Abstract

The design of multilayer mirrors with more than two materials is one of the key technologies for investigating lithography. We study a new procedure for optimizing multilayer mirrors of different combinations of materials at a wavelength of 13.4nm. By adding Be and C layers in different orders to a Si/Mo stack, we have observed enhancement of the reflectivity and a reduction in the number of layers. The Luus–Jaakola optimization procedure has been implemented for the global optimization of the multilayer mirrors. With this algorithm it is not necessary to specify initially the number of layers present in a given design.

© 2008 Optical Society of America

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References

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  12. R. Luus and T. Jaakola, “Optimization by direct search and systematic reduction of the size of search region,” AIChE. J. 19, 760-766 (1973).
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  13. R. Luus, “Use of Luus-Jaakola optimization procedure for singular optimal control problems,” Nonlinear Anal. 47, 5647-5658 (2001).
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  14. R. Luus, “Optimization of heat exchanger networks,” Ind. Eng. Chem. 32, 2633-2635 (1993).
    [CrossRef]
  15. Y. P. Lee, G. P. Rangahiah, and R. Luus, “Phase and chemical equilibrium calculations by direct search optimization,” Comput. Chem. Eng. 23, 1183 (1999); http://www.ingentaconnect.com/content/els/00981354/1999/00000023/00000009/art00283.
    [CrossRef]
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    [CrossRef]

2006 (1)

S. Al-Marzoug and R. Hodgson, “Luus-Jaakola optimization procedure for multilayer optical coatings,” Opt. Commun. 265, 234-240 (2006).
[CrossRef]

2005 (2)

B. Liao and R. Luus, “Comparison of the Luus-Jaakola optimization procedure and the genetic algorithm,” Eng. Optimiz. 37, 381-398 (2005).
[CrossRef]

S. Yulin, T. Feigl, N. Benoit, and N. Kaiser, “EUV/soft x-ray multilayer optics,” Proc. SPIE 5645, 289-298 (2005).
[CrossRef]

2004 (2)

P. Binda and F. Zocchi, “Genetic algorithm optimization of x-ray multilayer coatings,” Proc. SPIE 5536, 97-108 (2004).
[CrossRef]

V. Cotroneo and G. Pareschi, “Global optimization of x-ray multilayer mirrors with iterated simplex method,” Proc. SPIE 5536, 49-60 (2004).
[CrossRef]

2002 (2)

2001 (3)

R. Luus, “Use of Luus-Jaakola optimization procedure for singular optimal control problems,” Nonlinear Anal. 47, 5647-5658 (2001).
[CrossRef]

K. Powell, J. Tait, and A. Michette, “Simulated annealing in the design of broadband multilayers containing more than two materials,” Proc. SPIE 4145, 254-256 (2001).
[CrossRef]

S. Bajt, J. Alameda, T. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. Spiller, “Improved reflectance and stability of Mo/Si multilayers,” Proc. SPIE 4506, 65-75 (2001).
[CrossRef]

2000 (1)

1999 (2)

J. Folta, S. Bajt, T. Barbee Jr., R. Grabner, P. Mirkarimi, T. Nguyen, M. Schmidt, E. Spiller, C. Walton, M. Wedowski, and C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” Proc. SPIE 3676, 702-709 (1999).
[CrossRef]

Y. P. Lee, G. P. Rangahiah, and R. Luus, “Phase and chemical equilibrium calculations by direct search optimization,” Comput. Chem. Eng. 23, 1183 (1999); http://www.ingentaconnect.com/content/els/00981354/1999/00000023/00000009/art00283.
[CrossRef]

1998 (1)

R. Luus, “Determination of the region sizes for LJ optimization procedure,” Hung. J. Ind. Chem. 26, 281-286 (1998).

1996 (1)

1995 (1)

1993 (2)

1973 (1)

R. Luus and T. Jaakola, “Optimization by direct search and systematic reduction of the size of search region,” AIChE. J. 19, 760-766 (1973).
[CrossRef]

1954 (1)

L. G. Parratt, “Surface studies of soilds by total reflecation of x-ray,” Phys. Rev. 95, 359-369 (1954).
[CrossRef]

AIChE. J. (1)

R. Luus and T. Jaakola, “Optimization by direct search and systematic reduction of the size of search region,” AIChE. J. 19, 760-766 (1973).
[CrossRef]

Appl. Opt. (4)

Comput. Chem. Eng. (1)

Y. P. Lee, G. P. Rangahiah, and R. Luus, “Phase and chemical equilibrium calculations by direct search optimization,” Comput. Chem. Eng. 23, 1183 (1999); http://www.ingentaconnect.com/content/els/00981354/1999/00000023/00000009/art00283.
[CrossRef]

Eng. Optimiz. (1)

B. Liao and R. Luus, “Comparison of the Luus-Jaakola optimization procedure and the genetic algorithm,” Eng. Optimiz. 37, 381-398 (2005).
[CrossRef]

Hung. J. Ind. Chem. (1)

R. Luus, “Determination of the region sizes for LJ optimization procedure,” Hung. J. Ind. Chem. 26, 281-286 (1998).

Ind. Eng. Chem. (1)

R. Luus, “Optimization of heat exchanger networks,” Ind. Eng. Chem. 32, 2633-2635 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nonlinear Anal. (1)

R. Luus, “Use of Luus-Jaakola optimization procedure for singular optimal control problems,” Nonlinear Anal. 47, 5647-5658 (2001).
[CrossRef]

Opt. Commun. (1)

S. Al-Marzoug and R. Hodgson, “Luus-Jaakola optimization procedure for multilayer optical coatings,” Opt. Commun. 265, 234-240 (2006).
[CrossRef]

Phys. Rev. (1)

L. G. Parratt, “Surface studies of soilds by total reflecation of x-ray,” Phys. Rev. 95, 359-369 (1954).
[CrossRef]

Proc. SPIE (6)

S. Yulin, T. Feigl, N. Benoit, and N. Kaiser, “EUV/soft x-ray multilayer optics,” Proc. SPIE 5645, 289-298 (2005).
[CrossRef]

S. Bajt, J. Alameda, T. Barbee, W. M. Clift, J. A. Folta, B. Kaufmann, and E. Spiller, “Improved reflectance and stability of Mo/Si multilayers,” Proc. SPIE 4506, 65-75 (2001).
[CrossRef]

P. Binda and F. Zocchi, “Genetic algorithm optimization of x-ray multilayer coatings,” Proc. SPIE 5536, 97-108 (2004).
[CrossRef]

V. Cotroneo and G. Pareschi, “Global optimization of x-ray multilayer mirrors with iterated simplex method,” Proc. SPIE 5536, 49-60 (2004).
[CrossRef]

K. Powell, J. Tait, and A. Michette, “Simulated annealing in the design of broadband multilayers containing more than two materials,” Proc. SPIE 4145, 254-256 (2001).
[CrossRef]

J. Folta, S. Bajt, T. Barbee Jr., R. Grabner, P. Mirkarimi, T. Nguyen, M. Schmidt, E. Spiller, C. Walton, M. Wedowski, and C. Montcalm, “Advances in multilayer reflective coatings for extreme-ultraviolet lithography,” Proc. SPIE 3676, 702-709 (1999).
[CrossRef]

Other (1)

Lawrence Livermore National Laboratory optical constants database, ftp://www-phys.llnl.gov/pub/rayleigh.

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Figures (6)

Fig. 1
Fig. 1

Optical constants for Si, Mo, Be, and C at 13.4 nm .

Fig. 2
Fig. 2

Ideal standard Mo/Si multilayers (top left) consist of alternating Mo and Si layers. Three-component multilayer mirror (right) consists of Mo and Si layers separated with barriers. Three-component multilayers (bottom left) consists of three Mo, Si, and Be layers.

Fig. 3
Fig. 3

Optimized reflectivity (left) of multilayer mirrors from Table 1 at a wavelength of 13.4 nm and using the thickness design of a Mo/Si bilayer.

Fig. 4
Fig. 4

Optimized reflectivity of multilayer mirrors with barrier layer Be (left) and with barrier layer C (right) at the wavelength 13.4 nm .

Fig. 5
Fig. 5

Thickness design of Si/Be/Mo/Be stack.

Fig. 6
Fig. 6

Optimized reflectivity of multialyer mirrors with a third layer Be (top) and with a third layer C (bottom) at the wavelength 13.4 nm .

Tables (4)

Tables Icon

Table 1 Parameters for LJ Optimization

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Table 2 Optimized Normal Incidence Reflectances of Standard Multilayer Mirrors at 13.4 nm

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Table 3 Optimized Normal Incidence Reflectance of Multilayer Mirrors, Barrier at 13.4 nm

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Table 4 Optimized Normal Incidence Reflectance of Multilayer Mirrors, Three-Component Materials at 13.4 nm

Equations (1)

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FOM = 1 N i = 1 N [ R ( λ i ) - R des ( λ ) ] 2

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