Basic Principles of X-Ray Diffuse Scattering from Mesoscopic Structures

Abstract

In this chapter we review the most relevant aspects of the theory of X-ray diffuse scattering from mesoscopic structures. Owing to the extensive work that has been undertaken in past years, this cannot be a thorough review but has to be incomplete to some extent. Starting from basic considerations, various theoretical approaches to X-ray scattering, including kinematical theory, dynamical theory, and the distorted-wave Born approximation, are compared. We discuss how X-ray diffuse scattering can be used to extract essential morphological properties of mesoscopic structures, such as shape, size, strain, chemical composition, and positional correlation. Special attention is directed to a novel numerical brute-force technique where elasticity theory is utilized to calculate the strain field inside mesoscopic structures. The resulting strain field is then used as input for subsequent X-ray-scattering simulations. This method allows a systematic refinement of, for example, the shape, size, or composition until satisfactory agreement with experiment is achieved. Special attention is given to the theory of diffuse scattering from surface and interface roughness, which is described in a separate chapter. In order to describe the surface or interface morphology, sophisticated height--height correlation functions can be employed and the theoretical calculations can be fitted to the corresponding experimental data. In this sense, this procedure is different from the above-mentioned approach of using a structural model in real space which is used to calculate X-ray diffuse scattering and which is -- after comparison with experiment -- sequentially refined until sufficient agreement is achieved.