Theory of X-ray diffraction in solid state superlattices

The problem of Bragg's X-ray diffraction (XRD) in one-dimensional superlattices (SL) has been studied in detail. A comprehensive review of the publications devoted to this problem is given. A solution of the XRD problem for doped and composite SL with a random modulation law has been obtained in the general form within the kinematic approximation. The effect of the type of a modulating function upon the diffraction spectrum is discussed. In order to solve the problem of the dynamic XRD, we have introduced the concept of the eigen-solutions of the Takagi equations. This has enabled us to use effectively, when studying the problem at hand, the methods of perturbation theory and of slowly varyng amplitudes and to give a thorough analysis of the approximate solutions obtained. Based on the recurrent relations of a new type, the general solution of the problem of XRD in SL is obtained and discussed in various approximations. The exact solution is given for the model of the dynamic XRD in SL with the rectangular modulation. The relation is established between the results obtained with the help of the above methods and those obtained by other authors. The absorption effect is briefly discussed.