Abstract

The first experimental results to our knowledge on the refractive index ñ = 1 - δ + iβ of yttrium in the extreme-ultraviolet and soft x-ray energy ranges are discussed. To determine the absorptive part β, transmittance measurements were performed on pure yttrium films in the 50–1300-eV energy region at beamline 6.3.2 of the Advanced Light Source. The dispersive part δ was then calculated from the absorption results by means of the Kramers-Kronig transformation. Compared with prior tabulated values, the new set of data for the refractive index of yttrium is in better agreement with the sum rules and contains previously unresolved fine structure information in the regions of the M 2,3 and M 4,5 absorption edges, where yttrium-based multilayer mirrors operate.

© 2002 Optical Society of America

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References

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  1. Information about the Extreme Ultraviolet Explorer mission and the observed spectral lines can be obtained at http://ssl.berkeley.edu/euve .
  2. The experimental Multilayer Survey is available at http://www.cxro.lbl.gov/multilayer/survey.html .
  3. B. Sae-Lao, C. Montcalm, “Molybdenum-strontium multilayer mirrors for the 8–12-nm extreme ultraviolet wavelength region,” Opt. Lett. 26, 468–470 (2001).
    [CrossRef]
  4. B. Sae-Lao, C. Montcalm, “Normal-incidence multilayer mirrors for the 8–12 nm wavelength region,” Advanced Light Source Compendium of User Abstracts1999; available at http://alspubs.lbl.gov/compendium/ .
  5. B. Sae-Lao, S. Bajt, C. Montcalm, J. F. Seely, “Performance of normal-incidence molybdenum-yttrium multilayer-coated grating at a wavelength of 9 nm,” Appl. Opt. 41, 2394–2400 (2002).
    [CrossRef] [PubMed]
  6. 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); an updated version of these data is available at http://www-cxro.lbl.gov .
    [CrossRef]
  7. J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), Chap. 4.
  8. The imd program by D. L. Windt is available at http://www.cletus.phys.columbia.edu/∼windt/imd/ .
  9. H. J. Hagemann, W. Gudat, C. Kunz, “Optical constants from the far infrared to the X-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and A12O3,” J. Opt. Soc. Am. 65, 742–744 (1975).
    [CrossRef]
  10. E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
    [CrossRef]
  11. R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
    [CrossRef]
  12. D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B. 17, 4689–4694 (1978).
    [CrossRef]
  13. D. Y. Smith, “X-ray optical properties: a review of the constraints and the data base,” in X-ray and VUV Interaction Data Bases, Calculations, and Measurements, N. K. Del Grande, P. Lee, J. A. Samson, D. Y. Smith, eds., Proc. SPIE911, 86–99 (1988).
  14. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Readrog, Mass., 1989), Chap. 4.
  15. M. T. Wilson, technical paper available at http://www.puretechinc.com/tech_papers/tech_papers.htm .
  16. F. R. Powell, T. A. Johnson, “Filter windows for EUV lithography,” in Emerging Lithographic TechnologiesV. E. A. Dobisz, eds., Proc. SPIE4343, 585–589 (2001).
  17. J. H. Underwood, E. M. Gullikson, “High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50–1300 eV energy region,” J. Electron Spectrosc. Relat. Phenom. 92, 265–272 (1998).
    [CrossRef]
  18. E. M. Gullikson, S. Mrowka, B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” in Emerging Lithographic Technologies V, E. A. Dobisz, ed., Proc. SPIE4343, 363–373 (2001).
  19. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

2002 (1)

2001 (1)

1998 (2)

J. H. Underwood, E. M. Gullikson, “High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50–1300 eV energy region,” J. Electron Spectrosc. Relat. Phenom. 92, 265–272 (1998).
[CrossRef]

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
[CrossRef]

1994 (1)

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

1993 (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); an updated version of these data is available at http://www-cxro.lbl.gov .
[CrossRef]

1978 (1)

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B. 17, 4689–4694 (1978).
[CrossRef]

1975 (1)

Bajt, S.

Berkowitz, J.

J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), Chap. 4.

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); an updated version of these data is available at http://www-cxro.lbl.gov .
[CrossRef]

Denham, P.

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Gudat, W.

Gullikson, E. M.

J. H. Underwood, E. M. Gullikson, “High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50–1300 eV energy region,” J. Electron Spectrosc. Relat. Phenom. 92, 265–272 (1998).
[CrossRef]

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
[CrossRef]

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

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); an updated version of these data is available at http://www-cxro.lbl.gov .
[CrossRef]

E. M. Gullikson, S. Mrowka, B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” in Emerging Lithographic Technologies V, E. A. Dobisz, ed., Proc. SPIE4343, 363–373 (2001).

Hagemann, H. J.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Readrog, Mass., 1989), Chap. 4.

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); an updated version of these data is available at http://www-cxro.lbl.gov .
[CrossRef]

Johnson, T. A.

F. R. Powell, T. A. Johnson, “Filter windows for EUV lithography,” in Emerging Lithographic TechnologiesV. E. A. Dobisz, eds., Proc. SPIE4343, 585–589 (2001).

Kaufmann, B. B.

E. M. Gullikson, S. Mrowka, B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” in Emerging Lithographic Technologies V, E. A. Dobisz, ed., Proc. SPIE4343, 363–373 (2001).

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

Kunz, C.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

Montcalm, C.

Mrowka, S.

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

E. M. Gullikson, S. Mrowka, B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” in Emerging Lithographic Technologies V, E. A. Dobisz, ed., Proc. SPIE4343, 363–373 (2001).

Powell, F. R.

F. R. Powell, T. A. Johnson, “Filter windows for EUV lithography,” in Emerging Lithographic TechnologiesV. E. A. Dobisz, eds., Proc. SPIE4343, 585–589 (2001).

Sae-Lao, B.

Seely, J. F.

Shiles, E.

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B. 17, 4689–4694 (1978).
[CrossRef]

Smith, D. Y.

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B. 17, 4689–4694 (1978).
[CrossRef]

D. Y. Smith, “X-ray optical properties: a review of the constraints and the data base,” in X-ray and VUV Interaction Data Bases, Calculations, and Measurements, N. K. Del Grande, P. Lee, J. A. Samson, D. Y. Smith, eds., Proc. SPIE911, 86–99 (1988).

Soufli, R.

Underwood, J. H.

J. H. Underwood, E. M. Gullikson, “High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50–1300 eV energy region,” J. Electron Spectrosc. Relat. Phenom. 92, 265–272 (1998).
[CrossRef]

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

Appl. Opt. (2)

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); an updated version of these data is available at http://www-cxro.lbl.gov .
[CrossRef]

J. Electron Spectrosc. Relat. Phenom. (1)

J. H. Underwood, E. M. Gullikson, “High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50–1300 eV energy region,” J. Electron Spectrosc. Relat. Phenom. 92, 265–272 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Rev. B (1)

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Phys. Rev. B. (1)

D. Y. Smith, E. Shiles, “Finite-energy f-sum rules for valence electrons,” Phys. Rev. B. 17, 4689–4694 (1978).
[CrossRef]

Other (11)

D. Y. Smith, “X-ray optical properties: a review of the constraints and the data base,” in X-ray and VUV Interaction Data Bases, Calculations, and Measurements, N. K. Del Grande, P. Lee, J. A. Samson, D. Y. Smith, eds., Proc. SPIE911, 86–99 (1988).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Readrog, Mass., 1989), Chap. 4.

M. T. Wilson, technical paper available at http://www.puretechinc.com/tech_papers/tech_papers.htm .

F. R. Powell, T. A. Johnson, “Filter windows for EUV lithography,” in Emerging Lithographic TechnologiesV. E. A. Dobisz, eds., Proc. SPIE4343, 585–589 (2001).

J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), Chap. 4.

The imd program by D. L. Windt is available at http://www.cletus.phys.columbia.edu/∼windt/imd/ .

Information about the Extreme Ultraviolet Explorer mission and the observed spectral lines can be obtained at http://ssl.berkeley.edu/euve .

The experimental Multilayer Survey is available at http://www.cxro.lbl.gov/multilayer/survey.html .

B. Sae-Lao, C. Montcalm, “Normal-incidence multilayer mirrors for the 8–12 nm wavelength region,” Advanced Light Source Compendium of User Abstracts1999; available at http://alspubs.lbl.gov/compendium/ .

E. M. Gullikson, S. Mrowka, B. B. Kaufmann, “Recent developments in EUV reflectometry at the Advanced Light Source,” in Emerging Lithographic Technologies V, E. A. Dobisz, ed., Proc. SPIE4343, 363–373 (2001).

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, in Physik Daten-Optical Properties of Metals, H. Behrens, G. Ebel, eds. (Fachinformationszentrum, Karlsruhe, Germany, 1981), Vol. 18–2.

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Figures (9)

Fig. 1
Fig. 1

(a) X-ray diffraction results from three yttrium films measured at the Cu K a energy. The solid curves are fits to the data and were used to determine the yttrium film thickness. (b) The yttrium sputtering deposition rate is determined with the three experimental thickness results shown in (a).

Fig. 2
Fig. 2

Top: schematic diagram of the method used to obtain the transmittance of pure yttrium films. Bottom: measured transmittance versus energy of (a) a silicon nitride membrane, (b) a silicon nitride membrane with a 90-nm-thick yttrium film, (c) a 90-nm-thick yttrium film obtained from the measurements in (a) and (b) as is explained in the top diagram. The silicon L 2,3 (99.8-eV) and nitrogen K (409.9-eV) edges can be distinguished in (a) and (b) because of the constituents of the membrane. The yttrium M 4,5 (155.8-eV) and yttrium M 2,3 (298.8-eV) edge features are present in (b) and (c).

Fig. 3
Fig. 3

Transmittance versus energy obtained from 30-nm-, 52-nm-, and 90-nm-thick yttrium films.

Fig. 4
Fig. 4

Transmittance (logarithmic axis) versus yttrium thickness measured at 200, 500, and 1,000 eV for each of the 30-nm-, 52-nm-, and 90-nm-thick yttrium films. Transmittance curves at all three energies result in T Y = 1 when extrapolated to x = 0 yttrium film thickness, confirming the consistency between the film thickness determination and the experimental transmittance results.

Fig. 5
Fig. 5

Absorption β of yttrium versus energy. The new measurement values (solid curve) are significantly different from the CXRO tables (dashed curve) in the yttrium M 2,3 and M 4,5 energy regions.

Fig. 6
Fig. 6

β sum rule is computed with the new yttrium absorption data (solid curve) and the data from the CXRO tables (dashed curve). A 1.3-electron deficiency in the tabulated values is recovered with the new results.

Fig. 7
Fig. 7

Yttrium dispersion coefficient δ is plotted versus energy. Only slight differences exist between the new results (solid curve) and the tabulated values (dashed curve).

Fig. 8
Fig. 8

Sum rules are calculated with the new yttrium optical constants, expressed in terms of ε 2 , β, and Im (ε -1 ). The three sums rise monotonically with N eff,ε2 > N eff,β > N eff,ε-1 reaching gradually rising plateaus at the onset of the lowest core-level absorption (M 4,5 edge at 155.8 eV). The three sums show identical results from there on until they reach the value Z* = 38.83 at E → ∞.

Fig. 9
Fig. 9

Normal-incidence reflectance of Mo/Y multilayer mirrors calculated with the imd 8 program with the new yttrium optical constants (solid curve) and the previously tabulated values (dashed curve). The number of bilayers N = 120, the bilayer tickness ratio Γ = 0.425, and perfectly smooth substrate and layer interfaces were assumed in the calculations at all wavelengths.

Tables (1)

Tables Icon

Table 1 Measured Reflectance of Multilayers Operating at Normal Incidence in the 8–11-nm Wavelength Regiona

Equations (4)

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

I=I0 exp-4πβxλ,
T=II0=exp-4πβxλ.
δE=2π0EβEE2-E2dE,
Neff,AkE=Z*-2mε0na2πe22EEAkEdE, k=1, 2, 3,

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