Abstract

Optical proximity correction (OPC) and phase-shifting mask (PSM) are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. Traditional RETs, however, fix the source thus limiting the degrees of freedom during the optimization of the mask patterns. To overcome this restriction, a set of simultaneous source and mask optimization (SMO) methods have been developed recently where the resulting source and mask patterns fall well outside the realm of known design forms. This paper focuses on developing computationally efficient, pixel-based, simultaneous source mask optimization methods for both OPC and PSM designs, where the synergy is exploited in the joint optimization of source and mask patterns. The Fourier series expansion model is applied to approximate the partially coherent system as a sum of coherent systems. Cost sensitivity is used to drive the output pattern error in the descent direction. In order to influence the solution patterns to have more desirable manufacturability properties, topological constraints are added to the optimization framework. Several illustrative simulations are presented to demonstrate the effectiveness of the proposed algorithms.

© 2009 Optical Society of America

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References

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  1. A. K. Wong, Resolution Enhancement Techniques (SPIE Press, Bellingham, Washington, 2001).
    [CrossRef]
  2. S. A. Campbell, The Science and Engineering of MicroelectronicFfabrication, 2nd ed. (Publishing House of Electronics Industry, Beijing, 2003).
  3. F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future, Optical Microlithography," Proc. SPIE 5377, 1-20 (2004).
    [CrossRef]
  4. F. Schellenberg, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2004).
  5. L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
    [CrossRef]
  6. A. Poonawala and P. Milanfar, "Fast and low-complexity mask design in optical microlithography - An inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
    [CrossRef] [PubMed]
  7. M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
    [CrossRef]
  8. X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," in Proc. SPIE (San Jose, CA, 2007).
  9. X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007)
    [CrossRef]
  10. P. S. Davids and S. B. Bollepalli, "Generalized inverse problem for partially coherent projection lithography," Proc. SPIE 6924, 69240X (2008).
    [CrossRef]
  11. X. Ma and G. R. Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," Proc. SPIE 7140, 71401A (2008).
    [CrossRef]
  12. X. Ma and G. R. Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," J. Opt. Soc. Am. A 25, 2960-2970 (2008).
    [CrossRef]
  13. X. Ma and G. R. Arce, "PSM design for inverse lithography using illumination with samll partial coherence factor," in Proc. SPIE (San Jose, CA, 2009).
  14. X. Ma and G. R. Arce, "PSM design for inverse lithography with partially coherent illumination," Opt. Express 16, 20126-20141 (2008).
    [CrossRef]
  15. M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
    [CrossRef]
  16. T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
    [CrossRef]
  17. A. E. Rosenbluth, S. Bukofsky, C. Fonseca, and M. Hibbs, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., and Microsyst. 1, 13-30 (2002).
    [CrossRef]
  18. C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).
  19. S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
    [CrossRef]
  20. B. E. A. Saleh and M. Rabbani, "Simulation of partially coherent imagery in the space and frequency domains and by modal expansion," Appl. Opt. 21, 2770-2777 (1982).
    [CrossRef] [PubMed]
  21. Y. C. Pati and T. Kailath, "Phase-shifting masks for microlithography: Automated design and mask requirements," J. Opt. Soc. Am. A 11, 2438-2452 (1994).
    [CrossRef]
  22. M. Born and E. Wolfe, Principles of Optics (Cambridge University Press, 1999).
  23. R. Wilson, Fourier Series and Optical Transform Techniques in Contemporary Optics (John Wiley and Sons, 1995).
  24. P. Yu and D. Z. Pan, "TIP-OPC: a new topological invariant paradigm for pixel based optical proximity correction," in Proc. ACM/IEEE International Conference on Computer-Aided Design (ICCAD) (2007).
  25. L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
    [CrossRef]

2008

P. S. Davids and S. B. Bollepalli, "Generalized inverse problem for partially coherent projection lithography," Proc. SPIE 6924, 69240X (2008).
[CrossRef]

X. Ma and G. R. Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," Proc. SPIE 7140, 71401A (2008).
[CrossRef]

X. Ma and G. R. Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," J. Opt. Soc. Am. A 25, 2960-2970 (2008).
[CrossRef]

X. Ma and G. R. Arce, "PSM design for inverse lithography with partially coherent illumination," Opt. Express 16, 20126-20141 (2008).
[CrossRef]

2007

X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007)
[CrossRef]

A. Poonawala and P. Milanfar, "Fast and low-complexity mask design in optical microlithography - An inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

2005

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
[CrossRef]

2004

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future, Optical Microlithography," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

2001

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

2000

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

1998

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

1994

1992

L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
[CrossRef]

1982

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
[CrossRef]

B. E. A. Saleh and M. Rabbani, "Simulation of partially coherent imagery in the space and frequency domains and by modal expansion," Appl. Opt. 21, 2770-2777 (1982).
[CrossRef] [PubMed]

Arce, G. R.

Bollepalli, S. B.

P. S. Davids and S. B. Bollepalli, "Generalized inverse problem for partially coherent projection lithography," Proc. SPIE 6924, 69240X (2008).
[CrossRef]

Burkhardt, M.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

Chen, C. K.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Conley, W.

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

David, L.

S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
[CrossRef]

Davids, P. S.

P. S. Davids and S. B. Bollepalli, "Generalized inverse problem for partially coherent projection lithography," Proc. SPIE 6924, 69240X (2008).
[CrossRef]

Dunham, T.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Gau, T. S.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Ham, Y.

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

Hsia, C. C.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Kailath, T.

Lai, C. M.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Lam, L.

L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
[CrossRef]

Lavin, M.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Lee, S. W.

L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
[CrossRef]

Leipold, W.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Levenson, M. D.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
[CrossRef]

Liang, F. J.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Liebmann, L.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Liu, R. G.

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

Ma, X.

Mansfield, S.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Milanfar, P.

A. Poonawala and P. Milanfar, "Fast and low-complexity mask design in optical microlithography - An inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

Pati, Y. C.

Poonawala, A.

A. Poonawala and P. Milanfar, "Fast and low-complexity mask design in optical microlithography - An inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

Progler, C.

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

Rabbani, M.

Robert, S.

S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
[CrossRef]

Saleh, B. E. A.

Schellenberg, F.

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future, Optical Microlithography," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

Shi, X.

S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
[CrossRef]

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
[CrossRef]

Socha, B.

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

Suen, C. Y.

L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
[CrossRef]

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
[CrossRef]

Wells, G.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

Wong, A.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

Yen, A.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

Appl. Opt.

IBM J. Res. Dev.

L. Liebmann, S. Mansfield, A. Wong, M. Lavin, W. Leipold, and T. Dunham, "TCAD development for lithography resolution enhancement," IBM J. Res. Dev. 45, 651-665 (2001).
[CrossRef]

IEEE Trans. Electron. Devices

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, "Improving resolution in photolithography with a phase-shifting mask," IEEE Trans. Electron. Devices ED-29, 1828-1836 (1982).
[CrossRef]

IEEE Trans. Image Process.

A. Poonawala and P. Milanfar, "Fast and low-complexity mask design in optical microlithography - An inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell.

L. Lam, S. W. Lee, and C. Y. Suen, "Thinning methodologies-a comprehensive survey," IEEE Trans. Pattern Anal. Mach. Intell. 14, 869-885 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Microelectron. Eng.

M. Burkhardt, A. Yen, C. Progler, and G. Wells, "Illuminator design for the printing of regular contact patterns," Microelectron. Eng. 41, 91-95 (1998).
[CrossRef]

Opt. Express

Proc. SPIE

T. S. Gau, R. G. Liu, C. K. Chen, C. M. Lai, F. J. Liang, and C. C. Hsia, "The customized illumination aperture filter for low k1 photolithography process," Proc. SPIE 4000, 271-282 (2000).
[CrossRef]

P. S. Davids and S. B. Bollepalli, "Generalized inverse problem for partially coherent projection lithography," Proc. SPIE 6924, 69240X (2008).
[CrossRef]

X. Ma and G. R. Arce, "Binary mask optimization for inverse lithography with partially coherent illumination," Proc. SPIE 7140, 71401A (2008).
[CrossRef]

C. Progler, W. Conley, B. Socha, and Y. Ham, "Layout and source dependent phase mask transmission tuning," Proc. SPIE 5454, 315-326 (2005).

S. Robert, X. Shi, and L. David, "Simultaneous source mask optimization (SMO)," Proc. SPIE 5853, 180-193 (2005).
[CrossRef]

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future, Optical Microlithography," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

Other

F. Schellenberg, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2004).

A. K. Wong, Resolution Enhancement Techniques (SPIE Press, Bellingham, Washington, 2001).
[CrossRef]

S. A. Campbell, The Science and Engineering of MicroelectronicFfabrication, 2nd ed. (Publishing House of Electronics Industry, Beijing, 2003).

X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," in Proc. SPIE (San Jose, CA, 2007).

M. Born and E. Wolfe, Principles of Optics (Cambridge University Press, 1999).

R. Wilson, Fourier Series and Optical Transform Techniques in Contemporary Optics (John Wiley and Sons, 1995).

P. Yu and D. Z. Pan, "TIP-OPC: a new topological invariant paradigm for pixel based optical proximity correction," in Proc. ACM/IEEE International Conference on Computer-Aided Design (ICCAD) (2007).

X. Ma and G. R. Arce, "PSM design for inverse lithography using illumination with samll partial coherence factor," in Proc. SPIE (San Jose, CA, 2009).

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, and M. Hibbs, "Optimum mask and source patterns to print a given shape," J. Microlithogr., Microfabr., and Microsyst. 1, 13-30 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Optical lithography system with partially coherent illuminations

Fig. 2.
Fig. 2.

4-neighbors and 8-neighbors of pixel p

Fig. 3.
Fig. 3.

Pixel-based simultaneous source and binary mask optimization. Top row (from left to right) shows: the initial source pattern (σinner = 0.4 and σouter = 0.5), the initial binary mask pattern (critical dimension = 45nm), and the corresponding output intensity. Middle row (from left to right) shows: the initial source pattern (σinner = 0.4 and σouter = 0.5), the optimized binary mask pattern without simultaneous optimization of source pattern, and the corresponding output intensity. Bottom row (from left to right) shows: the optimized source pattern, the optimized binary mask pattern, and the corresponding output intensity. In the source and mask patterns, black and white represent 0 and 1 respectively.

Fig. 4.
Fig. 4.

Pixel-based simultaneous source and phase-shifting mask optimization. Top row (from left to right) shows: the initial source pattern (σ = 0.4), the initial phase-shifting mask pattern (critical dimension = 45nm), and the corresponding output intensity. Middle row (from left to right) shows: the initial source pattern (σ = 0.4), the optimized PSM without simultaneous optimization of source pattern, and the corresponding output intensity. Bottom row (from left to right) shows: the optimized source pattern, the optimized phase-shifting mask pattern, and the corresponding output intensity. In the source and mask patterns, black, gray and white represent -1, 0 and 1 respectively.

Tables (1)

Tables Icon

Table 1. The Pixel-based Simultaneous Source and Binary Mask Optimization Algorithm

Equations (19)

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

I ( r ) = ∫∫ M * ( r 1 ) M ( r 2 ) γ ( r 1 r 2 ) h * ( r r 1 ) h ( r r 2 ) d r 1 d r 2 ,
γ ( r ) = m Γ m exp ( j ω 0 m · r ) ,
Γ m = 1 D 2 A γ γ ( r ) exp ( j ω 0 m · r ) d r ,
I ( r ) = m Γ m M ( r ) h m ( r ) 2 ,
h m ( r ) = h ( r ) exp ( j ω 0 m · r ) .
γ ( r ) = J 1 ( 2 π r / 2 D cu ) 2 π r / 2 D cu D cu 2 D cl 2 J 1 ( 2 π r / 2 D cl ) 2 π r / 2 D cl ,
Γ m = { 4 D cu 2 D cl 2 π D 2 ( D cl 2 D cl 2 ) for D / 2 D cl m D / 2 D cu 0 elsewhere ,
γ ( r ) = J 1 ( 2 π r / 2 D c ) 2 π r / 2 D c ,
Γ m = { 4 D c 2 π D 2 m D / 2 D c 0 elsewhere ,
h ( r ) = J 1 ( 2 πrNA / λ ) 2 πrNA / λ .
D = d ( I ( x , y ) , I ̃ ( x , y ) ) = d ( T { Γ m , M ( x , y ) } , I ̃ ( x , y ) )
( Γ ̂ m , M ̂ ( x , y ) ) = arg min Γ m , M ( x , y ) d ( T { Γ m , M ( x , y ) } , I ̃ ( x , y ) ) .
I = m Γ m H m { M } 2 .
( Γ ̂ , M ̂ ) = arg min d Γ , M ( m Γ m H m { m ¯ } 2 , I ̃ ) .
i ¯ p = m Γ m q = 1 N 2 h p q m m ¯ q 2 , p = 1 , N 2 ,
d = F ( m ¯ ) = i ¯ i ¯ ̃ 2 2 = p = 1 N 2 ( i ¯ p * i ¯ p ) 2 ,
F Γ m = 2 ( i ¯ ̃ i ¯ ) T H m ( m ¯ ) 2
F M = 2 Re { m Γ m ( H m ) T [ ( i ¯ ~ i ¯ ) H m ( m ¯ ) ] } ,
F = ( F T Γ , F T M ) T .

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