Abstract

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy.

© 2006 Optical Society of America

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References

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  1. T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
    [CrossRef]
  2. K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).
  3. P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).
  4. J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).
  5. F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, "Aberration measurement of projection optics in lithographic tools by use of an alternating phase shifting mask," Appl. Opt. 45, 281-287 (2006).
    [CrossRef] [PubMed]
  6. K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).
  7. B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).
  8. H. Nomura and T. Sato, "Techniques for measuring aberrations in lenses used in photolithography with printed patterns," Appl. Opt. 38, 2800-2807 (1999).
    [CrossRef]
  9. H. Nomura, K. Tawarayama, and T. Kohno, "Aberration measurement from specific photolithographic images: a different approach," Appl. Opt. 39, 1136-1147 (2000).
    [CrossRef]
  10. J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).
  11. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press 1999), pp. 517-543.

2006 (1)

2004 (1)

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).

2003 (2)

K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

2002 (2)

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).

2001 (1)

J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).

2000 (1)

1999 (1)

1997 (1)

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press 1999), pp. 517-543.

Brunner, T.

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

Chen, J. J.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Conley, W.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).

Flagello, D. G.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Fu, S. C.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Gallatin, G. M.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).

Garreis, R. B.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Garza, C. M.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).

Goehnermeier, A.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Graeupner, P.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Heil, T.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Hirukawa, S.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).

Ho, C. T.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Hu, J.

Huang, C.-M.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Kirk, J. P.

J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).

Kohno, T.

Kunkel, G.

J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).

Kuo, C.-S.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Lai, K.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).

Lowisch, M.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

Ma, M.

Matsumoto, K.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).

Matsuyama, T.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).

Nomura, H.

Sato, T.

Shi, W.

Shiu, F.-J.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Smith, B. W.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).

Tawarayama, K.

Tsai, J. H.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

van de Kerkhof, M. A.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).

Wang, C.

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

Wang, F.

Wang, X.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press 1999), pp. 517-543.

Wong, A. K.

J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).

Zhang, D.

Appl. Opt. (3)

IBM J. Res. Dev. (1)

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

Other (7)

K. Matsumoto, T. Matsuyama, and S. Hirukawa, "Analysis of imaging performance degradation," in Proc. SPIE 5040, 119-130 (2003).

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Proc. SPIE 5040, 119-130 (2003).

J. J. Chen, C.-M. Huang, F.-J. Shiu, C.-S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, "Influence of coma effect on scanner overlay," in Proc. SPIE 4689, 280-285 (2002).

J. P. Kirk, G. Kunkel, and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," in Proc. SPIE 4346, 8-11 (2001).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press 1999), pp. 517-543.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Proc. SPIE 5377, 160-171 (2004).

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157 nm exposure system," in Proc. SPIE 4691, 1635-1643 (2002).

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Figures (10)

Fig. 1
Fig. 1

(Color online) Schematic of two-beam interference imaging.

Fig. 2
Fig. 2

(Color online) Measurement mark.

Fig. 3
Fig. 3

Schematic of the cross section of the fine grating pattern.

Fig. 4
Fig. 4

Sketch map of traditional box-in-bars mark.

Fig. 5
Fig. 5

Diffraction beams at the lens pupil.

Fig. 6
Fig. 6

Simulation results of the sensitivity of coma aberration.

Fig. 7
Fig. 7

Simulation results of the sensitivity of three-foil aberration.

Fig. 8
Fig. 8

Simulation results of the sensitivity of astigmatism aberration.

Fig. 9
Fig. 9

Input wavefront error for simulation.

Fig. 10
Fig. 10

(Color online) Comparison of the input and output wavefront error.

Tables (8)

Tables Icon

Table 1 Zernike Polynomials from First to Thirty-Seventh Orders

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Table 2 Conditions for Simulation

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Table 3 Variation Ranges of the Sensitivity of Coma Aberration

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Table 4 Measurement Accuracy of Coma Aberration in Different Techniques

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Table 5 Variation Ranges of the Sensitivity of Three-Foil Aberration

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Table 6 Measurement Accuracy of Three-Foil Aberration in Different Techniques

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Table 7 Variation Ranges of the Sensitivity of Astigmatism Aberration

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Table 8 Measurement Accuracy of Astigmatism Aberration in Different Techniques

Equations (26)

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

W ( ρ , θ ) = Z 1 + Z 2 ρ cos θ + Z 3 ρ sin θ + Z 4 ( 2 ρ 2 1 ) + Z 5 ρ 2 cos 2 θ + Z 6 ρ 2 sin 2 θ + Z 7 ( 3 ρ 2 2 ) ρ × cos θ + Z 8 ( 3 ρ 2 2 ) ρ sin θ +   ,
t ( x ) = { rect [ x + ( 3 / 8 ) P P / 4 ] + e / 2 rect ( x P / 2 ) + e j π rect [ x - ( 3 / 8 ) P P / 4 ] } [ 1 P comb ( x P ) ] .
E ( f x ) = { P 4 sin c ( P 4 f x ) [ e j π 3 ( P / 4 ) f x + e j [ π - π 3 ( P / 4 ) f x ] ] + P 2 sin c ( P 2 f x ) e j π / 2 } comb ( P f x ) = 1 2 j [ sin ( 3 π P 4 f x ) sin c ( P 4 f x ) + sin c ( P 2 f x ) ] × n = - δ ( f x - n P ) ,   n Z ,
λ NA P 2 λ NA ( 1 + σ ) ,
E ( f x ) = 1 2 j [ δ ( f x ) + 2 π δ ( f x 1 P ) ] .
I ( x , y ) = S σ + 1 J ( f x , f y ) | S E ( f x - f x , f y - f y ) × e j 2 π [ ( f x - f x ) x + ( f y - f y ) y ] d f x d f y | 2 d f x d f y = S σ + 1 J ( f x , f y ) [ 1 2 + 2 π 2 + 2 π cos ( 2 π x P ) ] d f x d f y ,
I ( x , y ) = S σ + 1 J ( f x , f y ) | S E ( f x - f x , f y - f y ) × e j 2 π [ ( f x - f x ) x + ( f y - f y ) y ] × e j 2 π λ W ( f x , f y ) d f x d f y | 2 d f x d f y = S σ + 1 J ( f x , f y ) { 1 2 + 2 π 2 + 2 π cos [ 2 π λ ( x P λ + W 0 ° ( f x + 1 p , f y ) W 0 ° ( f x , f y ) ) ] } d f x d f y ,
Δ x 0 ° = - P λ S σ + 1 J ( f x , f y ) [ W 0 ° ( f x + 1 P , f y ) W 0 ° ( f x , f y ) ] d f x d f y S σ + 1 J ( f x , f y ) d f x d f y ,
Δ x 0 ° = P λ S σ + 1 J ( ρ , θ ) [ W 0 ° ( ρ 1 , θ 1 ) W 0 ° ( ρ , θ ) ] ρ d ρ d θ S σ + 1 J ( ρ , θ ) ρ d ρ d θ ,
Δ x 180 ° = P λ S σ + 1 J ( ρ , θ ) [ W 180 ° ( ρ 1 , θ 1 ) W 180 ° ( ρ , θ ) ] ρ d ρ d θ S σ + 1 J ( ρ , θ ) ρ d ρ d θ ,
Δ y b = P λ S σ + 1 J ( ρ , θ ) [ W b ( ρ 1 , θ 1 ) W b ( ρ , θ ) ] ρ d ρ d θ S σ + 1 J ( ρ , θ ) ρ d ρ d θ ,
b = 90 ° , 270 ° .
W 0 ° ( ρ 1 , θ 1 ) W 0 ° ( ρ , θ ) = W 180 ° ( ρ 1 , θ 1 ) W 180 ° ( ρ , θ ) ,
W 90 ° ( ρ 1 , θ 1 ) W 90 ° ( ρ , θ ) = [ W 270 ° ( ρ 1 , θ 1 ) W 270 ° ( ρ , θ ) ] .
W 0 ° ( ρ 1 , θ 1 ) W 0 ° ( ρ , θ ) = [ W 180 ° ( ρ 1 , θ 1 ) W 180 ° ( ρ , θ ) ] ,
W 90 ° ( ρ 1 , θ 1 ) W 90 ° ( ρ , θ ) = W 270 ° ( ρ 1 , θ 1 ) W 270 ° ( ρ , θ ) .
Δ x Y 1 + Δ x Y 2 = ( Δ x 0 ° Δ x 2 ) + ( Δ x 180 ° Δ x 2 ) = S Z m Z m + C 1 ( m = 7 , 10 , 14 , 19 , 23 , 26 , 30 , 34 ) ,
Δ y X 1 + Δ y X 2 = ( Δ y 90 ° Δ y 2 ) + ( Δ y 270 ° Δ y 2 ) = S Z n Z n + C 2 ( n = 8 , 11 , 15 , 20 , 24 , 27 , 31 , 35 ) ,
Δ x Y 1 Δ x Y 2 = ( Δ x 0 ° Δ x 2 ) ( Δ x 180 ° Δ x 2 ) = S Z l Z l ( l = 4 , 5 , 9 , 12 , 16 , 17 , 21 , 25 ) ,
S Z j = 2 P λ 1 Z j S σ + 1 J ( ρ , θ ) [ W j c ( ρ 1 , θ 1 ) - W j c ( ρ , θ ) ] ρ d ρ d θ S σ + 1 J ( ρ , θ ) ρ d ρ d θ , { if     j = m , l , c = 0 ° if     j = n , c = 90 ° ,
{ Δ x Y 1 ( P 1 ) + Δ x Y 2 ( P 1 ) = S Z m ( P 1 ) Z m + C 1 Δ x Y 1 ( P 2 ) + Δ x Y 2 ( P 2 ) = S Z m ( P 2 ) Z m + C 1 Δ x Y 1 ( P 3 ) + Δ x Y 2 ( P 3 ) = S Z m ( P 3 ) Z m + C 1 ,
( m = 7 , 10 , 14 , 19 , 23 , 26 , 30 , 34 ) .
H 1 = k z 7 Z 7 + k z 14 Z 14 + k z 23 Z 23 + k z 34 Z 34 ,
MA Z k MA r | ( S Z k ) max ( S Z k ) min | ,
MA Z k MA f | ( S Z k ) max ( S Z k ) min | ,
S Z n = Δ x Z n Z n = Δ x Z n = 1   nm .

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