Abstract

Photolithography is at the core of the semiconductor industry that is used to fabricate microscale and nanoscale integrated circuits. Inverse lithography is a technique extensively used to compensate for lithography patterning distortions. It refers to methods that pre-distort the photomask patterns such that their projection, through the photolithography system, results in a pattern that is as close as possible to the intended original. However, most inverse lithography technique (ILT) methods suffer from large computational complexity. This paper develops a nonlinear compressive sensing framework for ILT that effectively improves the computational efficiency and image fidelity, while at the same time controlling the mask complexity. Based on a nonlinear lithography imaging model, the compressive ILT is formulated as an inverse optimization problem aimed at reducing the patterning error, and enforcing the sparsity and low rank properties of the mask pattern. A downsampling strategy is adopted to reduce the dimensionality of the cost function, thus alleviating the computational burden. Sparsity and low-rank regularizations are then used to constrain the solution space and reduce the mask complexity. The split Bregman algorithm is used to solve for the inverse optimization problem. The superiority of the proposed method is verified by a set of simulations and comparison to traditional ILT algorithms.

© 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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    [Crossref]
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  32. L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
  36. 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]
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    [Crossref]
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    [Crossref]

2018 (2)

2017 (1)

2015 (1)

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

2014 (1)

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

2013 (4)

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]

T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
[Crossref]

X. Ma, Z. Song, Y. Li, and G. R. Arce, “Block-based mask optimization for optical lithography,” Appl. Opt. 52(14), 3351–3363 (2013).
[Crossref]

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

2012 (1)

2011 (5)

X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19(3), 2165–2180 (2011).
[Crossref]

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust levelset-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[Crossref]

X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Micro/Nanolithogr., MEMS, MOEMS 10(2), 023009 (2011).
[Crossref]

X Ma, S. Jiang, and A. Zakhor, “A cost-driven fracture heuristics to minimize external sliver length,” Proc. SPIE 7973, 79732O (2011).
[Crossref]

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

2010 (5)

J. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Model. Simul. 8(2), 337–369 (2010).
[Crossref]

J. F. Cai, E. J. Candés, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Control 20(4), 1956–1982 (2010).
[Crossref]

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

J. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18(22), 23331–23342 (2010).
[Crossref]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 45601–45609 (2010).
[Crossref]

2009 (3)

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for $l_1$l1-regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

T. Blumensath and M. E. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. A. 27(3), 265–274 (2009).
[Crossref]

2008 (1)

T. Blumensath and M. E. Davies, “Iterative thresholding for sparse approximations,” J. Fourier Anal. Appl. 14(5-6), 629–654 (2008).
[Crossref]

2007 (1)

A. Poonawala and P. Milanfar, “Mask design for optical microlithography-an inverse imaging problem,” IEEE Trans. Image Processing 16(3), 774–788 (2007).
[Crossref]

2006 (4)

Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 5(4), 043002 (2006).
[Crossref]

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

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

E. 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]

2005 (1)

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

2003 (1)

F. Schellenberg, “A little light magic,” IEEE Spectrum 40(9), 34–39 (2003).
[Crossref]

1992 (1)

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semiconduct. Manufact. 5(2), 138–152 (1992).
[Crossref]

Arce, G. R.

Baik, K.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Blumensath, T.

T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
[Crossref]

T. Blumensath and M. E. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. A. 27(3), 265–274 (2009).
[Crossref]

T. Blumensath and M. E. Davies, “Iterative thresholding for sparse approximations,” J. Fourier Anal. Appl. 14(5-6), 629–654 (2008).
[Crossref]

Cai, J.

J. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Model. Simul. 8(2), 337–369 (2010).
[Crossref]

Cai, J. F.

J. F. Cai, E. J. Candés, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Control 20(4), 1956–1982 (2010).
[Crossref]

Candés, E.

E. 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]

Candés, E. J.

J. F. Cai, E. J. Candés, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Control 20(4), 1956–1982 (2010).
[Crossref]

Chandrasekaran, V.

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” arXiv:0906.2220v1, Jun. 2009.

Chen, H.

H. Chen, H. Kung, and M. Comiter, “Nonlinear compressive sensing for distorted measurements and application to improving efficiency of power amplifiers,“ IEEE International Conference on Communications, 1–7 (2017).

Chen, Z.

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

Chiou, K.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Cho, H.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Chu, C.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Chu, J.

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

Comiter, M.

H. Chen, H. Kung, and M. Comiter, “Nonlinear compressive sensing for distorted measurements and application to improving efficiency of power amplifiers,“ IEEE International Conference on Communications, 1–7 (2017).

Dam, T.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Davies, M. E.

T. Blumensath and M. E. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. A. 27(3), 265–274 (2009).
[Crossref]

T. Blumensath and M. E. Davies, “Iterative thresholding for sparse approximations,” J. Fourier Anal. Appl. 14(5-6), 629–654 (2008).
[Crossref]

Dong, L.

Donoho, D.

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

Frias, J. G.

Gao, H.

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

Goldstein, T.

T. Goldstein and S. Osher, “The split Bregman method for $l_1$l1-regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

Granik, Y.

Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 5(4), 043002 (2006).
[Crossref]

Gray, R.

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Han, C.

Hu, P.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Huang, J.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Irby, D.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Jia, N.

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust levelset-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[Crossref]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 45601–45609 (2010).
[Crossref]

Jiang, S.

X Ma, S. Jiang, and A. Zakhor, “A cost-driven fracture heuristics to minimize external sliver length,” Proc. SPIE 7973, 79732O (2011).
[Crossref]

Jiao, L.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Jin, L.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Ke, J.

J. Ke and E. Y. Lam, Nonlinear image reconstruction in block-based compressive imaging, IEEE International Symposium on Circuits and Systems, 2917–2920 (2012).

Kim, B.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Kim, D.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Kung, H.

H. Chen, H. Kung, and M. Comiter, “Nonlinear compressive sensing for distorted measurements and application to improving efficiency of power amplifiers,“ IEEE International Conference on Communications, 1–7 (2017).

Lam, E. Y.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust levelset-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[Crossref]

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 45601–45609 (2010).
[Crossref]

J. Ke and E. Y. Lam, Nonlinear image reconstruction in block-based compressive imaging, IEEE International Symposium on Circuits and Systems, 2917–2920 (2012).

Lee, S.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Li, L.

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

Li, P.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Li, Y.

Lin, H.

Lin, T.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Liu, S.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Liu, Y.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semiconduct. Manufact. 5(2), 138–152 (1992).
[Crossref]

Lv, W.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Ma, X

X Ma, S. Jiang, and A. Zakhor, “A cost-driven fracture heuristics to minimize external sliver length,” Proc. SPIE 7973, 79732O (2011).
[Crossref]

Ma, X.

X. Ma, Z. Wang, H. Lin, Y. Li, G. R. Arce, and L. Zhang, “Optimization of lithography source illumination arrays using diffraction subspaces,” Opt. Express 26(4), 3738–3755 (2018).
[Crossref]

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, 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]

X. Ma, Z. Song, Y. Li, and G. R. Arce, “Block-based mask optimization for optical lithography,” Appl. Opt. 52(14), 3351–3363 (2013).
[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, 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]

X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19(3), 2165–2180 (2011).
[Crossref]

X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Micro/Nanolithogr., MEMS, MOEMS 10(2), 023009 (2011).
[Crossref]

X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics, 1st ed. (John Wiley and Sons, 2010).

Martin, P. M.

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Milanfar, P.

A. Poonawala and P. Milanfar, “Mask design for optical microlithography-an inverse imaging problem,” IEEE Trans. Image Processing 16(3), 774–788 (2007).
[Crossref]

Moore, A.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Osher, S.

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

J. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Model. Simul. 8(2), 337–369 (2010).
[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for $l_1$l1-regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

Pang, L.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Parrilo, P. A.

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” arXiv:0906.2220v1, Jun. 2009.

Peng, D.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Poonawala, A.

A. Poonawala and P. Milanfar, “Mask design for optical microlithography-an inverse imaging problem,” IEEE Trans. Image Processing 16(3), 774–788 (2007).
[Crossref]

Progler, C. J.

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Romberg, J.

E. 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]

Sanghavi, S.

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” arXiv:0906.2220v1, Jun. 2009.

Schellenberg, F.

F. Schellenberg, “A little light magic,” IEEE Spectrum 40(9), 34–39 (2003).
[Crossref]

Shen, Y.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust levelset-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011).
[Crossref]

Shen, Z.

J. F. Cai, E. J. Candés, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Control 20(4), 1956–1982 (2010).
[Crossref]

J. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Model. Simul. 8(2), 337–369 (2010).
[Crossref]

Shi, D.

Son, D. H.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Song, Z.

Suh, S. S.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Tao, T.

E. 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]

Tolani, V.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

Tsaoa, B.

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

Wang, G.

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

Wang, M.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Wang, Z.

Wei, Y.

Y. Wei, Advanced Lithography Theory and Application of VLSI (Science Press, 2016).

Willsky, A. S.

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” arXiv:0906.2220v1, Jun. 2009.

Wong, A. K.

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).

Wong, N.

Woo, S. G.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

Wu, B.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Wu, X.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Xia, Q.

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

Xiao, G.

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

Yang, S.

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

Yu, H. Y.

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

Yu, J.

Yu, P.

Zakhor, A.

X Ma, S. Jiang, and A. Zakhor, “A cost-driven fracture heuristics to minimize external sliver length,” Proc. SPIE 7973, 79732O (2011).
[Crossref]

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semiconduct. Manufact. 5(2), 138–152 (1992).
[Crossref]

Zhang, L.

Appl. Comput. Harmon. A. (1)

T. Blumensath and M. E. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. A. 27(3), 265–274 (2009).
[Crossref]

Appl. Opt. (1)

IEEE Spectrum (1)

F. Schellenberg, “A little light magic,” IEEE Spectrum 40(9), 34–39 (2003).
[Crossref]

IEEE Trans. Geosci. Electron. (1)

S. Yang, M. Wang, P. Li, L. Jin, B. Wu, and L. Jiao, “Compressive hyperspectral imaging via sparse tensor and nonlinear compressed sensing,” IEEE Trans. Geosci. Electron. 53(11), 5943–5957 (2015).
[Crossref]

IEEE Trans. Image Processing (1)

A. Poonawala and P. Milanfar, “Mask design for optical microlithography-an inverse imaging problem,” IEEE Trans. Image Processing 16(3), 774–788 (2007).
[Crossref]

IEEE Trans. Inf. Theory (3)

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

E. 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]

T. Blumensath, “Compressed sensing with nonlinear observations and related nonlinear optimization problems,” IEEE Trans. Inf. Theory 59(6), 3466–3474 (2013).
[Crossref]

IEEE Trans. Semiconduct. Manufact. (1)

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semiconduct. Manufact. 5(2), 138–152 (1992).
[Crossref]

Inverse Probl. (1)

H. Gao, H. Y. Yu, S. Osher, and G. Wang, “Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM),” Inverse Probl. 27(11), 115012 (2011).
[Crossref]

J. Fourier Anal. Appl. (1)

T. Blumensath and M. E. Davies, “Iterative thresholding for sparse approximations,” J. Fourier Anal. Appl. 14(5-6), 629–654 (2008).
[Crossref]

J. Micro/Nanolithogr., MEMS, MOEMS (2)

Y. Granik, “Fast pixel-based mask optimization for inverse lithography,” J. Micro/Nanolithogr., MEMS, MOEMS 5(4), 043002 (2006).
[Crossref]

X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Micro/Nanolithogr., MEMS, MOEMS 10(2), 023009 (2011).
[Crossref]

J. Opt. (1)

N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12(4), 45601–45609 (2010).
[Crossref]

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

J. Vac. Sci. Technol., B (1)

W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol., B 31(4), 041605 (2013).
[Crossref]

J. X-Ray Sci. Technol. (1)

L. Li, Z. Chen, G. Wang, J. Chu, and H. Gao, “A tensor PRISM algorithm for multi-energy CT reconstruction and comparative studies,” J. X-Ray Sci. Technol. 22(2), 147–163 (2014).
[Crossref]

Multiscale Model. Simul. (1)

J. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Model. Simul. 8(2), 337–369 (2010).
[Crossref]

Opt. Express (6)

Proc. SPIE (5)

P. M. Martin, C. J. Progler, G. Xiao, R. Gray, L. Pang, and Y. Liu, “Manufacturability study of masks created by inverse lithography technology (ILT),” Proc. SPIE 5992, 599235 (2005).
[Crossref]

B. Kim, S. S. Suh, S. G. Woo, H. Cho, G. Xiao, D. H. Son, D. Irby, D. Kim, and K. Baik, “Inverse lithography technology (ILT) mask manufacturability for full-chip device,” Proc. SPIE 7488, 748812 (2009).
[Crossref]

C. Chu, B. Tsaoa, K. Chiou, S. Lee, J. Huang, Y. Liu, T. Lin, A. Moore, and L. Pang, “Enhancing DRAM printing process window by using inverse lithography technology (ILT),” Proc. SPIE 6154, 61543O (2006).
[Crossref]

X Ma, S. Jiang, and A. Zakhor, “A cost-driven fracture heuristics to minimize external sliver length,” Proc. SPIE 7973, 79732O (2011).
[Crossref]

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[Crossref]

SIAM J. Control (1)

J. F. Cai, E. J. Candés, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. Control 20(4), 1956–1982 (2010).
[Crossref]

SIAM J. Imaging Sci. (1)

T. Goldstein and S. Osher, “The split Bregman method for $l_1$l1-regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

Other (6)

V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, “Rank-sparsity incoherence for matrix decomposition,” arXiv:0906.2220v1, Jun. 2009.

H. Chen, H. Kung, and M. Comiter, “Nonlinear compressive sensing for distorted measurements and application to improving efficiency of power amplifiers,“ IEEE International Conference on Communications, 1–7 (2017).

J. Ke and E. Y. Lam, Nonlinear image reconstruction in block-based compressive imaging, IEEE International Symposium on Circuits and Systems, 2917–2920 (2012).

Y. Wei, Advanced Lithography Theory and Application of VLSI (Science Press, 2016).

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).

X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics, 1st ed. (John Wiley and Sons, 2010).

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Figures (7)

Fig. 1.
Fig. 1. Sketch of the deep ultraviolet photolithography system.
Fig. 2.
Fig. 2. Simulations of different ILT methods based on vertical line-space pattern.
Fig. 3.
Fig. 3. The convergence of average PEs on both focal and defocus planes obtained by different ILT methods using (a) the vertical line-space pattern and (b) the horizontal block pattern.
Fig. 4.
Fig. 4. The overlapped process windows obtained by different ILT methods for (a) the vertical line-space pattern and (b) the horizontal block pattern.
Fig. 5.
Fig. 5. The measurement positions of the process windows for (a) the vertical line-space pattern and (b) the horizontal block pattern.
Fig. 6.
Fig. 6. Simulations of different ILT methods based on horizontal block pattern.
Fig. 7.
Fig. 7. Simulations of different ILT methods based on complex layout pattern.

Tables (1)

Tables Icon

Table 1. The values of DOF (nm) corresponding to different ELs.

Equations (44)

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I = 1 J s u m x s y s [ J ( x s , y s ) × p = x , y , z | H p x s y s ( B x s y s M ) | 2 ] ,
Z = Γ { I t r } ,
s i g ( x , t r ) = 1 1 + e x p [ a ( x t r ) ] ,
M ^ = arg min M f ( M ) = arg min M Π ( Z ~ Z ) 2 2 = arg min M m = 1 N n = 1 N { Π ( m , n ) × [ Z ~ ( m , n ) Z ( m , n ) ] } 2 ,
f K ( M ) = Π K ( Z ~ K Z K ) 2 2 = m = 1 N / K n = 1 N / K { Π ( K m , K n ) × [ Z ~ ( K m , K n ) Z ( K m , K n ) ] } 2 .
d ( M ) = α f K ( M ) + ( 1 α ) f K ( M ) ,
f K ( M ) = Π K ( Z ~ K Z K ) 2 2 ,
M = 0.5 × ( 1 + cos Θ ) ,
Θ ^ = arg min Θ d ( Θ ) ,
Θ = Ψ Θ ¯ Ψ T ,
d ( Θ ) = α f K ( Θ ) + ( 1 α ) f K ( Θ ) + λ Θ + λ 1 Θ ¯ 1 ,
Θ = i = 1 r σ i ,
d ( Θ ) = α f K ( Θ ) + ( 1 α ) f K ( Θ ) + λ Θ + λ 1 Θ ¯ 1 + λ q R q ( Θ ) + λ w R w ( Θ ) ,
Θ ^ = arg min Θ { α f K ( Θ ) + ( 1 α ) f K ( Θ ) + λ Θ + λ 1 Θ ¯ 1 + λ q R q ( Θ ) + λ w R w ( Θ ) } .
Θ ^ = arg min Θ { α Π K [ Z ~ K Z K ( Θ ) + E K ] 2 2 + ( 1 α ) Π K [ Z ~ K Z K ( Θ ) + E K ] 2 2 + λ D + μ D Θ V 2 2 + λ 1 C 1 + μ 1 C Θ ¯ W 2 2 + λ q R q ( Θ ) + λ w R w ( Θ ) } ,
Θ n + 1 = arg min Θ { α Π K [ Z ~ K Z K ( Θ n ) + E K n ] 2 2 + ( 1 α ) Π K [ Z ~ K Z K ( Θ n ) + E K n ] 2 2 + μ D n Θ n V n 2 2 + μ 1 C n Θ ¯ n W n 2 2 + λ q R q ( Θ n ) + λ w R w ( Θ n ) } ,
E K n + 1 = E K n + Z ~ K Z K ( Θ n + 1 ) ,
E K n + 1 = E K n + Z ~ K Z K ( Θ n + 1 ) ,
D n + 1 = arg min D λ D n + μ D n ( Θ n + 1 + V n ) 2 2 ,
V n + 1 = V n + Θ n + 1 D n + 1 .
C n + 1 = arg min C λ 1 C n 1 + μ 1 C n ( Θ ¯ n + 1 + W n ) 2 2 ,
W n + 1 = W n + Θ ¯ n + 1 C n + 1 .
D n + 1 = S τ ( Θ n + 1 + V n )
X = U Σ Q T ,
S τ ( X ) = U Σ Q T .
C n + 1 = Λ { Θ ¯ n + 1 + W n , λ 1 / μ 1 } , λ 1 / μ 1 0 ,
Λ { X , λ 1 / μ 1 } = X X ¯ X ,
R c = O { N ~ s [ 36 N 2 + 20 N 2 log ( N 2 / K 2 ) + 6 N 2 / K 2 ] + r N 2 } O [ N ~ s ( 40 N 2 + 20 N 2 log N 2 ) ] = O ( 36 + 20 log N 2 20 log K 2 + 6 / K 2 + r / N ~ s ) O ( 40 + 20 log N 2 ) O ( 40 log N 40 log K ) O ( 40 log N ) = 1 O ( log K log N ) .
R q = i = 1 N j = 1 N { 1 [ 2 M ( i , j ) 1 ] 2 } = 1 N × 1 T [ 4 M ( 1 N × N M ) ] 1 N × 1 ,
R q = i = 1 N j = 1 N [ 1 cos 2 Θ ( i , j ) ] = 1 N × 1 T ( 1 N × N cos Θ cos Θ ) 1 N × 1 ,
A ( i , j ) = M ( 2 i 1 , 2 j 1 ) + M ( 2 i 1 , 2 j ) + M ( 2 i , 2 j 1 ) + M ( 2 i , 2 j ) ,
H ( i , j ) = M ( 2 i 1 , 2 j 1 ) M ( 2 i 1 , 2 j ) + M ( 2 i , 2 j 1 ) M ( 2 i , 2 j ) ,
V ( i , j ) = M ( 2 i 1 , 2 j 1 ) + M ( 2 i 1 , 2 j ) M ( 2 i , 2 j 1 ) M ( 2 i , 2 j ) ,
D ( i , j ) = M ( 2 i 1 , 2 j 1 ) M ( 2 i 1 , 2 j ) M ( 2 i , 2 j 1 ) + M ( 2 i , 2 j ) ,
R W = i = 1 N / 2 j = 1 N / 2 [ H ( i , j ) × H ( i , j ) + V ( i , j ) × V ( i , j ) + D ( i , j ) × D ( i , j ) ] .
G ( Θ ) = α T K + ( 1 α ) T K + μ D Θ V 2 2 + μ 1 C Θ ¯ W 2 2 + λ q R q ( Θ ) + λ w R w ( Θ ) ,
G ( Θ ) = α T K ( Θ ) + ( 1 α ) T K ( Θ ) + 2 μ ( Θ + V D ) + 2 μ 1 Ψ T ( Θ ¯ + W C ) Ψ + λ q R q ( Θ ) + λ w R w ( Θ ) ,
T K = Π K [ Z ~ K Z K ( Θ ) + E K ] 2 2 = m = 1 N / K n = 1 N / K { Π ( K m , K n ) × [ Z ~ ( K m , K n ) Z ( K m , K n ) + E K ( K m , K n ) ] } 2 .
T K M ( r , s ) = 4 a J s u m x s y s J ( x s , y s ) × p = x , y , z R e ( [ B x s y s ( r , s ) ] × m = 1 N / K n = 1 N / K [ H p x s y s ( K m r , K n s ) ] × { Π ( K m , K n ) × Z ( K m , K n ) × [ Z ~ ( K m , K n ) Z ( K m , K n ) + E K ( K m , K n ) ] × [ 1 Z ( K m , K n ) ] } × { r s H p x s y s ( K m r , K n s ) × [ B x s y s ( r , s ) × M ( r , s ) ] } ) ,
T K M u v ( a , b ) = 4 a J s u m x s y s J ( x s , y s ) × p = x , y , z R e ( [ B u v x s y s ( a , b ) ] × m = 1 N / K n = 1 N / K [ H p , u v x s y s ( m a , n b ) ] × { Π ( K m , K n ) × Z ( K m , K n ) × [ Z ~ ( K m , K n ) Z ( K m , K n ) + E K ( K m , K n ) ] × [ 1 Z ( K m , K n ) ] } × [ a = 0 N / K 1 b = 0 N / K 1 B u v x s y s ( a , b ) × H p , u v x s y s ( m a , n b ) × M u v ( a , b ) ] ) .
T K , u v = 4 a J s u m x s y s J ( x s , y s ) × p = x , y , z R e ( ( B u v x s y s ) ( H p , u v x s y s ) { [ H p , u v x s y s ( B u v x s y s M u v ) ] Π K ( Z ~ K Z K + E K ) Z K ( 1 K Z K ) } ) ,
T K ( K a + u , K b + v ) = T K , u v ( a , b ) ,
T K Θ ( r , s ) = T K M ( r , s ) × M ( r , s ) Θ ( r , s ) .
T K ( Θ ) = 1 2 T K s i n Θ .

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