Abstract

The merit function space of mirror system for extreme ultraviolet (EUV) lithography is studied. Local minima situated in the multidimensional optical merit function space are connected via links that contain saddle points and form a network. We present networks for EUV lithographic objective designs and discuss how these networks change when control parameters, such as aperture and field, are varied, and constraints are used to limit the variation domain of the variables. A good solution in a network, obtained with a limited number of variables, has been locally optimized with all variables to meet practical requirements.

© 2007 Optical Society of America

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  1. T. G. Kuper and T. I. Harris, "Global optimization for lens design--an emerging technology," Proc. SPIE 1780, 14-28 (1992).
  2. T. Kuper and T. Harris, "A New Look at Global Optimization for Optical Design," Photonics Spectra 151-160 (January 1992).
  3. J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 634263420O (2006).
  4. J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 634263420M (2006).
  5. M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).
  6. G. W. Forbes and A. E. W. Jones, "Towards global optimization with adaptive simulated annealing," Proc. SPIE 1354, 144-151 (1991).
  7. K. E. Moore, "Algorithm for global optimization of optical systems based on genetic competition," Proc. SPIE 3780, 40-47 (1999).
  8. F. Bociort, E. van Driel, and A. Serebriakov, "Networks of local minima in optical system optimization," Opt. Lett. 29, 189-191 (2004).
  9. E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).
  10. F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).
  11. F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).
  12. J. J. M. Braat, "Extreme UV lithography, "A candidate for next-generation lithography," Proc. SPIE 4016, 2-7 (2000).
  13. K. Diefendorff, "Extreme lithography," Microprocessor Report 1-10 (Reed Elsevier, 19 June 2000).
  14. S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).
  15. D. W. Sweeney, "Extreme ultraviolet lithography," in Encyclopedia of optical Engineering (Marcel Dekker, 2003), pp. 485-491.
  16. H. J. Levinson and W. H. Arnold, Handbook of Microlithography, Micromachining, and Microfabrication, Vol. PM39 of SPIE Press Monograph Series (SPIE Press, 1997), pp. 11-126.
  17. G. T. Barkema and N. Mousseau, "Event-based relaxation of continuous disordered systems," Phys. Rev. Lett. 77, 4358-4361 (1996).
  18. N. Mousscau and G. T. Barkema, "Travelling through potential energy landscapes of disordered materials: the activation-relaxation technique," Phys. Rev. E 57, 2419-2424 (1998).
  19. G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).
  20. code v, Optical Research Associates, Pasadena, Calif.
  21. M. F. Bal, F. Bociort, and J. J. M. Braat, "Lithographic apparatus, device manufacturing method, and device manufactured thereby," U.S. patent 6,556,648 (29 April 2003).
  22. D. M. Williamson, "High numerical aperture ring field optical reduction system," U.S. patent 5,815,310 (29 September 1998).
  23. R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,183,095 (6 February 2001).
  24. D. R. Shafer, "Projection lithography system and method using all-reflective optical elements," U.S. patent 5,686,728 (11 November 1997).
  25. J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,299,318 (9 October 2001).
  26. J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,255,661 (3 July 2001).
  27. J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,396,067 (28 May 2002).
  28. R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,033,079 (7 March 2000).
  29. W. Ulrich, "8-mirror microlithography projection optics," U.S. patent 6,710,917 B2 (23 March 2004).
  30. O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.
  31. M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).
  32. O. E. Marinescu, "Novel design methods for high-quality lithographic objectives," thesis, Delft University of Technology, Sieca, ISBN-13: 978-90-78314-02-8 (2006), also available at: http://wwwoptica.tn.tudelft.nl/publications/Thesis/Marinescu.pdf.
  33. M. F. Bal, F. Bociort, and J. J. M. Braat, "Analysis, search and classification for reflective ring-field projection systems," Appl. Opt. 42, 2301-2311 (2003).
  34. H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).
  35. N. Harned, L. Girard, P. Kuerz, and L. Marchetti, "State of the art optics polishing and metrology for EUV lithography mirrors," http://www.asml.com/asmldotcom/show.do?ctx=11140&rid=11141.

2006 (3)

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 634263420O (2006).

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 634263420M (2006).

O. E. Marinescu, "Novel design methods for high-quality lithographic objectives," thesis, Delft University of Technology, Sieca, ISBN-13: 978-90-78314-02-8 (2006), also available at: http://wwwoptica.tn.tudelft.nl/publications/Thesis/Marinescu.pdf.

2004 (6)

W. Ulrich, "8-mirror microlithography projection optics," U.S. patent 6,710,917 B2 (23 March 2004).

O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.

M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Networks of local minima in optical system optimization," Opt. Lett. 29, 189-191 (2004).

E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).

F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).

2003 (4)

F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).

D. W. Sweeney, "Extreme ultraviolet lithography," in Encyclopedia of optical Engineering (Marcel Dekker, 2003), pp. 485-491.

M. F. Bal, F. Bociort, and J. J. M. Braat, "Lithographic apparatus, device manufacturing method, and device manufactured thereby," U.S. patent 6,556,648 (29 April 2003).

M. F. Bal, F. Bociort, and J. J. M. Braat, "Analysis, search and classification for reflective ring-field projection systems," Appl. Opt. 42, 2301-2311 (2003).

2002 (2)

G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,396,067 (28 May 2002).

2001 (4)

R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,183,095 (6 February 2001).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,299,318 (9 October 2001).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,255,661 (3 July 2001).

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

2000 (4)

R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,033,079 (7 March 2000).

J. J. M. Braat, "Extreme UV lithography, "A candidate for next-generation lithography," Proc. SPIE 4016, 2-7 (2000).

K. Diefendorff, "Extreme lithography," Microprocessor Report 1-10 (Reed Elsevier, 19 June 2000).

S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).

1999 (1)

K. E. Moore, "Algorithm for global optimization of optical systems based on genetic competition," Proc. SPIE 3780, 40-47 (1999).

1998 (2)

N. Mousscau and G. T. Barkema, "Travelling through potential energy landscapes of disordered materials: the activation-relaxation technique," Phys. Rev. E 57, 2419-2424 (1998).

D. M. Williamson, "High numerical aperture ring field optical reduction system," U.S. patent 5,815,310 (29 September 1998).

1997 (2)

H. J. Levinson and W. H. Arnold, Handbook of Microlithography, Micromachining, and Microfabrication, Vol. PM39 of SPIE Press Monograph Series (SPIE Press, 1997), pp. 11-126.

D. R. Shafer, "Projection lithography system and method using all-reflective optical elements," U.S. patent 5,686,728 (11 November 1997).

1996 (1)

G. T. Barkema and N. Mousseau, "Event-based relaxation of continuous disordered systems," Phys. Rev. Lett. 77, 4358-4361 (1996).

1995 (1)

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

1992 (2)

T. G. Kuper and T. I. Harris, "Global optimization for lens design--an emerging technology," Proc. SPIE 1780, 14-28 (1992).

T. Kuper and T. Harris, "A New Look at Global Optimization for Optical Design," Photonics Spectra 151-160 (January 1992).

1991 (1)

G. W. Forbes and A. E. W. Jones, "Towards global optimization with adaptive simulated annealing," Proc. SPIE 1354, 144-151 (1991).

Arnold, W. H.

H. J. Levinson and W. H. Arnold, Handbook of Microlithography, Micromachining, and Microfabrication, Vol. PM39 of SPIE Press Monograph Series (SPIE Press, 1997), pp. 11-126.

Bal, M. F.

M. F. Bal, F. Bociort, and J. J. M. Braat, "Lithographic apparatus, device manufacturing method, and device manufactured thereby," U.S. patent 6,556,648 (29 April 2003).

M. F. Bal, F. Bociort, and J. J. M. Braat, "Analysis, search and classification for reflective ring-field projection systems," Appl. Opt. 42, 2301-2311 (2003).

Barkema, G. T.

N. Mousscau and G. T. Barkema, "Travelling through potential energy landscapes of disordered materials: the activation-relaxation technique," Phys. Rev. E 57, 2419-2424 (1998).

G. T. Barkema and N. Mousseau, "Event-based relaxation of continuous disordered systems," Phys. Rev. Lett. 77, 4358-4361 (1996).

Benschop, J.

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

Bociort, F.

O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.

F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Networks of local minima in optical system optimization," Opt. Lett. 29, 189-191 (2004).

E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).

M. F. Bal, F. Bociort, and J. J. M. Braat, "Lithographic apparatus, device manufacturing method, and device manufactured thereby," U.S. patent 6,556,648 (29 April 2003).

M. F. Bal, F. Bociort, and J. J. M. Braat, "Analysis, search and classification for reflective ring-field projection systems," Appl. Opt. 42, 2301-2311 (2003).

Braat, J.

O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.

Braat, J. J. M.

M. F. Bal, F. Bociort, and J. J. M. Braat, "Lithographic apparatus, device manufacturing method, and device manufactured thereby," U.S. patent 6,556,648 (29 April 2003).

M. F. Bal, F. Bociort, and J. J. M. Braat, "Analysis, search and classification for reflective ring-field projection systems," Appl. Opt. 42, 2301-2311 (2003).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,396,067 (28 May 2002).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,299,318 (9 October 2001).

J. J. M. Braat, "Mirror projection system for a scanning lithographic projection apparatus, and lithographic apparatus comprising such a system," U.S. patent 6,255,661 (3 July 2001).

J. J. M. Braat, "Extreme UV lithography, "A candidate for next-generation lithography," Proc. SPIE 4016, 2-7 (2000).

Derreumaux, P.

G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).

Descour, M. R.

S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).

Diefendorff, K.

K. Diefendorff, "Extreme lithography," Microprocessor Report 1-10 (Reed Elsevier, 19 June 2000).

Dinger, U.

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

Forbes, G. W.

G. W. Forbes and A. E. W. Jones, "Towards global optimization with adaptive simulated annealing," Proc. SPIE 1354, 144-151 (1991).

Gardner, L.

M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).

Girard, L.

N. Harned, L. Girard, P. Kuerz, and L. Marchetti, "State of the art optics polishing and metrology for EUV lithography mirrors," http://www.asml.com/asmldotcom/show.do?ctx=11140&rid=11141.

Gregory, G. G.

M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).

Harned, N.

N. Harned, L. Girard, P. Kuerz, and L. Marchetti, "State of the art optics polishing and metrology for EUV lithography mirrors," http://www.asml.com/asmldotcom/show.do?ctx=11140&rid=11141.

Harris, T.

T. Kuper and T. Harris, "A New Look at Global Optimization for Optical Design," Photonics Spectra 151-160 (January 1992).

Harris, T. I.

T. G. Kuper and T. I. Harris, "Global optimization for lens design--an emerging technology," Proc. SPIE 1780, 14-28 (1992).

Hiraga, K.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Hudyma, R.

R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,183,095 (6 February 2001).

R. Hudyma, "High numerical aperture ring field projection system for extreme ultraviolet lithography," U.S. patent 6,033,079 (7 March 2000).

Ishikawa, J.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Isshiki, M.

M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Jones, A. E. W.

G. W. Forbes and A. E. W. Jones, "Towards global optimization with adaptive simulated annealing," Proc. SPIE 1354, 144-151 (1991).

Kuerz, P.

N. Harned, L. Girard, P. Kuerz, and L. Marchetti, "State of the art optics polishing and metrology for EUV lithography mirrors," http://www.asml.com/asmldotcom/show.do?ctx=11140&rid=11141.

Kuper, T.

T. Kuper and T. Harris, "A New Look at Global Optimization for Optical Design," Photonics Spectra 151-160 (January 1992).

Kuper, T. G.

T. G. Kuper and T. I. Harris, "Global optimization for lens design--an emerging technology," Proc. SPIE 1780, 14-28 (1992).

Kurz, P.

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

Lerner, S. A.

S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).

Levinson, H. J.

H. J. Levinson and W. H. Arnold, Handbook of Microlithography, Micromachining, and Microfabrication, Vol. PM39 of SPIE Press Monograph Series (SPIE Press, 1997), pp. 11-126.

Marchetti, L.

N. Harned, L. Girard, P. Kuerz, and L. Marchetti, "State of the art optics polishing and metrology for EUV lithography mirrors," http://www.asml.com/asmldotcom/show.do?ctx=11140&rid=11141.

Marinescu, O.

O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.

Marinescu, O. E.

O. E. Marinescu, "Novel design methods for high-quality lithographic objectives," thesis, Delft University of Technology, Sieca, ISBN-13: 978-90-78314-02-8 (2006), also available at: http://wwwoptica.tn.tudelft.nl/publications/Thesis/Marinescu.pdf.

McGuire, J. P.

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 634263420O (2006).

Meiling, H.

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

Moore, K. E.

K. E. Moore, "Algorithm for global optimization of optical systems based on genetic competition," Proc. SPIE 3780, 40-47 (1999).

Mousscau, N.

N. Mousscau and G. T. Barkema, "Travelling through potential energy landscapes of disordered materials: the activation-relaxation technique," Phys. Rev. E 57, 2419-2424 (1998).

Mousseau, N.

G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).

G. T. Barkema and N. Mousseau, "Event-based relaxation of continuous disordered systems," Phys. Rev. Lett. 77, 4358-4361 (1996).

Nakadate, S.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Ono, H.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Rogers, J. R.

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 634263420M (2006).

Sasian, J. M.

S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).

Serebriakov, A.

F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).

E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Networks of local minima in optical system optimization," Opt. Lett. 29, 189-191 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).

Shafer, D. R.

D. R. Shafer, "Projection lithography system and method using all-reflective optical elements," U.S. patent 5,686,728 (11 November 1997).

Sweeney, D. W.

D. W. Sweeney, "Extreme ultraviolet lithography," in Encyclopedia of optical Engineering (Marcel Dekker, 2003), pp. 485-491.

Ulrich, W.

W. Ulrich, "8-mirror microlithography projection optics," U.S. patent 6,710,917 B2 (23 March 2004).

van Driel, E.

E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Networks of local minima in optical system optimization," Opt. Lett. 29, 189-191 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).

van Turnhout, M.

F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).

Wei, G.

G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).

Williamson, D. M.

D. M. Williamson, "High numerical aperture ring field optical reduction system," U.S. patent 5,815,310 (29 September 1998).

Appl. Opt. (1)

J. Chem. Phys. (1)

G. Wei, N. Mousseau, and P. Derreumaux, "Exploring the energy landscape of proteins: a characterization of the activation relaxation technique," J. Chem. Phys. 117, 11379-11387 (2002).

Opt. Eng. (1)

S. A. Lerner, J. M. Sasian, and M. R. Descour, "Design approach and comparison of projection cameras for EUV lithography," Opt. Eng. 39, 792-802 (2000).

Opt. Lett. (1)

Opt. Rev. (1)

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, "Lens design: global optimization with escape function," Opt. Rev. 6, 463-470 (1995).

Photonics Spectra (1)

T. Kuper and T. Harris, "A New Look at Global Optimization for Optical Design," Photonics Spectra 151-160 (January 1992).

Phys. Rev. E (1)

N. Mousscau and G. T. Barkema, "Travelling through potential energy landscapes of disordered materials: the activation-relaxation technique," Phys. Rev. E 57, 2419-2424 (1998).

Phys. Rev. Lett. (1)

G. T. Barkema and N. Mousseau, "Event-based relaxation of continuous disordered systems," Phys. Rev. Lett. 77, 4358-4361 (1996).

Proc. SPIE (12)

T. G. Kuper and T. I. Harris, "Global optimization for lens design--an emerging technology," Proc. SPIE 1780, 14-28 (1992).

H. Meiling, J. Benschop, U. Dinger, and P. Kurz, "Progress of the EUVL alpha tool," Proc. SPIE 4343, 38-50 (2001).

O. Marinescu, F. Bociort, and J. Braat, "Avoiding unstable regions in the design space of EUV mirror systems comprising high-order aspheric surfaces," Proc. SPIE 5523, 185-192 (2004) to be published in an updated version.

M. Isshiki, L. Gardner, and G. G. Gregory, "Automated control of manufacturing sensitivity during optimization," Proc. SPIE 5249, 343-352 (2004).

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 634263420O (2006).

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 634263420M (2006).

G. W. Forbes and A. E. W. Jones, "Towards global optimization with adaptive simulated annealing," Proc. SPIE 1354, 144-151 (1991).

K. E. Moore, "Algorithm for global optimization of optical systems based on genetic competition," Proc. SPIE 3780, 40-47 (1999).

E. van Driel, F. Bociort, and A. Serebriakov, "Topography of the merit function landscape in optical system design," Proc. SPIE 5249, 353-363 (2004).

F. Bociort, A. Serebriakov, and M. van Turnhout, "Saddle points in the merit function landscape of systems of thin lenses in contact," Proc. SPIE 5523, 174-184 (2004).

F. Bociort, E. van Driel, and A. Serebriakov, "Network structure of the set of local minima in optical system optimization," Proc. SPIE 5174, 26-34 (2003).

J. J. M. Braat, "Extreme UV lithography, "A candidate for next-generation lithography," Proc. SPIE 4016, 2-7 (2000).

Other (15)

K. Diefendorff, "Extreme lithography," Microprocessor Report 1-10 (Reed Elsevier, 19 June 2000).

code v, Optical Research Associates, Pasadena, Calif.

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Figures (8)

Fig. 1
Fig. 1

Illustration of the saddle point detection algorithm: (a) constraint local minimization in a set of hyperplanes orthogonal to s; (b) one-dimensional maximization along s.

Fig. 2
Fig. 2

Flow chart for the network search method.

Fig. 3
Fig. 3

Six-mirror microlithographic projection system with object heights between 114 and 118 mm, a numerical aperture of 0.16, and a magnification of 0.25. The aperture stop is placed at the second surface.

Fig. 4
Fig. 4

Network structure of a six-mirror system search with the specifications of the system shown in Fig. 3, where s represents saddle points, and m represents minima. The value of the merit function is also shown.

Fig. 5
Fig. 5

Network structure at reduced numerical aperture and field.

Fig. 6
Fig. 6

Network structure with real telecentricity requirement in the image space.

Fig. 7
Fig. 7

Optimized six-mirror projection system for EUV lithography. The aperture stop is situated at the second mirror. The system is unobstructed. At the wafer side the system is telecentric, i.e., the chief ray is (approximately) perpendicular on the image plane.

Fig. 8
Fig. 8

0.3 numerical aperture six-mirror projection system for EUV lithography.

Tables (4)

Tables Icon

Table 1 Specifications for the Optimized EUV Mirror System Presented in Fig. 7

Tables Icon

Table 2 Chief-Ray Angles of Incidence and the Angular Spread in the EUV Mirror System Shown in Fig. 7

Tables Icon

Table 3 Specifications and Performance of the Optimized EUV Mirror System Shown in Fig. 8

Tables Icon

Table 4 Chief Ray Angles of Incidence for the EUV Mirror System Presented in Fig. 9

Equations (4)

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F ( x 1 , x 2 , … ,  x N ) = F 0 + H i j x i x j ,
H i j = 1 2 2 F x i x j
F ( x ¯ 1 , x ¯ 2 , , x ¯ N ) = F 0 + λ i x ¯ i 2 ,
s 1 x 1 + s 2 x 2 + + s N x N = t ,

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