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Keywords:

  • grazing-incidence X-ray scattering (GIXS);
  • GIXS formulae;
  • independent scattering terms;
  • cross-scattering terms;
  • refraction effects;
  • reflection effects;
  • nanoporous dielectric thin films;
  • nanomaterials

A complete grazing-incidence X-ray scattering (GIXS) formula has been derived for nanopores buried in a polymer dielectric thin film supported by a substrate. Using the full power of the scattering formula, GIXS data from nanoporous polymethylsilsesquioxane dielectric thin films, a model nanoporous system, have successfully been analysed. The nanopores were found to be spherical and to have a certain degree of size distribution but were randomly dispersed in the film. In the film, GIXS was confirmed to arise predominantly via the first scattering process in which the incident X-ray beam scatters without reflection; the other scattering processes and their contributions were significantly dependent on the grazing angle. This study also confirmed that GIXS scattering can be analysed using only independent scattering terms, but this simple approach can only provide structural parameters. The cross terms were found to make a relatively small contribution to the intensity of the overall scattering but were required for the complete characterization of the measured two-dimensional scattering data, in particular the extracted out-of-plane scattering data, and their inclusion in the analysis enabled film properties such as film thickness, critical angle (i.e. electron density), refractive index and the absorption term to be determined.