Abstract

An innovative solution for the Schwarzschild optic, based on a modification of the position of the object, is proposed. This solution allows one to reach a larger numerical aperture and hence a better resolution compared with the standard configuration of the Schwarzschild optics. Furthermore, we propose an analytical solution that allows the optical system to be designed without the need of any ray-tracing software.

© 2006 Optical Society of America

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References

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  1. D. Attwood, Soft X-ray and Extreme Ultraviolet Radiation, 1st ed. (Cambridge U. Press, 2000).
  2. R. E. Gleason, "How far will circuits shrink," Sci. Spectra 20,32-40 (2000).
  3. K. Diefendorff, "Extreme lithography," Microdesign Resources Microprocessor Rep. (June 2000), pp. 1-10, www.MPRonline.com.
  4. I. A. Artioukov and K. M. Krymski, "Schwarzschild objective for soft x-ray," Opt. Eng. 39, 2163-2170 (2000).
    [CrossRef]
  5. D. Korsch, Reflective Optics (Academic, 1991).
  6. H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
    [CrossRef]
  7. S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
    [CrossRef]
  8. A. M. Hawryluk and L. G. Seppala, "Soft x-ray projection lithography using an x-ray reduction camera," J. Vac. Sci. Technol. B 6, 2162-2166 (1988).
    [CrossRef]
  9. I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
    [CrossRef]
  10. I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
    [CrossRef] [PubMed]
  11. D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
    [CrossRef]
  12. D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).
  13. D. L. Shealy, C. Wang, and R. B. Hoover, "Optical analysis of an ultra-high resolution two-mirror soft x-ray microscopy," J. X-Ray Sci. Technol. 5, 1-19 (1995).
    [CrossRef]
  14. I. A. Artioukov, X-ray Optics Group, P. N. Lebedev Physical Institute, Leninsky Prospekt 53, Moscow B-333, 117924, Russia; iart@sci.lebedev.ru (personal communication, 2004).

2000

I. A. Artioukov and K. M. Krymski, "Schwarzschild objective for soft x-ray," Opt. Eng. 39, 2163-2170 (2000).
[CrossRef]

1996

S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
[CrossRef]

1995

1993

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

1990

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

1989

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

1988

A. M. Hawryluk and L. G. Seppala, "Soft x-ray projection lithography using an x-ray reduction camera," J. Vac. Sci. Technol. B 6, 2162-2166 (1988).
[CrossRef]

Artioukov, I. A.

I. A. Artioukov and K. M. Krymski, "Schwarzschild objective for soft x-ray," Opt. Eng. 39, 2163-2170 (2000).
[CrossRef]

I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
[CrossRef] [PubMed]

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

I. A. Artioukov, X-ray Optics Group, P. N. Lebedev Physical Institute, Leninsky Prospekt 53, Moscow B-333, 117924, Russia; iart@sci.lebedev.ru (personal communication, 2004).

Asadchikov, V. E.

Attwood, D.

D. Attwood, Soft X-ray and Extreme Ultraviolet Radiation, 1st ed. (Cambridge U. Press, 2000).

Barbee, T. W.

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

Cerrina, F.

S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
[CrossRef]

Diefendorff, K.

K. Diefendorff, "Extreme lithography," Microdesign Resources Microprocessor Rep. (June 2000), pp. 1-10, www.MPRonline.com.

Fedorenko, A. I.

I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
[CrossRef] [PubMed]

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

Hawryluk, A. M.

A. M. Hawryluk and L. G. Seppala, "Soft x-ray projection lithography using an x-ray reduction camera," J. Vac. Sci. Technol. B 6, 2162-2166 (1988).
[CrossRef]

Hoover, R. B.

D. L. Shealy, C. Wang, and R. B. Hoover, "Optical analysis of an ultra-high resolution two-mirror soft x-ray microscopy," J. X-Ray Sci. Technol. 5, 1-19 (1995).
[CrossRef]

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).

Ishii, Y.

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

Kas'yanov, Yu. S.

Kinoshita, H.

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

Kondratenko, V. V.

I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
[CrossRef] [PubMed]

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

Korsch, D.

D. Korsch, Reflective Optics (Academic, 1991).

Krymski, K. M.

I. A. Artioukov and K. M. Krymski, "Schwarzschild objective for soft x-ray," Opt. Eng. 39, 2163-2170 (2000).
[CrossRef]

Kurihara, K.

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

Seppala, L. G.

A. M. Hawryluk and L. G. Seppala, "Soft x-ray projection lithography using an x-ray reduction camera," J. Vac. Sci. Technol. B 6, 2162-2166 (1988).
[CrossRef]

Serov, R. V.

Shealy, D. L.

D. L. Shealy, C. Wang, and R. B. Hoover, "Optical analysis of an ultra-high resolution two-mirror soft x-ray microscopy," J. X-Ray Sci. Technol. 5, 1-19 (1995).
[CrossRef]

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).

Singh, S.

S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
[CrossRef]

Solak, H.

S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
[CrossRef]

Torii, Y.

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

Vinogradov, A. V.

I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
[CrossRef] [PubMed]

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

Walker, A. B. C.

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

Wang, C.

D. L. Shealy, C. Wang, and R. B. Hoover, "Optical analysis of an ultra-high resolution two-mirror soft x-ray microscopy," J. X-Ray Sci. Technol. 5, 1-19 (1995).
[CrossRef]

D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).

Wu, J.

D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).

Yulin, S. A.

I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Yu. S. Kas'yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, "Schwarzschild soft-x-ray microscope for imaging of nonradiating objects," Opt. Lett. 20, 2451-2453 (1995).
[CrossRef] [PubMed]

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

J. Vac. Sci. Technol. B

H. Kinoshita, K. Kurihara, Y. Ishii, and Y. Torii, "Soft x-ray reduction lithography using multilayer mirrors," J. Vac. Sci. Technol. B 7, 1648-1651 (1989).
[CrossRef]

A. M. Hawryluk and L. G. Seppala, "Soft x-ray projection lithography using an x-ray reduction camera," J. Vac. Sci. Technol. B 6, 2162-2166 (1988).
[CrossRef]

J. X-Ray Sci. Technol.

D. L. Shealy, C. Wang, and R. B. Hoover, "Optical analysis of an ultra-high resolution two-mirror soft x-ray microscopy," J. X-Ray Sci. Technol. 5, 1-19 (1995).
[CrossRef]

Opt. Commun.

I. A. Artioukov, A. I. Fedorenko, V. V. Kondratenko, S. A. Yulin, and A. V. Vinogradov, "Soft x-ray submicron imaging experiments with nanosecond exposure," Opt. Commun. 102, 401-406 (1993).
[CrossRef]

Opt. Eng.

I. A. Artioukov and K. M. Krymski, "Schwarzschild objective for soft x-ray," Opt. Eng. 39, 2163-2170 (2000).
[CrossRef]

D. L. Shealy, R. B. Hoover, T. W. Barbee, and A. B. C. Walker, "Design and analysis of a Schwarzschild imaging multilayer x-ray microscope," Opt. Eng. 29, 721-727 (1990).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

S. Singh, H. Solak, and F. Cerrina, "Multilayer roughness and image formation in the Schwarzschild objective," Rev. Sci. Instrum. 67, 1-8 (1996).
[CrossRef]

Other

D. Korsch, Reflective Optics (Academic, 1991).

D. Attwood, Soft X-ray and Extreme Ultraviolet Radiation, 1st ed. (Cambridge U. Press, 2000).

R. E. Gleason, "How far will circuits shrink," Sci. Spectra 20,32-40 (2000).

K. Diefendorff, "Extreme lithography," Microdesign Resources Microprocessor Rep. (June 2000), pp. 1-10, www.MPRonline.com.

D. L. Shealy, C. Wang, J. Wu, and R. B. Hoover, "Design and analysis of soft x-ray imaging microscopes," in Proc. SPIE 1546,117-124 (1991).

I. A. Artioukov, X-ray Optics Group, P. N. Lebedev Physical Institute, Leninsky Prospekt 53, Moscow B-333, 117924, Russia; iart@sci.lebedev.ru (personal communication, 2004).

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Figures (12)

Fig. 1
Fig. 1

SO in a microscope scheme.

Fig. 2
Fig. 2

Image plane position (V 0 S ), object-to-image distance (V0 S + tS ), and magnification (M) versus the ratio r of the two mirrors' curvature radius for a standard SO.

Fig. 3
Fig. 3

V 2M 2 ratio as a function of M for the standard SO, obtained by ranging r between 2.7 and 3.7.

Fig. 4
Fig. 4

Normalized geometrical resolution (δgeo) and depth of focus (DOFgeo) versus the NA for a standard SO according to Eqs. (19) and (21), respectively.

Fig. 5
Fig. 5

Nonnormalized geometrical resolution (δgeo), diffraction limit (δdiff), and final resolution (δtot) versus the NA for a standard SO having a larger mirror diameter of 8 cm and operating at a wavelength λ = 14 nm. The result is calculated for r = 3.1793 (M = 10), but it is practically independent from r.

Fig. 6
Fig. 6

Coefficients V 1 and V 2 versus the object position (t) when t is close to the value calculated for a standard SO position (tS ). The coefficients are calculated by Eqs. (5) and (6) for r = 3.1793 (for M = 10 at t = tS ).

Fig. 7
Fig. 7

Behavior of V(α) − V 0 for different positions of the object: t = tS , t = tS + 0.8%, and t = tS  − 0.8% for a SO with r = 3.1793 (and hence tS = 0.8024 and M = 10). The values of αmax and αmin are purely indicative.

Fig. 8
Fig. 8

Difference between the object position for a MSO and that for a standard SO versus the NA for a mirror radius ratio r = 3.1793, that is, for a magnification M = 10 (the values are normalized to R 2).

Fig. 9
Fig. 9

Normalized geometrical resolution of a MSO (solid line) versus the NA for r = 3.1793 (M = 10) compared with that of a standard SO (dashed line).

Fig. 10
Fig. 10

Nonnormalized geometrical resolution (δgeo), diffraction limit (δdiff), and final resolution (δtot) versus the NA for a MSO with a larger mirror diameter of 8 cm and operating at a wavelength λ = 14 nm. The result is calculated for r = 3.1793 (M = 10), but, in practice, it does not depend on r.

Fig. 11
Fig. 11

Geometrical resolution (normalized to R 2) of a SO versus the object position t, nearby the standard position tS , for a mirror curvature ratio r = 3.1793 (that is, M ∼ 10 and tS = 0.8024) and a NA = 0.2.

Fig. 12
Fig. 12

Off-axis geometrical resolution of a standard SO (dashed curve) having the parameters of Table 1 of Ref. 9 (that is, M = 10.32, R 1 = 100 mm, R 2 = 31.66 mm, Φ1 = 60 mm, Φ2 = 12 mm, NA ∼ 0.24), of the correspondent MSO (solid curve), and of the correspondent NSO (dashed–dotted curve) as extracted from Fig. 2 of Ref. 9.

Equations (35)

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

M = Z 1 Z 0 = R 1 2 Z 0 R 1 R 2 2 Z 0 R 1 .
r = R 1 R 2 , t = Z 0 R 2 , V = Z 1 R 2 ,
V ( α ) = t [ sin ( α ) / sin ( α ) ] ,
α = 2 arcsin [ t sin ( α ) ] 2 arcsin [ t r sin ( α ) ] α .
V ( α ) = V 0 + V 1 α 2 + V 2 α 4 + ,
V 0 = 1 b 1 ,
V 1 = ( b 1     3 b 3 ) t 2 6 b 1     2 ,
V 2 = t 4 b 1     2 [ ( b 1     3 b 3 ) 2 36 b 1 3 40 b 5 + b 1     2 b 3 12 b 1     5 5 ! ] V 1 3 ,
t = t S = r r 1 + r , r > 1 .
M S = r 1 + r r 1 r ,
V 0 S = r r 1 r .
V 2 S ( r ) = t S      4 ( 3 40 b 5 b 1     2 + b 3 12 b 1     3 5 ! ) ,
r = [ M + 1 + ( M + 1 ) 2 + 4 ( M 1 ) 2 2 ( M 1 ) ] 2 ,
Φ 1 2 ( t S + r ) t g ( α max ) ,
α max = arcsin ( NA )
Φ 2 2 ( V 0 S 1 ) t g ( α max ) .
Φ 2 2 1 + r r 1 r t g ( α max M ) ,
α min = arctg ( Φ 2 / 2 t S + 1 ) .
δ geo = 1 M α min α max { [ V ( α ) V im ] t g ( α ) } 2 sin ( α ) d α α min α max sin ( α ) d α .
δ geo = 1 M 2 1 C 2 [ C 4 ( V 0 V im ) 2 + 2 ( C 6 V 1 + C 8 V 2 ) ( V 0 V im ) + C 8 V 1     2 + 2 C 10 V 1 V 2 + C 12 V 2     2 ] ,
V im = V 0 + C 6 C 4 V 1 + C 8 C 4 V 2 .
V im = α min α max V ( α ) α 2 sin ( α ) d α α min α max α 2 sin ( α ) d α α min α max V ( α ) α 3 d α α min α max α 3 d α .
δ geo = 1 M 2
× 1 C 2 [ C 4 ( V 0 V im ) 2 + 2 C 8 V 2 ( V 0 V im ) + C 12 V 2     2 ] ,
V im = V 0 + C 8 C 4 V 2 ,
δ geo = V 2 M 2 C 12 C 2 C 8     2 C 2 C 4 .
DOF 2 δ / NA ,
DOF geo = V 2 M 2 C 12 C 4 ( C 8 C 4 ) 2 ,
α mo = α min             2 + α max                 2 2 .
2 V 1 α mo + 4 V 2 α mo           3 = 0     V 1 + 2 V 2 α mo           2 = 0.
t mo t S = 2 α mo           2 V 2 ( r , t S ) V 1 ( r , t S ) + 2 α mo           2 V 2 ( r , t S ) ,
V 1 ( r , t S ) = 1 2 1 2 ( t S b 1 ) 2 + ( b 1     3 b 3 ) ( t S b 1 1 ) 3 b 1     3 ,
V 2 ( r , t S ) = t S     3 b 3 3 ( t S b 1 ) 3 30 3 10 t S     3 b 5 b 1 2 + 3 20 t S     2 b 5 b 1 3 + ( t S b 1 ) 2 60 + 1 12 1 4 ( t S b 1 ) 2 .
δ geo = 1 M 1 C 2 [ C 4 ( V 0 V im ) 2 + 2 ( C 6 V 1 + C 8 V 2 ) ( V 0 V im ) + C 8 V 1     2 + 2 C 10 V 1 V 2 + C 12 V 2     2 ] ,
DOF geo = V 2 C 12 C 4 ( C 8 C 4 ) 2   or   DOF geo = δ geo M C 2 C 4 .

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