Description of x-ray reflection and diffraction from periodical multilayers and superlattices by the eigenwave method

The analytical solution of recurrent equations for amplitudes of electromagnetic field is found for description of x-ray reflection and diffraction from periodical multilayered media. The method proposed uses the Bloch eigenwaves approach for periodical structure, which reduces considerably the computer time required for simulation of diffracted/reflected x-ray intensity and, therefore, accelerates the fitting trial-and-error procedure for sample model parameters. Numerical examples and fit results for experimental x-ray data are provided to demonstrate the effectiveness of method. A new parameter describing the fluctuation of superlattice period is introduced and its influence on experimental data interpretation is discussed.