Abstract

Fast source optimization (SO) is in demand urgently for holistic lithography on-line at 14-5 nm nodes. Our earlier works of fast compressive sensing (CS) SO methods adopted randomly sampling monitoring pixels on layout patterns, consequently resulting in failure of SO sometimes and poor image fidelity compared to gradient-based SO with complete sampling (SD-SO). This paper proposes a novel certain contour sampling-Bayesian compressive sensing SO (CCS-BCS-SO) method to achieve the goals of fast SO and high fidelity patterns simultaneously. The CCS assures the optimized source uniquely and reduces the computational complexity significantly. The BCS theory, to our best knowledge, is for the first time applied to resolution enhancement techniques (RETs) in lithography systems to ensure high fidelity patterns. The results demonstrate that CCS-BCS-SO simultaneously achieves fast SO like CS-SO and high fidelity patterns like SD-SO.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2019 (1)

2018 (2)

2017 (5)

X. Ma, D. Shi, Z. Wang, Y. Li, and G. R. Arce, “Lithographic source optimization based on adaptive projection compressive sensing,” Opt. Express 25(6), 7131–7149 (2017).
[Crossref]

H. You, Z. Ma, W. Li, and J. Zhu, “A speech enhancement method based on multi-task Bayesian compressive sensing,” IEICE Tran. Inf. & Syst. E100.D(3), 556–563 (2017).
[Crossref]

X. Gu, P. Zhou, and X. Gu, “Bayesian compressive sensing for thermal imagery using Gaussian-Jeffreys prior,” Infrared Phys. Techn. 83, 51–61 (2017).
[Crossref]

K. Huang, S. Tan, Y. Luo, X. Guo, and G. Wang, “Enhanced radio tomographic imaging with heterogeneous Bayesian compressive sensing,” Pervasive and Mobile Computing 40, 450–463 (2017).
[Crossref]

T. Li and Y. Li, “Lithographic source and mask optimization with low aberration sensitivity,” IEEE Trans. Nanotechnol. 16(6), 1099–1105 (2017).
[Crossref]

2016 (1)

M. V. D. Brink, “Holistic lithography and metrology’s importance in driving patterning fidelity,” Proc. SPIE 9778, 977802 (2016).
[Crossref]

2015 (4)

X. Ma, L. Dong, C. Han, J. Gao, Y. Li, and G. R. Arce, “Gradient-based joint source polarization mask optimization for optical lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 14(2), 023504 (2015).
[Crossref]

C. Han, Y. Li, X. Ma, and L. Liu, “Robust hybrid source and mask optimization to lithography source blur and flare,” Appl. Opt. 54(17), 5291–5302 (2015).
[Crossref]

L. Wang, S. Li, X. Wang, G. Yan, and C. Yang, “Source optimization using particle swarm optimization algorithm in optical lithography,” Acta Opt. Sin. 35(4), 0422002 (2015).
[Crossref]

H. Jiang and T. Xing, “A method of source optimization to maximize process window,” Laser Optoelectron. Prog. 52(10), 101101 (2015).
[Crossref]

2014 (2)

X. Guo, Y. Li, L. Dong, L. Liu, X. Ma, and C. Han, “Parametric source-mask-numerical aperture co-optimization for immersion lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 13(4), 043013 (2014).
[Crossref]

Z. Song, X. Ma, J. Gao, J. Wang, Y. Li, and G. R. Arce, “Inverse lithography source optimization via compressive sensing,” Opt. Express 22(12), 14180–14198 (2014).
[Crossref]

2013 (3)

2012 (4)

2011 (4)

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2x node logic,” Proc. SPIE 8166, 81662A (2011).
[Crossref]

S. G. Hansen, “Source mask polarization optimization,” J. Micro/Nanolithogr., MEMS, MOEMS 10(3), 033003 (2011).
[Crossref]

J. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
[Crossref]

J. Wu, F. Liu, L. Jiao, and X. Wang, “Compressive sensing SAR image reconstruction based on Bayesian framework and evolutionary computation,” IEEE T. Image Proces. 20(7), 1904–1911 (2011).
[Crossref]

2010 (3)

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in DOE modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 764025 (2010).
[Crossref]

S. Mosci, L. Rosasco, S. Matteo, A. Verri, and S. Villa, “Solving structured sparsity regularization with proximal methods,” Lect. Notes. Artif. Int. 6322, 418–433 (2010).
[Crossref]

2009 (2)

K. Tian, A. Krasnoperova, D. Melville, A. E. Rosenbluth, D. Gil, J. Tirapu-Azpiroz, K. Lai, S. Bagheri, C. C. Chen, and B. Morgenfeld, “Benefits and trade-offs of global source optimization in optical lithography,” Proc. SPIE 7274, 72740C (2009).
[Crossref]

X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783–5793 (2009).
[Crossref]

2008 (1)

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE T. Signal Proces. 56(6), 2346–2356 (2008).
[Crossref]

2006 (2)

E. J. Candés, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (1)

P. Combettes and V. Wajs, “Signal recovering by proximal forward-backing splitting,” Multiscale Model. Simul. 4(4), 1168–1200 (2005).
[Crossref]

2004 (3)

D. P. Wipf and B. D. Rao, “Sparse Bayesian learning for basis selection,” IEEE T. Signal Proces. 52(8), 2153–2164 (2004).
[Crossref]

Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. 3(4), 509–522 (2004).

A. Erdmann, T. Fühner, T. Schnattinger, and B. Tollkühn, “Towards automatic mask and source optimization for optical lithography,” Proc. SPIE 5377, 646–657 (2004).
[Crossref]

2002 (1)

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. 1(1), 486 (2002).
[Crossref]

2000 (1)

M. E. Tipping, “Spare Bayesian learning and the relevance vector machine,” Appl. Phys. Lett. 1, 211–244 (2000).
[Crossref]

1996 (1)

R. Tibshirani, “Regression shrinkage and selection via the Lasso,” J. Roy. Stat. Soc. B. Met. 58(1), 267–288 (1996).

1992 (1)

D. J. C. MacKay, “Bayesian interpolation,” Neural Comp. 4(3), 415–447 (1992).
[Crossref]

Adrichem, P. V.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2x node logic,” Proc. SPIE 8166, 81662A (2011).
[Crossref]

Arce, G. R.

Aschke, L.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Bagheri, S.

K. Tian, A. Krasnoperova, D. Melville, A. E. Rosenbluth, D. Gil, J. Tirapu-Azpiroz, K. Lai, S. Bagheri, C. C. Chen, and B. Morgenfeld, “Benefits and trade-offs of global source optimization in optical lithography,” Proc. SPIE 7274, 72740C (2009).
[Crossref]

Bisschop, P. D.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2x node logic,” Proc. SPIE 8166, 81662A (2011).
[Crossref]

Bizjak, T.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 764024 (2010).
[Crossref]

Brink, M. V. D.

M. V. D. Brink, “Holistic lithography and metrology’s importance in driving patterning fidelity,” Proc. SPIE 9778, 977802 (2016).
[Crossref]

Bukofsky, S.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. 1(1), 486 (2002).
[Crossref]

Candés, E. J.

E. J. Candés, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Carin, L.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE T. Signal Proces. 56(6), 2346–2356 (2008).
[Crossref]

Carriere, J. T.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in DOE modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 764025 (2010).
[Crossref]

Chao, H. Y.

Chen, C. C.

K. Tian, A. Krasnoperova, D. Melville, A. E. Rosenbluth, D. Gil, J. Tirapu-Azpiroz, K. Lai, S. Bagheri, C. C. Chen, and B. Morgenfeld, “Benefits and trade-offs of global source optimization in optical lithography,” Proc. SPIE 7274, 72740C (2009).
[Crossref]

Combettes, P.

P. Combettes and V. Wajs, “Signal recovering by proximal forward-backing splitting,” Multiscale Model. Simul. 4(4), 1168–1200 (2005).
[Crossref]

Dong, L.

X. Ma, Z. Wang, Y. Li, G. R. Arce, L. Dong, and J. G. Frias, “Fast optical proximity correction method based on nonlinear compressive sensing,” Opt. Express 26(11), 14479–14498 (2018).
[Crossref]

X. Ma, L. Dong, C. Han, J. Gao, Y. Li, and G. R. Arce, “Gradient-based joint source polarization mask optimization for optical lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 14(2), 023504 (2015).
[Crossref]

X. Guo, Y. Li, L. Dong, L. Liu, X. Ma, and C. Han, “Parametric source-mask-numerical aperture co-optimization for immersion lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 13(4), 043013 (2014).
[Crossref]

X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, “Pixelated source and mask optimization for immersion lithography,” J. Opt. Soc. Am. A 30(1), 112–123 (2013).
[Crossref]

X. Ma, Y. Li, X. Guo, and L. Dong, “Vectorial mask optimization method for robust optical lithography,” J. Micro/Nanolith. MESM. MOEMS. 11(4), 043008 (2012).
[Crossref]

X. Ma, Y. Li, and L. Dong, “Mask optimization approaches in optical lithography based on a vector imaging model,” J. Opt. Soc. Am. A 29(7), 1300–1312 (2012).
[Crossref]

Donoho, D.

D. Donoho, “Compressive sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Erdmann, A.

A. Erdmann, T. Fühner, T. Schnattinger, and B. Tollkühn, “Towards automatic mask and source optimization for optical lithography,” Proc. SPIE 5377, 646–657 (2004).
[Crossref]

Fonseca, C.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. 1(1), 486 (2002).
[Crossref]

Frias, J. G.

Fühner, T.

A. Erdmann, T. Fühner, T. Schnattinger, and B. Tollkühn, “Towards automatic mask and source optimization for optical lithography,” Proc. SPIE 5377, 646–657 (2004).
[Crossref]

Gao, J.

X. Ma, L. Dong, C. Han, J. Gao, Y. Li, and G. R. Arce, “Gradient-based joint source polarization mask optimization for optical lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 14(2), 023504 (2015).
[Crossref]

Z. Song, X. Ma, J. Gao, J. Wang, Y. Li, and G. R. Arce, “Inverse lithography source optimization via compressive sensing,” Opt. Express 22(12), 14180–14198 (2014).
[Crossref]

Gil, D.

K. Tian, A. Krasnoperova, D. Melville, A. E. Rosenbluth, D. Gil, J. Tirapu-Azpiroz, K. Lai, S. Bagheri, C. C. Chen, and B. Morgenfeld, “Benefits and trade-offs of global source optimization in optical lithography,” Proc. SPIE 7274, 72740C (2009).
[Crossref]

Granik, Y.

Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. 3(4), 509–522 (2004).

Gronlund, K.

K. Iwase, P. D. Bisschop, B. Laenens, Z. Li, K. Gronlund, P. V. Adrichem, and S. Hsu, “A new source optimization approach for 2x node logic,” Proc. SPIE 8166, 81662A (2011).
[Crossref]

Gu, X.

X. Gu, P. Zhou, and X. Gu, “Bayesian compressive sensing for thermal imagery using Gaussian-Jeffreys prior,” Infrared Phys. Techn. 83, 51–61 (2017).
[Crossref]

X. Gu, P. Zhou, and X. Gu, “Bayesian compressive sensing for thermal imagery using Gaussian-Jeffreys prior,” Infrared Phys. Techn. 83, 51–61 (2017).
[Crossref]

Guo, X.

K. Huang, S. Tan, Y. Luo, X. Guo, and G. Wang, “Enhanced radio tomographic imaging with heterogeneous Bayesian compressive sensing,” Pervasive and Mobile Computing 40, 450–463 (2017).
[Crossref]

X. Guo, Y. Li, L. Dong, L. Liu, X. Ma, and C. Han, “Parametric source-mask-numerical aperture co-optimization for immersion lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 13(4), 043013 (2014).
[Crossref]

X. Ma, Y. Li, X. Guo, and L. Dong, “Vectorial mask optimization method for robust optical lithography,” J. Micro/Nanolith. MESM. MOEMS. 11(4), 043008 (2012).
[Crossref]

Han, C.

X. Ma, L. Dong, C. Han, J. Gao, Y. Li, and G. R. Arce, “Gradient-based joint source polarization mask optimization for optical lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 14(2), 023504 (2015).
[Crossref]

C. Han, Y. Li, X. Ma, and L. Liu, “Robust hybrid source and mask optimization to lithography source blur and flare,” Appl. Opt. 54(17), 5291–5302 (2015).
[Crossref]

X. Guo, Y. Li, L. Dong, L. Liu, X. Ma, and C. Han, “Parametric source-mask-numerical aperture co-optimization for immersion lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 13(4), 043013 (2014).
[Crossref]

X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, “Pixelated source and mask optimization for immersion lithography,” J. Opt. Soc. Am. A 30(1), 112–123 (2013).
[Crossref]

Hansen, S. G.

S. G. Hansen, “Source mask polarization optimization,” J. Micro/Nanolithogr., MEMS, MOEMS 10(3), 033003 (2011).
[Crossref]

Hibbs, M.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. 1(1), 486 (2002).
[Crossref]

Himel, M. D.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in DOE modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 764025 (2010).
[Crossref]

Hsu, S.

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Figures (11)

Fig. 1.
Fig. 1. Sampling regions based on different sampling methods.
Fig. 2.
Fig. 2. Target layouts at 14 nm technology node.
Fig. 3.
Fig. 3. Simulations of different SO methods at 14 nm technology node.
Fig. 4.
Fig. 4. Pattern error results of different SO methods at 14 nm technology node.
Fig. 5.
Fig. 5. The runtime of different SO methods at 14 nm technology node.
Fig. 6.
Fig. 6. Simulations of different SO methods based on CCS method at 14 nm technology node.
Fig. 7.
Fig. 7. Pattern error results of different SO methods based on CCS method.
Fig. 8.
Fig. 8. The runtime of different SO methods based on CCS method at 14 nm technology node.
Fig. 9.
Fig. 9. Simulations of different sampling methods at 14 nm technology node.
Fig. 10.
Fig. 10. Pattern error results of different sampling methods at 14 nm technology node.
Fig. 11.
Fig. 11. The runtime of different sampling methods at 14 nm technology node.

Tables (2)

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Table 1. The image fidelity obtained by the proposed CCS-BCS-SO method with different α and β .

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Table 2. Number of sampling pixels in different sampling methods.

Equations (18)

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y = Φ x + ε ,
p ( x ; γ ) = N ( 0 , γ ) = i = 1 N ( 2 π γ i ) 1 2 exp ( x i 2 2 γ i ) ,
L ( γ ) = log p ( y | x ) p ( x ; γ ) d x = log | Σ y | + y T Σ y 1 y ,
x = Γ Φ T Σ y 1 y .
x o p t = arg min | | y Φ x | | 2 2 + 2 σ 2 i = 1 N z i 1 / 2 | x i | ,
γ i = z i 1 / 2 | x o p t , i | ,
z = d i a g ( Φ T Σ y 1 Φ ) ,
I = 1 J sum x S y S [ J ( x S , y S ) × p = x , y , z | H p x S , y S ( B x S , y S B ) | 2 ] ,
I = I c c J ,
J o p t = arg min J | | α Z s I s | | 2 2 + β i = 1 N s 2 w i | J i |  =  arg min J | | α Z s I c c s J | | 2 2 + β i = 1 N s 2 w i | J i | ,
γ i = w i 1 J o p t , i ,
w = s q r t ( d i a g ( ( I c c s ) T ( β E + I c c s d i a g ( γ ) ( I c c s ) T ) 1 I c c s ) ) ,
u = arg min u | | α Z s Φ u | | 2 2 + β | | u | | 1 ,
f ( u ) = g ( u ) + h ( u ) = | | α Z s Φ u | | 2 2 + β | | u | | 1 ,
v = u k s t e p × g ( u k ) ,
u k + 1 , i = s h r i n k ( v i , β / 2 ) = { v i + β / 2 , v i β / 2 0 , | v i | < β / 2 v i β / 2 , v i β / 2 ,
PAE = | | Z r e s i s t ( I ) | | 2 2 ,
r e s i s t ( I ) = Γ { I t r } ,

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