Abstract

We discuss the aberration-induced intensity imbalance of alternating phase-shifting mask (Alt-PSM) in lithographic imaging, in contrast to numerous studies on mask-induced intensity imbalance. Based on the Hopkins theory of partial coherent imaging, a linear relationship between the intensity difference of adjacent peaks in an Alt-PSM image and even aberration is established by formulations and verified by numerical results. The application of the linear relationship is briefly discussed.

© 2010 Optical Society of America

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Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

2007

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

2006

2003

2002

K. Adam and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 1, 253 (2002).
[CrossRef]

2001

J. P. Kirk, S. Schank, and C.-Y. LinProc. SPIE 4346, 1355 (2001).
[CrossRef]

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

1998

R. L. Gordon, C. A. Mack, and J. S. Petersen, Proc. SPIE 3546, 606 (1998).
[CrossRef]

1953

H. H. Hopkins, Proc. R. Soc. London Ser. A 217, 408 (1953).
[CrossRef]

Adam, K.

K. Adam and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 1, 253 (2002).
[CrossRef]

Cao, Y.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Chen, G.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Chen, L.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Dierichs, M.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Feng, M.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Gordon, R. L.

R. L. Gordon, C. A. Mack, and J. S. Petersen, Proc. SPIE 3546, 606 (1998).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Proc. R. Soc. London Ser. A 217, 408 (1953).
[CrossRef]

Jiang, J.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Johnson, E.

Kirk, J. P.

J. P. Kirk, S. Schank, and C.-Y. LinProc. SPIE 4346, 1355 (2001).
[CrossRef]

Lee, S.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Lee, S. -W.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Lin, C. -Y.

J. P. Kirk, S. Schank, and C.-Y. LinProc. SPIE 4346, 1355 (2001).
[CrossRef]

Liu, H. -Y.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Liu, P.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Ma, M.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Mack, C. A.

R. L. Gordon, C. A. Mack, and J. S. Petersen, Proc. SPIE 3546, 606 (1998).
[CrossRef]

McCoo, E.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Neureuther, A. R.

K. Adam and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 1, 253 (2002).
[CrossRef]

Petersen, J. S.

R. L. Gordon, C. A. Mack, and J. S. Petersen, Proc. SPIE 3546, 606 (1998).
[CrossRef]

Pitchumani, M.

Pongers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Qiu, Z.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Schank, S.

J. P. Kirk, S. Schank, and C.-Y. LinProc. SPIE 4346, 1355 (2001).
[CrossRef]

Stoffels, F.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Suh, S.

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

Sung, J.

Tirapu-Azpiroz, J.

van der Laan, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

van Greevenbroek, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Wang, F.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Wang, X.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Willekers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

Yablonovitch, E.

Yuan, Q.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Appl. Opt.

J. Microlithogr. Microfabr. Microsyst.

K. Adam and A. R. Neureuther, J. Microlithogr. Microfabr. Microsyst. 1, 253 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Microelectron. Eng.

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, Microelectron. Eng. 86, 78 (2009).
[CrossRef]

Proc. R. Soc. London Ser. A

H. H. Hopkins, Proc. R. Soc. London Ser. A 217, 408 (1953).
[CrossRef]

Proc. SPIE

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, Proc. SPIE 4346, 394 (2001).
[CrossRef]

R. L. Gordon, C. A. Mack, and J. S. Petersen, Proc. SPIE 3546, 606 (1998).
[CrossRef]

P. Liu, Y. Cao, L. Chen, G. Chen, M. Feng, J. Jiang, H.-Y. Liu, S. Suh, S.-W. Lee, and S. Lee, Proc. SPIE 6520, 65200R (2007).
[CrossRef]

J. P. Kirk, S. Schank, and C.-Y. LinProc. SPIE 4346, 1355 (2001).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Illustration of an optical lithography imaging system. (b) Top-down and (c) transverse views of an Alt-PSM mask.

Fig. 2
Fig. 2

Goodness of linearity between intensity difference and even aberration. (a) Intensity difference of adjacent peaks in the Alt-PSM image as a function of aberration. (b) Residual of first-degree polynomial fitting as a function of aberration ( L = 100   nm , W = 200   nm , NA = 0.5 , σ = 0.28 , φ = 90 ° ).

Equations (16)

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I ( x i ̂ , y i ̂ ) = + TCC ( f ̂ , g ̂ ; f ̂ , g ̂ ) O ( f ̂ , g ̂ ) O ( f ̂ , g ̂ ) e i 2 π [ ( f ̂ f ̂ ) x i ̂ + ( g ̂ g ̂ ) y i ̂ ] d f ̂ d g ̂ d f ̂ d g ̂ ,
TCC ( f ̂ , g ̂ ; f ̂ , g ̂ ) = + J ( f ̂ , g ̂ ) H ( f ̂ + f ̂ , g ̂ + g ̂ ) H ( f ̂ + f ̂ , g ̂ + g ̂ ) d f ̂ d g ̂ ,
O ( f ̂ ) = W L + W n = N + N δ ( f ̂ n λ ( 2 L + 2 W ) NA ) sinc ( W NA λ f ̂ ) exp ( i φ 2 ) cos [ 2 π ( L + W ) NA λ f ̂ + φ 2 ] ,
I ( x i ̂ ) = C 1 + C 3   cos ( 4 π f 0 ̂ x i ̂ + ϕ ) ,
I ( x i ̂ ) = C 1 + C 2   sin ( 2 π f 0 ̂ x i ̂ ) + C 3   cos ( 4 π f 0 ̂ x i ̂ ) ,
c = ( W L + W ) 2 ,
C 1 = c [ 2   TCC ( f 0 ̂ , 0 ; f 0 ̂ , 0 ) sinc 2 ( W NA λ f 0 ̂ ) sin 2 ( φ 2 ) + TCC ( 0 , 0 ; 0 , 0 ) cos 2 ( φ 2 ) ] ,
C 2 = 2 c   sinc ( W NA λ f 0 ̂ ) sin ( φ ) Im [ TCC ( f 0 ̂ , 0 ; 0 , 0 ) ] ,
C 3 = 2 c sinc 2 ( W NA λ f 0 ̂ ) sin 2 ( φ 2 ) TCC ( f 0 ̂ , 0 ; f 0 ̂ , 0 ) ,
ϕ = A rg [ TCC ( f 0 ̂ , 0 ; f 0 ̂ , 0 ) ] .
I diff = 2 C 2 = n = 1 37 S n Z n ,     n Z ,
S n = 8 π λ c   sinc ( W NA λ f 0 ̂ ) sin ( φ ) + J ( f ̂ , g ̂ ) [ R n ( f ̂ , g ̂ ) R n ( f ̂ + f 0 ̂ , g ̂ ) ] d f ̂ d g ̂ .
O ( f ̂ ) = W 2 L + 2 W n = N + N δ ( f ̂ n λ ( 2 L + 2 W ) NA ) sinc ( W   NA   f ̂ λ ) [ t 1 e i α e i π f ̂ ( NA / λ ) ( L + W ) + t 2 e i ( β + φ ) e i π f ̂ ( NA / λ ) ( L + W ) ] ,     n Z ,
I diff = C + n = 1 37 S n Z n ,     n Z ,
C = 2 c   sinc ( W   NA   f 0 ̂ λ ) ( t 2 2 t 1 2 ) + J ( f ̂ , g ̂ ) d f ̂ d g ̂ ,
S n = 8 π λ c t 1 t 2   sin ( β + φ α ) sinc ( W   NA   f 0 ̂ λ ) + J ( f ̂ , g ̂ ) [ R n ( f ̂ , g ̂ ) R n ( f ̂ + f 0 ̂ , g ̂ ) ] d f ̂ d g ̂ .

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