problem for the finite number N of basic periods of the superlattice;d) calculation of the intensity distribution of the scattering patterns by an analytical formula based on step c).;This allows the calculation of an X-ray scattering pattern of a periodically multilayered film sample on a substrate which is fast and simple to carry out.