Abstract

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

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References

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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).

1992 (2)

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992).
[CrossRef]

1991 (4)

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]

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]

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]

R. R. Freeman, R. H. Stulen, “Developing a soft x-ray projection lithography tool,” AT&T Tech. J. (November/December1991), pp. 37–48.

1988 (2)

E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
[CrossRef] [PubMed]

M. Stedman, “Limits of topographic measurements by the scanning tunneling and atomic force microscopes,” J. Microsc. 152, 611–618 (1988).
[CrossRef]

1979 (1)

Bennett, J. M.

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]

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 3.

Church, E. L.

Elson, J. M.

Fitzgerald, E. A.

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]

Freeman, R. R.

R. R. Freeman, R. H. Stulen, “Developing a soft x-ray projection lithography tool,” AT&T Tech. J. (November/December1991), pp. 37–48.

Griffith, J. E.

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]

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]

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” Appl. Phys. Rev. (to be published).

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).

Grigg, D. A.

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]

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]

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).

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” Appl. Phys. Rev. (to be published).

Hull, R.

D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992).
[CrossRef]

Jacobs, J.

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]

Jankowski, T.

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]

Kariotis, R.

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]

Kleiner, J.

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]

Kochanski, G. P.

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).

Kortright, J. B.

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.

Lagally, M. G.

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]

Lucas, C. A.

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.

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 3.

Miller, G. L.

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]

Nguyen, T. D.

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.

Phang, Y.-H.

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]

Russell, P. E.

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]

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).

Savage, D. E.

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]

Schimke, N.

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]

Stearns, D. G.

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

D. G. Stearns, “A stochastic model for thin film growth and erosion,” J. Appl. Phys. (to be published).

Stedman, M.

M. Stedman, “Limits of topographic measurements by the scanning tunneling and atomic force microscopes,” J. Microsc. 152, 611–618 (1988).
[CrossRef]

Stulen, R. H.

R. R. Freeman, R. H. Stulen, “Developing a soft x-ray projection lithography tool,” AT&T Tech. J. (November/December1991), pp. 37–48.

Tidswell, I. M.

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.

Vasile, M. J.

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]

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).

Wagner, E. R.

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]

Waskiewicz, W. K.

D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992).
[CrossRef]

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).

Windt, D. L.

D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992).
[CrossRef]

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).

Appl. Opt. (1)

AT&T Tech. J. (1)

R. R. Freeman, R. H. Stulen, “Developing a soft x-ray projection lithography tool,” AT&T Tech. J. (November/December1991), pp. 37–48.

J. Appl. Phys. (2)

D. G. Stearns, “X-ray scattering from interfacial roughness in multilayer structures,” J. Appl. Phys. 71, 4286–4298 (1992).
[CrossRef]

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]

J. Appl. Phys. (1)

D. L. Windt, R. Hull, W. K. Waskiewicz, “Interface imperfections in metal/Si multilayers,” J. Appl. Phys. 71, 2675–2678 (1992).
[CrossRef]

J. Microsc. (1)

M. Stedman, “Limits of topographic measurements by the scanning tunneling and atomic force microscopes,” J. Microsc. 152, 611–618 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

Rev. Sci. Instrum. (1)

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]

Rev. Sci. Instrum. (1)

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]

Other (8)

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).

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).

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.

D. G. Stearns, “A stochastic model for thin film growth and erosion,” J. Appl. Phys. (to be published).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 3.

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.

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.

J. E. Griffith, D. A. Grigg, “Dimensional metrology with scanning probe microscopes,” Appl. Phys. Rev. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Normal-incidence reflectance scans of three multilayer x-ray mirrors. All samples were coated during the same deposition run with 40 bilayers of Mo/Si, so any differences in the reflectance curves are presumed to be due to differences in the surface finish of the substrates.

Fig. 2
Fig. 2

Surface–height data for the three samples shown in Fig. 1. Top row, sample A; middle row, sample B; bottom row, sample C; left column, WYKO TOPO-3D, 20× magnification; middle column, WYKO TOPO-3D, 40× magnification; right column, AFM, 1-μm scan length. Note that the vertical scales are the same in all cases to emphasize intrinsic differences in the samples over different spatial frequency bandwidths.

Fig. 3
Fig. 3

PSD functions for samples A, B, and C shown in Fig. 1.

Fig. 4
Fig. 4

PSD functions for two portions of a single substrate; one portion was coated with a Mo/Si multilayer.

Fig. 5
Fig. 5

Nonspecular scattering data for samples A, B, and C shown in Fig. 1. The quasi-Bragg diffraction peaks are the result of resonant scattering that is due to partially correlated interfacial roughness in the multilayer stack.

Tables (1)

Tables Icon

Table 1 RMS Surface Roughness and Peak Reflectance Computed from PSD Data

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

S ( f x ) = lim L 2 L | L / 2 + L / 2 d x Z ( x ) exp ( i 2 π f x x ) | 2
σ 2 = 0 d f x S ( f x ) ,
l = 1 2 σ 4 0 d f x S 2 ( f x ) .
S ( f x ) = K n / f x n .
d P ( θ , ϕ ) / d Ω = ( 16 π 2 / λ 4 ) C ( θ , ϕ ) S ( f ) ,

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