## Efficient source mask optimization with Zernike polynomial functions for source representation |

Optics Express, Vol. 22, Issue 4, pp. 3924-3937 (2014)

http://dx.doi.org/10.1364/OE.22.003924

Acrobat PDF (1438 KB)

### Abstract

In 22nm optical lithography and beyond, source mask optimization (SMO) becomes vital for the continuation of advanced ArF technology node development. The pixel-based method permits a large solution space, but involves a time-consuming optimization procedure because of the large number of pixel variables. In this paper, we introduce the Zernike polynomials as basis functions to represent the source patterns, and propose an improved SMO algorithm with this representation. The source patterns are decomposed into the weighted superposition of some well-chosen Zernike polynomial functions, and the number of variables decreases significantly. We compare the computation efficiency and optimization performance between the proposed method and the conventional pixel-based algorithm. Simulation results demonstrate that the former can obtain substantial speedup of source optimization while improving the pattern fidelity at the same time.

© 2014 Optical Society of America

## 1. Introduction

1. A. K. Wong, *Resolution Enhancement Technologies in Optical Lithography* (SPIE, 2001). [CrossRef]

2. A. E. Rosenbluth, D. O. Melville, K. Tian, S. Bagheri, J. Tirapu-Azpiroz, K. Lai, A. Waechter, T. Inoue, L. Ladanyi, F. Barahona, K. Scheinberg, M. Sakamoto, H. Muta, E. Gallagher, T. Faure, M. Hibbs, A. Tritchkov, and Y. Granik, “Intensive optimization of masks and sources for 22nm lithography,” Proc. SPIE **7274**, 727409 (2009). [CrossRef]

3. M. Mulder, A. Engelen, O. Noordman, G. Streutker, B. van Drieenhuizen, C. van Nuenen, W. Endendijk, J. Verbeeck, W. Bouman, A. Bouma, R. Kazinczi, R. Socha, D. Jürgens, J. Zimmermann, B. Trauter, J. Bekaert, B. Laenens, D. Corliss, and G. McIntyre, “Performance of FlexRay: a fully programmable illumination system for generation of freeform sources on high NA immersion systems,” Proc. SPIE **7640**, 76401P (2010). [CrossRef]

4. K. Tian, M. Fakyry, A. Dave, A. Tritchkov, J. Tirapu-Azpiroz, A. E. Rosenbluth, D. Melville, M. Sakamoto, T. Inoue, S. Mansfield, A. Wei, Y. Kim, B. Durgan, K. Adam, G. Berger, G. Bhatara, J. Meiring, H. Haffner, and B.-S. Kim, “Applicability of global source mask optimization to 22/20nm node and beyond,” Proc. SPIE **7973**, 79730C (2011). [CrossRef]

5. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express **19**, 19384–19398 (2011). [CrossRef] [PubMed]

7. J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented Lagrangian methods in optical lithography,” Opt. Express **21**, 8076–8090 (2013). [CrossRef] [PubMed]

8. N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. **12**, 045601 (2010). [CrossRef]

9. K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22-nm logic lithography process,” Proc. SPIE **7274**, 72740A (2009). [CrossRef]

10. J. Bekaert, P. van Adrichem, R. Socha, O. Mouraille, J. Zimmermann, P. Grupner, K. Schreel, S. Hsu, B. Laenens, S. Verhaegen, H.-Y. Liu, M. Dusa, J. T. Neumann, L. V. Look, D. Trivkovic, F. Lazzarino, and G. Vandenberghe, “Experimental verification of source-mask optimization and freeform illumination for 22-nm node static random access memory cells,” J. Micro/Nanolith. MEMS MOEMS **10**, 013008 (2011). [CrossRef]

11. E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express **17**, 12259–12268 (2009). [CrossRef] [PubMed]

15. A. Poonawala, W. Stanton, and C. Sawh, “Source mask optimization for advanced lithography nodes,” Proc. SPIE **7640**, 76401M (2010). [CrossRef]

6. T. Fühner and A. Erdmann, “Improved mask and source representations for automatic optimization of lithographic process conditions using a genetic algorithm,” Proc. SPIE **5754**, 415–426 (2005). [CrossRef]

17. S. Liu, W. Liu, X. Zhou, and P. Gong, “Kernel-based parametric analytical model of source intensity distributions in lithographic tools,” Appl. Opt. **51**, 1479–1486 (2012). [CrossRef] [PubMed]

18. J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express **20**, 21792–21804 (2012). [CrossRef] [PubMed]

20. 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**, 112–123 (2013). [CrossRef]

21. T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” Proc. SPIE **7823**, 78233X (2010). [CrossRef]

*et al.*for efficient source optimization with a large mask pattern [22

22. J.-C. Yu, P. Yu, and H.-Y. Chao, “Library-based illumination synthesis for critical CMOS patterning,” IEEE Trans. Image Process. **22**, 2811–2821 (2013). [CrossRef] [PubMed]

23. J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. **19**, 1510–1518 (1980). [CrossRef] [PubMed]

24. M. Born and E. Wolf, *Principle of Optics*, 7 (Cambridge University, 1999). [CrossRef]

25. S. Liu, X. Zhou, W. Lv, S. Xu, and H. Wei, “Convolution-variation separation method for efficient modeling of optical lithography,” Opt. Lett. **38**, 2168–2170 (2013). [CrossRef] [PubMed]

26. J. Aluizio Prata and W. V. T. Rusch, “Algorithm for computation of Zernike polynomials expansion coefficients,” Appl. Opt. **28**, 749–754 (1989). [CrossRef]

27. S. Liu, X. Wu, W. Liu, and C. Zhang, “Fast aerial image simulations using one basis mask pattern for optical proximity correction,” J. Vac. Sci. Technol. B **29**, 06FH03 (2011). [CrossRef]

## 2. Fast aerial image calculation

*I*on the wafer plane can be expressed, using Abbe’s formulation, as [28

28. A. K. Wong, *Optical Imaging in Projection Microlithography* (SPIE, 2005). [CrossRef]

*x*,

*y*) are the spatial coordinates, (

*f*,

*g*) are the spatial frequency coordinates,

*J*is the illumination source,

*O*is the mask spectrum,

*H*is the projection pupil, 𝔉 denotes the Fourier transform, † denotes the complex conjugate, and

*T*is the transmission cross coefficient (TCC) defined by In this system,

*J*(

*f*,

*g*) is conventionally a circular function with radius

*σ*, also known as the partial coherence factor. To improve the resolution, lithographers have developed off-axis illumination, including annular, dipole and quadrupole sources, and more recently the technology has enabled the use of more customized sources with a variety of shapes. These customized sources can be represented by several methods, including sector/track-based, and pixel-based. The former uses a small number of variables to represent the source patterns, but with limited flexibility. The latter permits much more flexible designs, leading to the highest possibility to improve the resolution. However, this representation method requires a large number of pixel variables.

24. M. Born and E. Wolf, *Principle of Optics*, 7 (Cambridge University, 1999). [CrossRef]

28. A. K. Wong, *Optical Imaging in Projection Microlithography* (SPIE, 2005). [CrossRef]

*P*terms of Zernike polynomials, i.e. where

*ψ*is the corresponding Zernike coefficient, and

_{l}*Z*is the

_{l}*l*th Zernike polynomial. For convenience, we can change this to a matrix representation using lexicographic ordering. Equation (4) can then be rewritten as where Ψ is the vector of Zernike coefficients Ψ = [

*ψ*

_{1}

*ψ*

_{2}...]

^{T}, and

**Z**is a

*N*×

_{s}*N*. Moreover, we note that for a partially coherent imaging system, the effective source intensity is limited to a unit disk, and only the pixels within the circle shown in Fig. 2 are of interest. Thus, we only need to consider the values within the unit disk for the Zernike polynomial functions.

_{s}*P*can be quite large to represent a free-form source, which would require significant computation as a result. However, realistic source patterns in optical lithography often have some characteristics such as symmetry to reduce the pattern placement shift [9

9. K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22-nm logic lithography process,” Proc. SPIE **7274**, 72740A (2009). [CrossRef]

29. J. L. Sturtevant, L. Hong, S. Jayaram, S. P. Renwick, M. McCallum, and P. D. Bisschop, “Impact of illumination source symmetrization in OPC,” Proc. SPIE **7028**, 70283M (2008). [CrossRef]

*T̂*is The equivalent matrix form of Eq. (9) is Again, the generation of this matrix form of TCC follows the same method as Eqs. (5) and (8).

_{l}*ψ*vary when the source pattern changes, and the new TCC can be calculated through a linear combination of these bases, which can be very efficient. We depict this in Fig. 4, where Fig. 4(a) shows the Zernike coefficients, Figs. 4(b), 4(c), and 4(d) are the basis Zernike polynomial functions, basis TCCs, and basis images, respectively, and Figs. 4(e), 4(f), and 4(g) are correspondingly the source pattern, the TCC, and the aerial image in the imaging systems.

_{p}## 3. Inverse problem formulation

### 3.1. Mask optimization

27. S. Liu, X. Wu, W. Liu, and C. Zhang, “Fast aerial image simulations using one basis mask pattern for optical proximity correction,” J. Vac. Sci. Technol. B **29**, 06FH03 (2011). [CrossRef]

*K*be the number of singular values used for the computation. After the TCC is computed efficiently through Eq. (9), the decomposition can be expressed as where

*λ*is the

_{n}*n*th eigenvalue, and

*ϕ*is the corresponding eigenvector. Then the aerial image can be calculated through where

_{n}*M*is the mask pattern in the spatial domain, Φ

*is the Fourier transform of the eigenfunction*

_{n}*ϕ*(

_{n}*f*,

*g*), and

***denotes 2-D convolution.

*I*and the target pattern

_{r}*I*as a measure of the image fidelity. The resist image is obtained from the aerial image with a sigmoid function modeled as the resist effect where

_{t}*t*is the threshold in the photoresist effect, and

_{r}*α*indicates the steepness of the sigmoid function. Then the image fidelity term

*ℛ*is given by In addition, to enhance image contrast, we define a penalty term

_{m}*ℛ*on the aerial image as This term can force the aerial image to be 0 while the target is 0, and the aerial image to be 2

_{a}*t*while the target is 1. More explanations about this term can be found in Ref. [5

_{r}5. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express **19**, 19384–19398 (2011). [CrossRef] [PubMed]

*ℒ*for mask optimization can be represented as where

_{m}*τ*is a weight assigned to the image contrast term. Therefore the mask optimization can be formulated as A conjugate gradient method can be employed to optimize the mask pattern iteratively [5

5. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express **19**, 19384–19398 (2011). [CrossRef] [PubMed]

### 3.2. Source optimization

*et al.*[30

30. J.-C. Yu, P. Yu, and H.-Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express **20**, 8161–8174 (2012). [CrossRef] [PubMed]

*ℛ*and the side-lobes compressing term

_{c}*ℛ*

_{0}. The former forces the intensity on the contour to be equal to the threshold, as defined by where

**Î**

*is a*

_{c}*N*×

_{c}*P*matrix denoting the aerial images extracted from

**Î**by choosing those located on the mask edge position,

*N*is the number of points on these position, and

_{c}**t**

*is a*

_{r}*N*-element vector whose values are all

_{c}*t*. The latter suppresses the side-lobes by forcing the aerial image around the main features to be small, as given by where

_{r}**Î**

_{0}is a

*N*

_{0}×

*P*matrix denoting the aerial images located on a closed curve surrounding the main features of the mask,

*N*

_{0}is the number of points on the curve, and

*∊*is a

*N*

_{0}length vector with all its values equal to

*ε*, which is a small positive value. The distance between the curve and the main features is half a pitch for periodic patterns and 0.61

*λ*/NA for isolated and semi-isolated patterns, where

*λ*is the wavelength of the source, and NA is the numerical aperture.

*μ*signifies the relative importance of the two terms. This cost function can be written as a quadratic form where

**Q**and

**b**are

*P*×

*P*and

*P*× 1, respectively, and

*c*is a scalar.

*S*

_{max}. As the source patterns with the Zernike representation can be expressed as

**Z**Ψ, these two requirements can be satisfied by setting a linear constraint on the source patterns as 0 ≤

**Z**Ψ ≤

*S*

_{max}.

*t*in the resist model. Here, we fix the threshold value, and limit the total intensity of the illumination source to a certain value

_{r}*D*

_{max}. The total intensity of the source can be calculated as the summation of all the pixel values of the source patterns, that is,

**EZ**Ψ, where

**E**is an

**EZ**Ψ ≤

*D*

_{max}in the optimization process.

31. M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.0 beta,” http://cvxr.com/cvx (2013).

## 4. Simulations

### 4.1. Selection of the Zernike polynomials

24. M. Born and E. Wolf, *Principle of Optics*, 7 (Cambridge University, 1999). [CrossRef]

*P*=

*L*(

*L*+ 1)/2 if the first

*L*orders of radial components are selected. Here, we set

*L*ranges from 2 to 17, and the corresponding

*P*equals to 3, 6, 10,···, 136. Each Zernike polynomial, and therefore the source pattern, is represented by a 65 × 65 pixel image. The number of source pixels of interest located within the unit disk is 3785. The source wavelength is 193nm, and the NA is 1.35. The

*t*and

_{r}*α*in the sigmoid function to calculate the resist image are 0.3 and 85, respectively. We also set the weight

*μ*= 0.1,

*ε*= 0.001 in the source optimization, and the maximum pixel values

*S*

_{max}= 1 and

*D*

_{max}= 500.

*P*= 78 in our following simulations of source mask optimization. This is because the optimization process can approximate the largest solution space when

*P*= 78, and the increase of terms can only add computational burden.

### 4.2. Optimization results

**19**, 19384–19398 (2011). [CrossRef] [PubMed]

*N*= 65, and the spatial frequencies ranges from −1 to 1 after normalization by NA/

_{s}*λ*. Similar to the earlier simulation, we set

*S*

_{max}= 1,

*D*

_{max}= 500, and

*μ*=

*τ*= 0.1. Furthermore, in mask optimization, the number of kernels maintained for the aerial image calculation is

*K*= 10.

## 5. Conclusions

## Acknowledgments

## References and links

1. | A. K. Wong, |

2. | A. E. Rosenbluth, D. O. Melville, K. Tian, S. Bagheri, J. Tirapu-Azpiroz, K. Lai, A. Waechter, T. Inoue, L. Ladanyi, F. Barahona, K. Scheinberg, M. Sakamoto, H. Muta, E. Gallagher, T. Faure, M. Hibbs, A. Tritchkov, and Y. Granik, “Intensive optimization of masks and sources for 22nm lithography,” Proc. SPIE |

3. | M. Mulder, A. Engelen, O. Noordman, G. Streutker, B. van Drieenhuizen, C. van Nuenen, W. Endendijk, J. Verbeeck, W. Bouman, A. Bouma, R. Kazinczi, R. Socha, D. Jürgens, J. Zimmermann, B. Trauter, J. Bekaert, B. Laenens, D. Corliss, and G. McIntyre, “Performance of FlexRay: a fully programmable illumination system for generation of freeform sources on high NA immersion systems,” Proc. SPIE |

4. | K. Tian, M. Fakyry, A. Dave, A. Tritchkov, J. Tirapu-Azpiroz, A. E. Rosenbluth, D. Melville, M. Sakamoto, T. Inoue, S. Mansfield, A. Wei, Y. Kim, B. Durgan, K. Adam, G. Berger, G. Bhatara, J. Meiring, H. Haffner, and B.-S. Kim, “Applicability of global source mask optimization to 22/20nm node and beyond,” Proc. SPIE |

5. | N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express |

6. | T. Fühner and A. Erdmann, “Improved mask and source representations for automatic optimization of lithographic process conditions using a genetic algorithm,” Proc. SPIE |

7. | J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented Lagrangian methods in optical lithography,” Opt. Express |

8. | N. Jia and E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. |

9. | K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22-nm logic lithography process,” Proc. SPIE |

10. | J. Bekaert, P. van Adrichem, R. Socha, O. Mouraille, J. Zimmermann, P. Grupner, K. Schreel, S. Hsu, B. Laenens, S. Verhaegen, H.-Y. Liu, M. Dusa, J. T. Neumann, L. V. Look, D. Trivkovic, F. Lazzarino, and G. Vandenberghe, “Experimental verification of source-mask optimization and freeform illumination for 22-nm node static random access memory cells,” J. Micro/Nanolith. MEMS MOEMS |

11. | E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express |

12. | E. Y. Lam and A. K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/Nanolith. MEMS MOEMS |

13. | D. G. Flagello and D. G. Smith, “Calculation and uses of the lithographic aerial image,” Adv. Opt. Technol. |

14. | Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys. |

15. | A. Poonawala, W. Stanton, and C. Sawh, “Source mask optimization for advanced lithography nodes,” Proc. SPIE |

16. | A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. F. Molless, R. N. Singh, and A. K. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsys. |

17. | S. Liu, W. Liu, X. Zhou, and P. Gong, “Kernel-based parametric analytical model of source intensity distributions in lithographic tools,” Appl. Opt. |

18. | J. Li, Y. Shen, and E. Y. Lam, “Hotspot-aware fast source and mask optimization,” Opt. Express |

19. | Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. |

20. | 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 |

21. | T. Mülders, V. Domnenko, B. Küchler, T. Klimpel, H.-J. Stock, A. A. Poonawala, K. N. Taravade, and W. A. Stanton, “Simultaneous source-mask optimization: a numerical combining method,” Proc. SPIE |

22. | J.-C. Yu, P. Yu, and H.-Y. Chao, “Library-based illumination synthesis for critical CMOS patterning,” IEEE Trans. Image Process. |

23. | J. Y. Wang and D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. |

24. | M. Born and E. Wolf, |

25. | S. Liu, X. Zhou, W. Lv, S. Xu, and H. Wei, “Convolution-variation separation method for efficient modeling of optical lithography,” Opt. Lett. |

26. | J. Aluizio Prata and W. V. T. Rusch, “Algorithm for computation of Zernike polynomials expansion coefficients,” Appl. Opt. |

27. | S. Liu, X. Wu, W. Liu, and C. Zhang, “Fast aerial image simulations using one basis mask pattern for optical proximity correction,” J. Vac. Sci. Technol. B |

28. | A. K. Wong, |

29. | J. L. Sturtevant, L. Hong, S. Jayaram, S. P. Renwick, M. McCallum, and P. D. Bisschop, “Impact of illumination source symmetrization in OPC,” Proc. SPIE |

30. | J.-C. Yu, P. Yu, and H.-Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express |

31. | M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.0 beta,” http://cvxr.com/cvx (2013). |

**OCIS Codes**

(110.5220) Imaging systems : Photolithography

(110.1758) Imaging systems : Computational imaging

(110.4235) Imaging systems : Nanolithography

**ToC Category:**

Physical Optics

**History**

Original Manuscript: November 25, 2013

Revised Manuscript: January 28, 2014

Manuscript Accepted: January 30, 2014

Published: February 12, 2014

**Citation**

Xiaofei Wu, Shiyuan Liu, Jia Li, and Edmund Y. Lam, "Efficient source mask optimization with Zernike polynomial functions for source representation," Opt. Express **22**, 3924-3937 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-3924

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### References

- A. K. Wong, Resolution Enhancement Technologies in Optical Lithography (SPIE, 2001). [CrossRef]
- A. E. Rosenbluth, D. O. Melville, K. Tian, S. Bagheri, J. Tirapu-Azpiroz, K. Lai, A. Waechter, T. Inoue, L. Ladanyi, F. Barahona, K. Scheinberg, M. Sakamoto, H. Muta, E. Gallagher, T. Faure, M. Hibbs, A. Tritchkov, Y. Granik, “Intensive optimization of masks and sources for 22nm lithography,” Proc. SPIE 7274, 727409 (2009). [CrossRef]
- M. Mulder, A. Engelen, O. Noordman, G. Streutker, B. van Drieenhuizen, C. van Nuenen, W. Endendijk, J. Verbeeck, W. Bouman, A. Bouma, R. Kazinczi, R. Socha, D. Jürgens, J. Zimmermann, B. Trauter, J. Bekaert, B. Laenens, D. Corliss, G. McIntyre, “Performance of FlexRay: a fully programmable illumination system for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7640, 76401P (2010). [CrossRef]
- K. Tian, M. Fakyry, A. Dave, A. Tritchkov, J. Tirapu-Azpiroz, A. E. Rosenbluth, D. Melville, M. Sakamoto, T. Inoue, S. Mansfield, A. Wei, Y. Kim, B. Durgan, K. Adam, G. Berger, G. Bhatara, J. Meiring, H. Haffner, B.-S. Kim, “Applicability of global source mask optimization to 22/20nm node and beyond,” Proc. SPIE 7973, 79730C (2011). [CrossRef]
- N. Jia, E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011). [CrossRef] [PubMed]
- T. Fühner, A. Erdmann, “Improved mask and source representations for automatic optimization of lithographic process conditions using a genetic algorithm,” Proc. SPIE 5754, 415–426 (2005). [CrossRef]
- J. Li, S. Liu, E. Y. Lam, “Efficient source and mask optimization with augmented Lagrangian methods in optical lithography,” Opt. Express 21, 8076–8090 (2013). [CrossRef] [PubMed]
- N. Jia, E. Y. Lam, “Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis,” J. Opt. 12, 045601 (2010). [CrossRef]
- K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. Tirapu-Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22-nm logic lithography process,” Proc. SPIE 7274, 72740A (2009). [CrossRef]
- J. Bekaert, P. van Adrichem, R. Socha, O. Mouraille, J. Zimmermann, P. Grupner, K. Schreel, S. Hsu, B. Laenens, S. Verhaegen, H.-Y. Liu, M. Dusa, J. T. Neumann, L. V. Look, D. Trivkovic, F. Lazzarino, G. Vandenberghe, “Experimental verification of source-mask optimization and freeform illumination for 22-nm node static random access memory cells,” J. Micro/Nanolith. MEMS MOEMS 10, 013008 (2011). [CrossRef]
- E. Y. Lam, A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express 17, 12259–12268 (2009). [CrossRef] [PubMed]
- E. Y. Lam, A. K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/Nanolith. MEMS MOEMS 9, 033002 (2010). [CrossRef]
- D. G. Flagello, D. G. Smith, “Calculation and uses of the lithographic aerial image,” Adv. Opt. Technol. 1, 237–248 (2012).
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