Abstract

Thin-film interference effects were observed in the normal-incidence efficiency of a 2400-groove/mm replica grating. The efficiency was measured in the 100–350-Å wavelength range and had an oscillatory behavior that resulted from the presence of a thin SiO2 coating. The thicknesses of the SiO2 and the underlying oxidized aluminum layers were inferred from computer modeling of the zero-order efficiency. The efficiencies in the diffracted orders were calculated with the modified integral approach and accounting for the multilayer coating and the groove profile derived from atomic force microscopy. The calculated and measured efficiencies were in good agreement.

© 1999 Optical Society of America

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References

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  1. J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
    [CrossRef]
  2. M. Nevière, “Multilayer-coated gratings for x-ray diffraction: differential theory,” J. Opt. Soc. Am. A 8, 1468–1473 (1991).
    [CrossRef]
  3. M. Nevière, “Bragg–Fresnel multilayer gratings: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1835–1845 (1994).
    [CrossRef]
  4. L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
    [CrossRef]
  5. L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2515, 240–245 (1995).
    [CrossRef]
  6. M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
    [CrossRef]
  7. J. C. Rife, H. R. Sadeghi, W. R. Hunter, “Upgrades and recent performance of the grating/crystal monochromator,” Rev. Sci. Instrum. 60, 2064–2067 (1989).
    [CrossRef]
  8. W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods A 246, 465–468 (1986).
    [CrossRef]
  9. B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
    [CrossRef]
  10. D. Maystre, “A new general integral theory for dielectric coated gratings,” J. Opt. Soc. Am. 68, 490–495 (1978).
    [CrossRef]
  11. J. F. Seely, M. P. Kowalski, W. R. Hunter, J. C. Rife, T. W. Barbee, G. E. Holland, C. N. Boyer, C. M. Brown, “On-blaze operation of a Mo/Si multilayer-coated, concave diffraction grating in the 136–142-Å wavelength region and near normal incidence,” Appl. Opt. 32, 4890–4897 (1993).
    [CrossRef] [PubMed]

1997 (2)

1994 (1)

1993 (2)

J. F. Seely, M. P. Kowalski, W. R. Hunter, J. C. Rife, T. W. Barbee, G. E. Holland, C. N. Boyer, C. M. Brown, “On-blaze operation of a Mo/Si multilayer-coated, concave diffraction grating in the 136–142-Å wavelength region and near normal incidence,” Appl. Opt. 32, 4890–4897 (1993).
[CrossRef] [PubMed]

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
[CrossRef]

1991 (1)

1989 (1)

J. C. Rife, H. R. Sadeghi, W. R. Hunter, “Upgrades and recent performance of the grating/crystal monochromator,” Rev. Sci. Instrum. 60, 2064–2067 (1989).
[CrossRef]

1986 (1)

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods A 246, 465–468 (1986).
[CrossRef]

1978 (1)

Barbee, T. W.

Boyer, C. N.

Brown, C. M.

Chernov, B. C.

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2515, 240–245 (1995).
[CrossRef]

Cruddace, R. G.

Davis, J. C.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
[CrossRef]

Goray, L. I.

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
[CrossRef]

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2515, 240–245 (1995).
[CrossRef]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
[CrossRef]

Heidemann, K. F.

Heinzmann, U.

Henke, B. L.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
[CrossRef]

Holland, G. E.

Hunter, W. R.

Kleineberg, U.

Kowalski, M. P.

Maystre, D.

Menke, D.

Nevière, M.

Osterried, K.

Rife, J. C.

Sadeghi, H. R.

J. C. Rife, H. R. Sadeghi, W. R. Hunter, “Upgrades and recent performance of the grating/crystal monochromator,” Rev. Sci. Instrum. 60, 2064–2067 (1989).
[CrossRef]

Seely, J. F.

Appl. Opt. (3)

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993). Updated optical constants were obtained from the internet site cindy.lbl.gov/optical_constants .
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nucl. Instrum. Methods A (1)

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods A 246, 465–468 (1986).
[CrossRef]

Rev. Sci. Instrum. (1)

J. C. Rife, H. R. Sadeghi, W. R. Hunter, “Upgrades and recent performance of the grating/crystal monochromator,” Rev. Sci. Instrum. 60, 2064–2067 (1989).
[CrossRef]

Other (2)

L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
[CrossRef]

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2515, 240–245 (1995).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

AFM image of the surface topology reference sample. The image size is 4 µm. The scan positions across the edges of the hole are indicated.

Fig. 2
Fig. 2

(a)–(d) AFM scan data across the edges of a hole on the surface topology reference sample. (e)–(h) The LSF’s.

Fig. 3
Fig. 3

PSD of the surface topology reference sample derived from AFM images of sizes (a) 20 µm and (b) 4 µm.

Fig. 4
Fig. 4

AFM image of two grooves across the 2400-groove/mm replica grating. The image size is 1 µm by 1 µm. The horizontal and vertical scales are indicated.

Fig. 5
Fig. 5

PSD of the 2400-groove/mm replica grating derived from an AFM image of size 2 µm.

Fig. 6
Fig. 6

Typical groove profile derived from the AFM image of the 2400-groove/mm replica grating. The average peak-to-valley groove depth is 85 Å. The blaze angles, measured from the horizontal, of the left and right facets are 3.4° and 6.2°, respectively.

Fig. 7
Fig. 7

Measured grating efficiency, as a function of the diffraction angle, for a wavelength of 187.9 Å and an angle of incidence of 15.2°. The inside (m > 0) and outside (m < 0) diffraction orders are indicated.

Fig. 8
Fig. 8

Fit of Gaussian profiles (smooth curves) to the measured grating efficiencies (data points). The wavelength of the incident radiation was 187.9 Å and the angle of incidence was 15.2°.

Fig. 9
Fig. 9

(a) Measured grating efficiency in the zero order at an angle of incidence of 15.2°. (b) The reflectance of 743 Å of SiO2 and 30 Å of Al2O3 on opaque aluminum calculated at an angle of incidence of 15.2°.

Fig. 10
Fig. 10

Calculated reflectance of a layer of SiO2 of variable thickness and a 30-Å layer of Al2O3 on opaque aluminum for the three wavelengths: (a) 217.0 Å, (b) 169.0 Å, and (c) 127.5 Å. The vertical dashed line indicates the only SiO2 thickness (743 Å) at which the maxima of the three reflectance curves coincide.

Fig. 11
Fig. 11

Comparison of the measured grating efficiency (data points) and the calculated efficiency (curves without data points) for the diffraction orders (a) +1, (b) +2, (c) -1, (d) -2, (e) 0, and (f) sum of all orders.

Fig. 12
Fig. 12

(a) Measured and (b) calculated grating efficiencies in the indicated orders.

Fig. 13
Fig. 13

Efficiency in the +1 order calculated for assumed groove depths of 75, 85, and 95 Å. The measured +1 order efficiency is shown by the data points.

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