Difference between revisions of "X-ray waveguiding"

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(Created page with "==References== * Jin Wang, Michael J. Bedzyk, Thomas L. Penner & Martin Caffrey [https://www.nature.com/articles/354377a0 Structural studies of membranes and surface layers up...")
 
 
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In grazing-incidence scattering ([[GISAXS]]), the incident beam can be strongly [[refraction|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.
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Consider several cases:
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# 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).
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# 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).
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# 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.
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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.
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==References==
 
==References==
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===Initial===
 
* Jin Wang, Michael J. Bedzyk, Thomas L. Penner & Martin Caffrey [https://www.nature.com/articles/354377a0 Structural studies of membranes and surface layers up to 1,000 Å thick using X-ray standing waves] ''Nature'' '''1991''', 354, 377–380 [http://dx.doi.org/10.1038/354377a0 doi:10.1038/354377a0]
 
* Jin Wang, Michael J. Bedzyk, Thomas L. Penner & Martin Caffrey [https://www.nature.com/articles/354377a0 Structural studies of membranes and surface layers up to 1,000 Å thick using X-ray standing waves] ''Nature'' '''1991''', 354, 377–380 [http://dx.doi.org/10.1038/354377a0 doi:10.1038/354377a0]
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* 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. [http://dx.doi.org/10.1126/science.1439784  doi: 10.1126/science.1439784]
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* Jin Wang, Martin Caffrey, Michael J. Bedzyk, and Thomas L. Penner [https://pubs.acs.org/doi/abs/10.1021/la001542x 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 [http://dx.doi.org/10.1021/la001542x doi: 10.1021/la001542x]
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===Main===
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* Xuesong Hu, Zhang Jiang, Suresh Narayanan, Xuesong Jiao, Alec R. Sandy, Sunil K. Sinha, Laurence B. Lurio, and Jyotsana Lal [https://journals.aps.org/pre/abstract/10.1103/PhysRevE.74.010602 Observation of a low-viscosity interface between immiscible polymer layers] ''Phys. Rev. E.'' '''2006''', 74, 010602(R) [http://dx.doi.org/10.1103/PhysRevE.74.010602 doi: 10.1103/PhysRevE.74.010602]
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* M. K. Mukhopadhyay, X. Jiao, L. B. Lurio, Z. Jiang, J. Stark, M. Sprung, S. Narayanan, A. R. Sandy, and S. K. Sinha [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.115501 Thickness Induced Structural Changes in Polystyrene Films] ''Phys. Rev. Lett.'' '''2008''', 101, 115501 [https://doi.org/10.1103/PhysRevLett.101.115501 doi: 10.1103/PhysRevLett.101.115501]
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* D. R. Lee, A. Hagman, Xuefa Li, S. Narayanan, and Jin Wang [http://aip.scitation.org/doi/abs/10.1063/1.2191091 Perturbation to the resonance modes by gold nanoparticles in a thin-film-based x-ray waveguide] ''Appl. Phys. Lett.'' '''2006''', 88, 153101 [https://doi.org/10.1063/1.2191091 doi: 10.1063/1.2191091]
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* Zhang Jiang, Dong Ryeol Lee, Suresh Narayanan, Jin Wang, and Sunil K. Sinha [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.84.075440 Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films] ''Phys. Rev. B'' '''2011''', 84, 075440 [https://doi.org/10.1103/PhysRevB.84.075440 doi: 10.1103/PhysRevB.84.075440]
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===Depth Profiling===
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* M. A. Singh and M. N. Groves  [http://scripts.iucr.org/cgi-bin/paper?S0108767309007508 Depth profiling of polymer films with grazing-incidence small-angle X-ray scattering] ''Acta Cryst.'' '''2009''', A65, 190-201. [https://doi.org/10.1107/S0108767309007508 doi: 10.1107/S0108767309007508]
  
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* D. R. Lee, A. Hagman, Xuefa Li, S. Narayanan, and Jin Wang [http://aip.scitation.org/doi/abs/10.1063/1.2191091 Perturbation to the resonance modes by gold nanoparticles in a thin-film-based x-ray waveguide] ''Appl. Phys. Lett.'' '''2006''', 88, 153101 [https://doi.org/10.1063/1.2191091 doi: 10.1063/1.2191091]
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==See Also==
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* [[Refraction]]
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* [[DWBA]]

Latest revision as of 10:53, 6 March 2018

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:

  1. 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).
  2. 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).
  3. 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.


References

Initial

Main

Depth Profiling

See Also

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