In grazing-incidence scattering (GISAXS), the incident beam can be strongly refracted at the film-vacuum interface, and can be reflected at the film-vacuum and/or film-substrate interfaces. This can give rise to x-ray waveguiding or x-ray standing wave effects.
Consider several cases:
- If the incident angle is below the critical angle, the beam will be totally reflected. The transmitted beam (to the extent it exists at all) is travelling in the plane of the film (specifically trapped at the film-vacuum interface). In this configuration, the incident x-rays do not penetrate into the film, except for a short-range evanescent field that bleeds into the film. The measured scattering pattern thus arises entirely from the structure at the top of the film (within a few nm of the top).
- If the incident beam is very close to the film-vacuum critical angle, it will be refracted such that it is essentially travelling within the plane of the film. Such a beam will probe an effectively larger scattering volume, which will lead to a strong increase in the intensity of scattering. For beams travelling within the film nearly parallel to the interfaces, reflection from both the top (film-vacuum) and bottom (film-substrate) interfaces will be quite large. Thus one can imagine the beam bouncing back-and-forth between these interfaces, trapped as if in a waveguide (similar to how light becomes trapped in a fiber-optic).
- If the incident angle is slightly above the critical angle, the beam will penetrate into the film (with refraction). Given how shallow the angle is, the beam will likely be completely reflected by the substrate interface. The beam will then be partially reflected at the film-vacuum interface as it exits the film. This reflected beam can again be reflected by the substrate. Given the low incidence angle, the interfaces are strongly reflective, and thus these multiple-reflected events will occur with high probability. A large fraction of the beam is thus bouncing back-and-forth between the interfaces (as if in a waveguide). The interference among these beams will give rise to a standing-wave pattern within the film, with nodes and anti-nodes at specific depths.
X-ray waveguiding can be used to exploit the overall scattering intensity. Indeed this is one way in which GISAXS generically gives rise to stronger scattering, since when the incident angle of the beam (or the exit angle of scattering) is close to the critical angle, one will see a vast increase in effective scattering volume. The standing waves can also be exploited to do depth-profiling. By selecting the appropriate incident angle (for the given thin film thickness and refractive index), one can position a node of high-intensity x-rays at a specific depth within the film, thereby preferentially probing the structure at that depth.
- Jin Wang, Michael J. Bedzyk, Thomas L. Penner & Martin Caffrey Structural studies of membranes and surface layers up to 1,000 Å thick using X-ray standing waves Nature 1991, 354, 377–380 doi:10.1038/354377a0
- Wang J, Bedzyk MJ, Caffrey M. [Resonance-Enhanced X-rays in Thin Films: A Structure Probe for Membranes and Surface Layers] Science 1992, 258(5083), 775-8. doi: 10.1126/science.1439784
- Jin Wang, Martin Caffrey, Michael J. Bedzyk, and Thomas L. Penner Direct Profiling and Reversibility of Ion Distribution at a Charged Membrane/Aqueous Interface: An X-ray Standing Wave Study Langmuir 2001, 17 (12), 3671–3681 doi: 10.1021/la001542x
- Xuesong Hu, Zhang Jiang, Suresh Narayanan, Xuesong Jiao, Alec R. Sandy, Sunil K. Sinha, Laurence B. Lurio, and Jyotsana Lal Observation of a low-viscosity interface between immiscible polymer layers Phys. Rev. E. 2006, 74, 010602(R) doi: 10.1103/PhysRevE.74.010602
- M. K. Mukhopadhyay, X. Jiao, L. B. Lurio, Z. Jiang, J. Stark, M. Sprung, S. Narayanan, A. R. Sandy, and S. K. Sinha Thickness Induced Structural Changes in Polystyrene Films Phys. Rev. Lett. 2008, 101, 115501 doi: 10.1103/PhysRevLett.101.115501
- D. R. Lee, A. Hagman, Xuefa Li, S. Narayanan, and Jin Wang Perturbation to the resonance modes by gold nanoparticles in a thin-film-based x-ray waveguide Appl. Phys. Lett. 2006, 88, 153101 doi: 10.1063/1.2191091
- Zhang Jiang, Dong Ryeol Lee, Suresh Narayanan, Jin Wang, and Sunil K. Sinha Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films Phys. Rev. B 2011, 84, 075440 doi: 10.1103/PhysRevB.84.075440
- M. A. Singh and M. N. Groves Depth profiling of polymer films with grazing-incidence small-angle X-ray scattering Acta Cryst. 2009, A65, 190-201. doi: 10.1107/S0108767309007508