Abstract

Coherent radiation from undulator beamlines has been used to directly measure the real and imaginary parts of the index of refraction of several materials at both extreme-ultraviolet and soft-x-ray wavelengths. Using the XOR interferometer, we measure the refractive indices of silicon and ruthenium, essential materials for extreme-ultraviolet lithography. Both materials are tested at wavelength (13.4  nm) and across silicon's L2(99.8  eV) and L3(99.2  eV) absorption edges. We further extend this direct phase measurement method into the soft-x-ray region, where measurements of chromium and vanadium are performed around their L 3 absorption edges at 574.1 and 512.1   eV, respectively. These are the first direct measurements, to our knowledge, of the real part of the index of refraction made in the soft-x-ray region.

© 2006 Optical Society of America

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References

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  1. P. Naulleau, K. Goldberg, S. Lee, C. Chang, D. Attwood, and J. Bokor, "Extreme-ultraviolet phase-shifting point-diffraction interferometer: a wave-front metrology tool with subangstrom reference-wave accuracy," Appl. Opt. 38, 7252-7263 (1999).
  2. S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
    [CrossRef]
  3. D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 1999).
  4. A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (Van Nostrand, 1935).
  5. B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
    [CrossRef]
  6. R. de L. Kronig and H. A. Kramers, "La diffusion de la lumiere par les atomes," Atti Congr. Intern. Fisici Como 2, 545-557 (1927).
  7. R. Soufli and E. Gullikson, "Reflectance measurements on clean surface for the determination of optical constants of silicon in the extreme ultraviolet-soft-x-ray region," Appl. Opt. 36, 5499-5507 (1997).
  8. L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
    [CrossRef]
  9. M. Magnusson and C. Hague, "Determination of the refractive index at soft x-ray resonances," J. Electron. Spectrosc. Relat. Phenom. 137-140, 519-522 (2004).
    [CrossRef]
  10. D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
    [CrossRef]
  11. A. Rosenbluth and P. Lee, "Bragg condition in absorbing x-ray multilayers," Appl. Phys. Lett. 40, 466-468 (1982).
    [CrossRef]
  12. See http://www-als.lbl.gov/.
  13. C. Chang, P. Naulleau, E. Anderson, and D. Attwood, "Spatial coherence characterization of undulator radiation," Opt. Commun. 182, 25-34 (2000).
    [CrossRef]
  14. C. Chang, P. Naulleau, E. Anderson, K. Rosfjord, and D. Attwood, "Diffractive optical elements based on Fourier optical techniques: a new class of optics for extreme ultraviolet and soft x-ray wavelengths," Appl. Opt. 41, 7384-7389 (2002).
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  16. K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
    [CrossRef]
  17. E. Gullikson, "Filter transmission," http://www-cxro.lbl.gov/opticallowbarconstants/filter2.html.
  18. K.-J. Kim, "Characteristics of synchrotron radiation," in Physics of Particle Accelerators, M. Month and M. Dienes, eds. (American Institute of Physics, 1989), pp. 565-632.
  19. T. Namioka, "Diffraction gratings," in Vacuum Ultraviolet Spectroscopy I, Vol. 31 of Experimental Methods in the Physical Sciences, J. A. Samson and D. L. Ederer, eds. (Academic, 2000), p. 347.
  20. J. Janesick, Scientific Charge-Coupled Devices (SPIE Press, 2001).
  21. C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. T. Attwood, "Direct measurement of index of refraction at the extreme-ultraviolet wavelength region with a novel interferometer," Opt. Lett. 27, 1028-1030 (2002).
  22. M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
  23. E. Gullikson, "The atomic scattering factor files," http://www-cxro.lbl.gov/opticallowbarconstants/asf.html.
  24. E. Gullikson, "Index of refraction," http://www-cxro.lbl.gov/opticallowbarconstants/getdb2.html.
  25. J. Svatos, D. Joyeux, D. Phalippou, and F. Polack, "Soft-x-ray interferometer for measuring the refractive index of materials," Opt. Lett. 18, 1367-1369 (1993).
  26. U. Bonse and M. Hart, "An x-ray interferometer," Appl. Phys. Lett. 6, 155-156 (1965).
    [CrossRef]

2004

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

M. Magnusson and C. Hague, "Determination of the refractive index at soft x-ray resonances," J. Electron. Spectrosc. Relat. Phenom. 137-140, 519-522 (2004).
[CrossRef]

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
[CrossRef]

2002

2000

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, "Spatial coherence characterization of undulator radiation," Opt. Commun. 182, 25-34 (2000).
[CrossRef]

1999

1998

L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
[CrossRef]

1997

1993

J. Svatos, D. Joyeux, D. Phalippou, and F. Polack, "Soft-x-ray interferometer for measuring the refractive index of materials," Opt. Lett. 18, 1367-1369 (1993).

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

1982

1965

U. Bonse and M. Hart, "An x-ray interferometer," Appl. Phys. Lett. 6, 155-156 (1965).
[CrossRef]

1927

R. de L. Kronig and H. A. Kramers, "La diffusion de la lumiere par les atomes," Atti Congr. Intern. Fisici Como 2, 545-557 (1927).

Allison, S. K.

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (Van Nostrand, 1935).

Anderson, E.

Attwood, D.

Attwood, D. T.

K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
[CrossRef]

C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. T. Attwood, "Direct measurement of index of refraction at the extreme-ultraviolet wavelength region with a novel interferometer," Opt. Lett. 27, 1028-1030 (2002).

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 1999).

Bokor, J.

Bonse, U.

U. Bonse and M. Hart, "An x-ray interferometer," Appl. Phys. Lett. 6, 155-156 (1965).
[CrossRef]

Chang, C.

Christensen, F. E.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Compton, A. H.

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (Van Nostrand, 1935).

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Donguy, S.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Eberhardt, W.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Eisebitt, S.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Goldberg, K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gullikson, E.

C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. T. Attwood, "Direct measurement of index of refraction at the extreme-ultraviolet wavelength region with a novel interferometer," Opt. Lett. 27, 1028-1030 (2002).

R. Soufli and E. Gullikson, "Reflectance measurements on clean surface for the determination of optical constants of silicon in the extreme ultraviolet-soft-x-ray region," Appl. Opt. 36, 5499-5507 (1997).

E. Gullikson, "Index of refraction," http://www-cxro.lbl.gov/opticallowbarconstants/getdb2.html.

E. Gullikson, "Filter transmission," http://www-cxro.lbl.gov/opticallowbarconstants/filter2.html.

E. Gullikson, "The atomic scattering factor files," http://www-cxro.lbl.gov/opticallowbarconstants/asf.html.

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Hague, C.

M. Magnusson and C. Hague, "Determination of the refractive index at soft x-ray resonances," J. Electron. Spectrosc. Relat. Phenom. 137-140, 519-522 (2004).
[CrossRef]

Hailey, C. J.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Harrison, F. A.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Hart, M.

U. Bonse and M. Hart, "An x-ray interferometer," Appl. Phys. Lett. 6, 155-156 (1965).
[CrossRef]

Hellwig, O.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Honkimaki, V.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Ina, H.

Janesick, J.

J. Janesick, Scientific Charge-Coupled Devices (SPIE Press, 2001).

Joyeux, D.

Kim, K.-J.

K.-J. Kim, "Characteristics of synchrotron radiation," in Physics of Particle Accelerators, M. Month and M. Dienes, eds. (American Institute of Physics, 1989), pp. 565-632.

Kobayashi, S.

Koglin, J.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Kramers, H. A.

R. de L. Kronig and H. A. Kramers, "La diffusion de la lumiere par les atomes," Atti Congr. Intern. Fisici Como 2, 545-557 (1927).

Kronig, R. de L.

R. de L. Kronig and H. A. Kramers, "La diffusion de la lumiere par les atomes," Atti Congr. Intern. Fisici Como 2, 545-557 (1927).

Lee, P.

A. Rosenbluth and P. Lee, "Bragg condition in absorbing x-ray multilayers," Appl. Phys. Lett. 40, 466-468 (1982).
[CrossRef]

Lee, S.

Liu, Y.

K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
[CrossRef]

Lorgen, M.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Luning, J.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Magnusson, M.

M. Magnusson and C. Hague, "Determination of the refractive index at soft x-ray resonances," J. Electron. Spectrosc. Relat. Phenom. 137-140, 519-522 (2004).
[CrossRef]

Namioka, T.

T. Namioka, "Diffraction gratings," in Vacuum Ultraviolet Spectroscopy I, Vol. 31 of Experimental Methods in the Physical Sciences, J. A. Samson and D. L. Ederer, eds. (Academic, 2000), p. 347.

Naulleau, P.

Phalippou, D.

Polack, F.

Raoux, D.

L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
[CrossRef]

Rosenbluth, A.

A. Rosenbluth and P. Lee, "Bragg condition in absorbing x-ray multilayers," Appl. Phys. Lett. 40, 466-468 (1982).
[CrossRef]

Rosfjord, K.

Rosfjord, K. M.

K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
[CrossRef]

Schlotter, W. F.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Seve, L.

L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
[CrossRef]

Soufli, R.

Stohr, J.

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Svatos, J.

Takeda, M.

Tonnerre, J.-M.

L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
[CrossRef]

Windt, D. L.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Ziegler, E.

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Rosenbluth and P. Lee, "Bragg condition in absorbing x-ray multilayers," Appl. Phys. Lett. 40, 466-468 (1982).
[CrossRef]

U. Bonse and M. Hart, "An x-ray interferometer," Appl. Phys. Lett. 6, 155-156 (1965).
[CrossRef]

Data Nucl. Data Tables

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. M. Rosfjord, Y. Liu, and D. T. Attwood, "Tunable coherent soft x-rays," IEEE J. Sel. Top. Quantum Electron. 10, 1405-1413 (2004).
[CrossRef]

J. Appl. Cryst.

L. Seve, J.-M. Tonnerre, and D. Raoux, "Determination of the anomalous scattering factors in the soft-x-ray range using diffraction from a multilayer," J. Appl. Cryst. 31, 700-707 (1998).
[CrossRef]

J. Electron. Spectrosc. Relat. Phenom.

M. Magnusson and C. Hague, "Determination of the refractive index at soft x-ray resonances," J. Electron. Spectrosc. Relat. Phenom. 137-140, 519-522 (2004).
[CrossRef]

J. Opt. Soc. Am.

Nature

S. Eisebitt, J. Luning, W. F. Schlotter, M. Lorgen, O. Hellwig, W. Eberhardt, and J. Stohr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004).
[CrossRef]

Opt. Commun.

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, "Spatial coherence characterization of undulator radiation," Opt. Commun. 182, 25-34 (2000).
[CrossRef]

Opt. Lett.

Proc. SPIE

D. L. Windt, S. Donguy, C. J. Hailey, J. Koglin, V. Honkimaki, E. Ziegler, F. E. Christensen, and F. A. Harrison, "Optical constants for hard x-ray multialyers over the energy range E = 35-180 keV," in Proc. SPIE 5168, 35-40 (2004).
[CrossRef]

Other

See http://www-als.lbl.gov/.

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, 1999).

A. H. Compton and S. K. Allison, X-Rays in Theory and Experiment (Van Nostrand, 1935).

R. de L. Kronig and H. A. Kramers, "La diffusion de la lumiere par les atomes," Atti Congr. Intern. Fisici Como 2, 545-557 (1927).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

E. Gullikson, "Filter transmission," http://www-cxro.lbl.gov/opticallowbarconstants/filter2.html.

K.-J. Kim, "Characteristics of synchrotron radiation," in Physics of Particle Accelerators, M. Month and M. Dienes, eds. (American Institute of Physics, 1989), pp. 565-632.

T. Namioka, "Diffraction gratings," in Vacuum Ultraviolet Spectroscopy I, Vol. 31 of Experimental Methods in the Physical Sciences, J. A. Samson and D. L. Ederer, eds. (Academic, 2000), p. 347.

J. Janesick, Scientific Charge-Coupled Devices (SPIE Press, 2001).

E. Gullikson, "The atomic scattering factor files," http://www-cxro.lbl.gov/opticallowbarconstants/asf.html.

E. Gullikson, "Index of refraction," http://www-cxro.lbl.gov/opticallowbarconstants/getdb2.html.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for direct index of refraction measurements. Spectrally coherent illumination is diffracted from a pinhole and then directed to two off-axis foci by the XOR at the sample mask. The two waves interfere at a downstream CCD camera. Note: figure is not to scale.

Fig. 2
Fig. 2

(a) δ and (b) β measurements taken in the vicinity of 92.5 eV (13.4 nm) for ruthenium. The experimental data are shown with error bars and referenced against data taken using absorption measurements.[23] The error bars on the data are a result of changing upstream alignment of the system due to the time of data acquisition. This changing alignment effects the pinhole illumination, specifically in the vertical direction as discussed in the text.

Fig. 3
Fig. 3

(a) δ and (b) β measurements in the vicinity of 92.5 eV (13.4 nm), including silicon's L 2 and L 3 absorption edges (99.8 and 99.2 eV, respectively). Although the sample material was originally thought to be pure silicon, RBS measurements determined it to be Si93.96Ar5.98In0.06. The experimental data are shown with error bars. Referenced data are also shown, obtained from absorption measurements for pure silicon[23] and Si93.96Ar5.98In0.06.[24]

Fig. 4
Fig. 4

RBS results of silicon sample. From the areal density it was found that, for thickness t and density n, (nt)α-Si = 6.35 ± 0.196 × 1017 at.s∕cm2, 93.96 at. %, (nt)Ar = 4.04 ± 0.152 × 1016 atoms∕cm2, 5.98 at. %, and (nt)In = 4.40 ± 0.4 × 1014 atoms∕cm2, 0.06 at. %, resulting in an overall density of 2.31 g∕cm3. RBS measurement courtesy of Motorola.

Fig. 5
Fig. 5

(a) δ and (b) β measurements taken about 512.1 eV (2.42 nm) for vanadium. The experimental data are shown with error bars and referenced against data taken using absorption measurements.[23] The sample used had a thickness of 350 nm and a RBS-determined density of 5.89 g∕cm3. Note the increase in the magnitude of the error bars at energies higher than the absorption edge.

Fig. 6
Fig. 6

(a) δ and (b) β measurements taken about 574.1 eV (2.16 nm) for chromium. The experimental data are shown with error bars and referenced against data taken using absorption measurements.[23] The sample used had a thickness of 310 nm and a RBS-determined density of 7.12 g∕cm3. Note the increase in the magnitude of the error bars at energies higher than the absorption edge.

Tables (1)

Tables Icon

Table 1 Transmission of Higher Harmonics through the 2.1 μm Gold Used as the Pinhole Absorber at Soft-X-Ray Wavelengths a

Equations (75)

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

( 13.4   nm )
L 2 ( 99.8   eV )
L 3 ( 99.2   eV )
512.1   eV
n ( ω ) = 1 δ ( ω ) + i β ( ω ) ,
β / δ 1
L 3
512 .1   eV
13.4   nm
( 92.5   eV )
13.4   nm
z D d 1.22 λ ,
400 μ m
Δ r  
200   nm
16 μ m
200   nm
100   nm
f = D Δ r λ .
13.4   nm
( 92.5   eV
5.97   mm
300   nm
1   in . × 1   in . ( 2 .54   cm × 2 .54   cm )
2.5 μ m
500   eV
2.1 μ m
280 μ m
140   nm
7.84 μ m
2.5   nm   ( 500   eV
15.7   mm
200   nm
8.0 × 10 3
500  eV
p = 248   mm
500   eV
1 μ m
1.44   m
E 1
E = n E 1 ,
500   eV
E 5 = 833.3   eV
E 7 = 1166.7   eV
1200   eV
θ q = θ i + q λ 0 n Λ ,
λ 0 / n
θ i
θ q
2.1 μ m
92.5   eV
Δϕ
13.4   nm
5 %
13 %
L 2 ( 99.8   eV )
L 3 ( 99.2   eV )
93.96 %
5.98 %
0.06 %
Si 93.96 Ar 5 .98 In 0 .06
Si 93.96 Ar 5 .98 In 0 .06
δ = 0.0015
β = 0.0022
13.4   nm
L 3
574.1   eV
0.1 %
0.5   eV
44 μ m
2.7 μ m
580   eV
281.8   eV
8.05 k eV
1   keV

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