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Applied Optics

Applied Optics


  • Vol. 33, Iss. 10 — Apr. 1, 1994
  • pp: 2025–2031

Surface finish requirements for soft x-ray mirrors

D. L. Windt, W. K. Waskiewicz, and J. E. Griffith  »View Author Affiliations

Applied Optics, Vol. 33, Issue 10, pp. 2025-2031 (1994)

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We have examined the correlations between direct surface-finish metrology techniques and normal-incidence, soft x-ray reflectance measurements of highly polished x-ray multilayer mirrors. We find that, to maintain high reflectance, the rms surface roughness of these mirrors must be less than ~1 Å over the range of spatial frequencies extending approximately from 1 to 100 μm−1 (i.e., spatial wavelengths from 1 μm to 10 nm). This range of spatial frequencies is accessible directly only through scanning-probe metrology. Because the surface-finish Fourier spectrum of such highly polished mirrors is described approximately by an inverse power law (unlike a conventional surface), bandwidth-limited rms roughness values measured with instruments that are sensitive to only lower spatial frequencies (i.e., optical or stylus profileres) are generally uncorrelated with the soft x-ray reflectance and can lead to erroneous conclusions regarding the expected performance of substrates for x-ray mirrors.

© 1994 Optical Society of America

Original Manuscript: April 14, 1993
Revised Manuscript: August 27, 1993
Published: April 1, 1994

D. L. Windt, W. K. Waskiewicz, and J. E. Griffith, "Surface finish requirements for soft x-ray mirrors," Appl. Opt. 33, 2025-2031 (1994)

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  1. R. R. Freeman, R. H. Stulen, “Developing a soft x-ray projection lithography tool,” AT&T Tech. J. (November/December1991), pp. 37–48.
  2. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988). [CrossRef] [PubMed]
  3. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 3.
  4. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979). [CrossRef]
  5. D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992). [CrossRef]
  6. D. E. Savage, J. Kleiner, N. Schimke, Y.-H. Phang, T. Jankowski, J. Jacobs, R. Kariotis, M. G. Lagally, “Determination of roughness correlations in multilayer films for x-ray mirrors,” J. Appl. Phys. 69, 1411–1424 (1991). [CrossRef]
  7. J. B. Kortright, T. D. Nguyen, I. M. Tidswell, C. A. Lucas, “Substrate effects on x-ray specular reflectance and nonspecular scattering from x-ray multilayers,” in Physics of X-Ray Multilayer Structures, Vol. 7 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 102–104.
  8. One is generally interested in controlling the surface of an x-ray mirror over all spatial frequencies. Low-frequency figure errors give rise to reduced image resolution, whereas high-frequency finish errors result in scattering and hence reduced reflectance. Because this work is confined to the effect of surface finish on reflectance, and because there is no universally accepted definition for the spatial frequency that separates surface figure from surface finish, here we take the pragmatic approach of defining that spatial frequency cutoff in terms of the available metrology tool, the soft x-ray reflectometer, as it is this tool that is used to measure reflectance. However, it should be noted that this cutoff is somewhat artificial, as it specifically depends on the detector collection angle used in the measurement, which is arbitrary. That is, although a detector collection angle of a few degrees is typical, small variations in this angle from instrument to instrument will result in correspondingly small variations in the long-wavelength spatial wavelength cutoff.
  9. J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” Appl. Phys. Rev. (to be published).
  10. D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992). [CrossRef]
  11. G. L. Miller, J. E. Griffith, E. R. Wagner, D. A. Grigg, “A rocking beam electrostatic balance for the measurement of small forces,” Rev. Sci. Instrum. 62, 705–709 (1991). [CrossRef]
  12. M. J. Vasile, D. A. Grigg, J. E. Griffith, E. A. Fitzgerald, P. E. Russell, “Scanning probe tips formed by focussed ion beams,” Rev. Sci. Instrum. 62, 2167–2171 (1991). [CrossRef]
  13. M. Stedman, “Limits of topographic measurements by the scanning tunneling and atomic force microscopes,” J. Microsc. 152, 611–618 (1988). [CrossRef]
  14. D. A. Grigg, J. E. Griffith, G. P. Kochanski, M. J. Vasile, P. E. Russell, “Scanning probe metrology,” in Integrated Circuit Metrology, Inspection, and Process Control VI, M. T. Postek, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1673, 557–567 (1992).
  15. D. L. Windt, W. K. Waskiewicz, “Soft x-ray reflectometry of multilayer coatings using a laser-plasma source,” Multilayer Optics for Advanced X-Ray Applications, N. M. Ceglio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1547, 144–158 (1991).
  16. Over spatial frequency regions for which the value of the PSD function (and hence the rms surface roughness) is relatively small, the intrinsic finish of the surface is masked by measurement errors, because of poor signal-to-noise ratio. The visibility of such measurement artifacts is enhanced in frequency space by the logarithmic scale, as shown in Fig. 3. Although these artifacts can be significant, in this case they are much smaller, in fact, than the inherent differences between the three samples discussed in the text.
  17. D. G. Stearns, “A stochastic model for thin film growth and erosion,” J. Appl. Phys. (to be published).

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