Phenomenological analysis of heterogeneous strain fields in epitaxial thin films using x-ray scattering

A model that allows the quantitative analysis of heterogeneous strain fields in epitaxial thin films using x-ray diffraction (XRD) is presented. Particular emphasis is laid on the modelling of the two-component XRD profiles (i.e. profiles made of the superposition of a narrow coherent Bragg peak and a broad diffuse scattering profile) encountered in the XRD investigation of epitaxial thin films containing localized strain fields. The spatial properties of the strain field are included in a correlation function based on phenomenological parameters such as the defect correlation length ξ and the level of disorder σ∞. No assumption regarding the nature of the defect is hence required. The statistical properties of the strain field are described by means of Levy-stable distributions which allow us to account for profile shapes ranging between the Gaussian and profiles exhibiting pronounced power law-type tails, as well as for asymmetrical profiles. The effects of finite size of the domains (crystallites) over which diffraction is coherent are rigorously taken into account by calculating the auto-correlation function of the crystallite shape including the size distribution effects. The effects of each parameter are presented and discussed in detail and the applicability of the model is illustrated with two examples.