Abstract

In this theoretical study we show that by removing or depositing additional multilayer (ML) periods of a thin-film interference coating, distortions in the reflected wave front induced by surface figure errors can be corrected. At λ = 13.4 nm in the extreme-ultraviolet region the removal or deposition of a single period of the standard two-component molybdenum-silicon (Mo/Si) ML interference coating induces an effective phase change of magnitude 0.043π with respect to an identical optical thickness in vacuum. The magnitude of this wave-front shift can be enhanced with multicomponent MLs optimized for phase change on reflection. We briefly discuss the contributions of the shift in the effective reflection surface of the ML on the phase change. We also predict the feasibility of novel phase-shifting masks for subwavelength imaging applications.

© 2003 Optical Society of America

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References

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  1. C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
    [CrossRef]
  2. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986), pp. 11–43.
  3. 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), http://www-cxro.lbl.gov/optical_constants .
    [CrossRef]
  4. J. J. M. Braat, “Phase correcting layers in EUV imaging systems for microlithography,” in Extreme Ultraviolet Lithography, G. Kubiak, D. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 152–155.
  5. M. Yamamoto, “Sub-nanometer figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res. A 467–468, 1282–1285 (2001).
    [CrossRef]
  6. M. Singh, J. J. M. Braat, “Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity,” Appl. Opt. 39, 2189–2197 (2000).
    [CrossRef]
  7. M. Singh, J. J. M. Braat, “Improved theoretical reflectivities of extreme-ultraviolet mirrors,” in Emerging Lithographic Technologies IV, E. A. Dobisz, ed., Proc. SPIE3997, 412–419 (2000).
    [CrossRef]
  8. J. I. Larruquert, “Reflectance enhancement in the extreme ultraviolet and soft x rays by means of multilayers with more that two materials,” J. Opt. Soc. Am. A 19, 391–397 (2002).
    [CrossRef]
  9. C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis (Wiley Interscience, New York, 1999), p. 285.
  10. M. F. Bal, F. Bociort, J. J. M. Braat, “The influence of multilayers on the optical performance of extreme ultraviolet projection systems”, in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 149–157 (2002).
    [CrossRef]

2002

2001

M. Yamamoto, “Sub-nanometer figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res. A 467–468, 1282–1285 (2001).
[CrossRef]

2000

1998

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

1993

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), http://www-cxro.lbl.gov/optical_constants .
[CrossRef]

Attwood, D.

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

Bal, M. F.

M. F. Bal, F. Bociort, J. J. M. Braat, “The influence of multilayers on the optical performance of extreme ultraviolet projection systems”, in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 149–157 (2002).
[CrossRef]

Bociort, F.

M. F. Bal, F. Bociort, J. J. M. Braat, “The influence of multilayers on the optical performance of extreme ultraviolet projection systems”, in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 149–157 (2002).
[CrossRef]

Braat, J. J. M.

M. Singh, J. J. M. Braat, “Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity,” Appl. Opt. 39, 2189–2197 (2000).
[CrossRef]

J. J. M. Braat, “Phase correcting layers in EUV imaging systems for microlithography,” in Extreme Ultraviolet Lithography, G. Kubiak, D. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 152–155.

M. F. Bal, F. Bociort, J. J. M. Braat, “The influence of multilayers on the optical performance of extreme ultraviolet projection systems”, in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 149–157 (2002).
[CrossRef]

M. Singh, J. J. M. Braat, “Improved theoretical reflectivities of extreme-ultraviolet mirrors,” in Emerging Lithographic Technologies IV, E. A. Dobisz, ed., Proc. SPIE3997, 412–419 (2000).
[CrossRef]

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), http://www-cxro.lbl.gov/optical_constants .
[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), http://www-cxro.lbl.gov/optical_constants .
[CrossRef]

Gwyn, C. W.

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

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), http://www-cxro.lbl.gov/optical_constants .
[CrossRef]

Larruquert, J. I.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986), pp. 11–43.

Madsen, C. K.

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis (Wiley Interscience, New York, 1999), p. 285.

Singh, M.

M. Singh, J. J. M. Braat, “Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity,” Appl. Opt. 39, 2189–2197 (2000).
[CrossRef]

M. Singh, J. J. M. Braat, “Improved theoretical reflectivities of extreme-ultraviolet mirrors,” in Emerging Lithographic Technologies IV, E. A. Dobisz, ed., Proc. SPIE3997, 412–419 (2000).
[CrossRef]

Stulen, R.

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

Sweeney, D.

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

Yamamoto, M.

M. Yamamoto, “Sub-nanometer figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res. A 467–468, 1282–1285 (2001).
[CrossRef]

Zhao, J. H.

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis (Wiley Interscience, New York, 1999), p. 285.

Appl. Opt.

At. Data Nucl. Data Tables

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), http://www-cxro.lbl.gov/optical_constants .
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

C. W. Gwyn, R. Stulen, D. Sweeney, D. Attwood, “Extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 16, 3142–3149 (1998).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

M. Yamamoto, “Sub-nanometer figure error correction of an extreme ultraviolet multilayer mirror by its surface milling,” Nucl. Instrum. Methods Phys. Res. A 467–468, 1282–1285 (2001).
[CrossRef]

Other

M. Singh, J. J. M. Braat, “Improved theoretical reflectivities of extreme-ultraviolet mirrors,” in Emerging Lithographic Technologies IV, E. A. Dobisz, ed., Proc. SPIE3997, 412–419 (2000).
[CrossRef]

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis (Wiley Interscience, New York, 1999), p. 285.

M. F. Bal, F. Bociort, J. J. M. Braat, “The influence of multilayers on the optical performance of extreme ultraviolet projection systems”, in International Optical Design Conference 2002, P. K. Manhart, J. M. Sasian, eds., Proc. SPIE4832, 149–157 (2002).
[CrossRef]

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986), pp. 11–43.

J. J. M. Braat, “Phase correcting layers in EUV imaging systems for microlithography,” in Extreme Ultraviolet Lithography, G. Kubiak, D. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 152–155.

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Figures (5)

Fig. 1
Fig. 1

Reflectivity and phase change as a function of the thickness of the Mo correction layer with reference to a vacuum layer of equal thickness. The inset shows schematically the correction methods for the two types of substrate figure error.

Fig. 2
Fig. 2

Numerical simulation of the phase change with respect to a vacuum layer (inset) associated with 0–10 Mo/Si periods. The line through the data points is a least-squares fit. The inset is a schematic representation of the geometry and the associated phase shifts due to additional (or removed) ML periods. The correction ML of physical thickness d corrects for the idealized figure error. The expressions |r j |exp(-iϕ j ) are the amplitude reflectivities with their associated phase change on reflection.

Fig. 3
Fig. 3

Magnitude of the phase change associated with various ML stacks deposited on a base Mo/Si ML as a function of the physical thickness d. The data points correspond to Δϕ at each complete additional ML period. The MLs correspond to designs 1, 6, 8, and 11 in Table 2.

Fig. 4
Fig. 4

Evolution of the depth of the effective reflection surface of a Mo/Si ML as a function of the number of periods. The inset is the expanded scale between 40 and 60 periods.

Fig. 5
Fig. 5

Difference in the phase shifts due to the two MLs deposited on the base ML. A π-rad phase difference in the wave front is achieved after 12 periods.

Tables (2)

Tables Icon

Table 1 Optical Constants of the Materialsa

Tables Icon

Table 2 Phase Sensitivity and Effective Peak Reflectivity of Various Correction ML Designs Deposited on an Optimized 50-Period Mo/Si Base ML Tuned for λ = 13.4-nm Operation with a Peak R of 0.748

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