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Abstract
The self-assembly of matter in nano-confinements is a potential cost-effective method for fabricating ultra-dense films of ordered nanomaterials. Non-destructively probing the depth-dependent lateral order in such films challenges conventional microscopy techniques, and the submicron size of a single confinement is impractical for scattering experiments. This problem can be overcome if the confining medium is made up of an array of identical confining cells, such as a diffraction grating, because scattering then appears at Bragg peaks. The caveat is that the periodicity of the sample amplifies dynamical scattering effects that are not accounted for in approximate scattering theories and a complete dynamical theory (DT) calculation becomes unavoidable. Unlike traditional diffraction techniques that measure in reciprocal space and must resolve individual Bragg peaks, the Spin-Echo Scattering Angle Measurement (SESAME) technique overcomes this resolution problem by Fourier transforming the scattering signal and directly measuring real-space density correlations. In addition, the technique allows access to length scales of interest (few-tens-of-nanometers to several-microns). The combination of DT and SESAME has been successfully tested on periodic nanostructures and has been implemented in the study of confined matter. The dynamical theory can also be used as a reference for studying the limits of validity of approximate theories (such as DWBA and POA) on periodic systems