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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 11 — Jun. 3, 2013
  • pp: 13105–13117

Extended theory of soft x-ray reflection for realistic lamellar multilayer gratings

R. van der Meer, I.V. Kozhevnikov, H.M.J. Bastiaens, K.-J. Boller, and F. Bijkerk  »View Author Affiliations


Optics Express, Vol. 21, Issue 11, pp. 13105-13117 (2013)
http://dx.doi.org/10.1364/OE.21.013105


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Abstract

An extended set of coupled wave equations were derived to describe non-idealized lamellar multilayer grating structures with properties as obtained with state-of-the-art fabrication techniques. These generalized equations can include all relevant effects describing the influence of passivation and contamination layers, non-rectangular lamel profiles and sidewall scalloping. The calculations showed that passivation and contamination plays an important role in that it may significantly reduce peak reflectivity. However, we also derived a condition for layer thicknesses having negligible effects. Slightly positive tapered lamel profiles are shown to further reduce the bandwidth as compared to a rectangular lamel profile, whereas negative tapers significantly increased the bandwidth. The influence of intriguing effects, such as the sidewall scalloping caused by Bosch Deep Reactive Ion Etching, are also modeled. We identified the signature of such scalloping as additional side peaks in the reflectivity spectrum and present parameters with which these can be effectively suppressed.

© 2013 OSA

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(230.1480) Optical devices : Bragg reflectors
(230.4170) Optical devices : Multilayers
(340.0340) X-ray optics : X-ray optics
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

ToC Category:
X-ray Optics

History
Original Manuscript: April 19, 2013
Revised Manuscript: May 11, 2013
Manuscript Accepted: May 11, 2013
Published: May 21, 2013

Citation
R. van der Meer, I.V. Kozhevnikov, H.M.J. Bastiaens, K.-J. Boller, and F. Bijkerk, "Extended theory of soft x-ray reflection for realistic lamellar multilayer gratings," Opt. Express 21, 13105-13117 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-11-13105


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References

  1. I. V. Kozhevnikov, R. van der Meer, H. M. J. Bastiaens, K.-J. Boller, and F. Bijkerk, “High-resolution, high-reflectivity operation of lamellar multilayer amplitude gratings: identification of the single-order regime,” Opt. Exp.18, 16234–16242 (2010). [CrossRef]
  2. I. V. Kozhevnikov, R. van der Meer, H. M. J. Bastiaens, K.-J. Boller, and F. Bijkerk, “Analytic theory of soft x-ray diffraction by lamellar multilayer gratings,” Opt. Exp.19, 9172–9184 (2011). [CrossRef]
  3. A. Sammar, J.-M. André, and B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the x-uv region,” Opt. Comm.86, 245–254 (1991). [CrossRef]
  4. A. I. Erko, B. Vidal, P. Vincent, Y. A. Agafonov, V. V. Martynov, D. V. Roschupkin, and M. Brunel, “Multilayer gratings efficiency: numerical and physical experiments,” Nucl. Instr. Meth. Phys. Res. A333, 599–606 (1993). [CrossRef]
  5. R. Benbalagh, “Monochromateurs multicouches à bande passante étroite et à faible fond continu pour le rayonnement X-UV,” Ph.D. thesis, Universite Pierre et Marie Curie (2003).
  6. P. Jonnard, K. Le Guen, J.-M. André, J. R. Coudevylle, and N. Isac, “An etched multilayer as a dispersive element in a curved--crystal spectrometer: implementation and performance,” J. X-ray Spect. 44, 308–312 (2012). [CrossRef]
  7. R. van der Meer, B. Krishnan, I. V. Kozhevnikov, M. J. de Boer, B. Vratzov, H. M. J. Bastiaens, J. Huskens, W. G. van der Wiel, P. E. Hegeman, G. C. S. Brons, K.-J. Boller, and F. Bijkerk, “Improved resolution for soft-x-ray monochromatization using lamellar multilayer gratings,” Proc. of SPIE8139, 81390Q–8 (2011). [CrossRef]
  8. R. van der Meer, B. Krishnan, M. J. de Boer, and F. Bijkerk, are preparing a manuscript to be called “Improved etch anisotropy using thin-layer mixed-material.”
  9. H. V. Jansen, M. J. de Boer, S. Unnikrishnan, M. C. Louwerse, and M. C. Elwenspoek, “Black silicon method x: a review on high speed and selective plasma etching of silicon with profile control: an in-depth comparison between bosch and cryostat drie processes as a roadmap to next generation equipment,” J. Micromech. Microeng. 19, 033001 (2009). [CrossRef]
  10. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray database of x-ray interactions with matter,” http://henke.lbl.gov/optical_constants/
  11. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, z=1-92,” At. Data Nucl. Data Tables54, 181 – 342 (1993). [CrossRef]
  12. R. van der Meer, I. Kozhevnikov, B. Krishnan, J. Huskens, P. Hegeman, C. Brons, B. Vratzov, B. Bastiaens, K. Boller, and F. Bijkerk, “Single-order operation of lamellar multilayer gratings in the soft x-ray spectral range,” AIP Advances3, 012103 (2013). [CrossRef]
  13. I. V. Kozhevnikov and A. V. Vinogradov, “Basic formulae of xuv multilayer optics,” Phys. Scripta Vol. T17, 137–145 (1987). [CrossRef]
  14. L. L. Balakireva and I. V. Kozhevnikov, “Two-period multilayer mirrors for the soft x-ray region,” Proc. of SPIE2453, 67–79 (1995). [CrossRef]
  15. I. V. Kozhevnikov, S. Yulin, T. Feigl, and N. Kaiser, “Effect of anomalous transmittance in EUV multilayer optics,” Opt. Commun.2813025–3031 (2008). [CrossRef]

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