Iterative solution of the inverse problem of dynamic diffraction in inhomogeneous crystals

Abstract

One of the central problems in solid-state physics is the investigation of the spatial distributions of structural characteristics of crystals using x-ray diffraction. This problem has taken on crucial significance in the last 20‐25 years in connection with the development of new semiconductor devices. Despite the large number of publications devoted to this subject ~see, for example, Refs. 1‐10!, a generally accepted, universal method for solving the inverse problem of x-ray diffraction has still not been developed. Therefore, the search continues for new avenues for progress in this area of solidstate physics. In Ref. 8 we developed a method for solving the inverse problem within the kinematic approximation. Alongside some other approaches, this method has been used to obtain the spatial structural characteristics of a thin graded singlecrystal AlGaAs film on a thick GaAs substrate. 10 However, this method is not applicable to relatively thick heteroepitaxial systems, since the kinematic ~Born! approximation is valid only for thin layers. Therefore, the purpose of the present work is to develop a more general approach to the solution of the inverse problem within an iterative procedure. 2. BASIC EQUATIONS