## Hotspot-aware fast source and mask optimization |

Optics Express, Vol. 20, Issue 19, pp. 21792-21804 (2012)

http://dx.doi.org/10.1364/OE.20.021792

Acrobat PDF (914 KB)

### Abstract

Source mask optimization (SMO) is a useful technique for printing the integrated circuit (IC) on a wafer with increasingly smaller feature size. However, complex SMO algorithms generally lead to undesirably long runtime resulting from an optimization of largely identical regions over the whole mask pattern. In this work, a weighted SMO scheme incorporating both an awareness of the hotspots and robustness against process variations is proposed. We show how optimal solutions are reached with fewer iterations by applying various degrees of correction in the corresponding regions. The proposed method includes identifying the hotspots and combining a weight matrix to the cost function for adjustment and control. Simulation results are compared with the mask optimization (under a fixed source) and conventional SMO to illustrate the performance improvement in terms of pattern fidelity, convergence rate and process window size.

© 2012 OSA

## 1. Introduction

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

2. S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express **16**, 14746–14760 (2008). [CrossRef] [PubMed]

3. S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process. **4**, 1252–1257 (1995). [CrossRef] [PubMed]

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

9. D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in *Optical Microlithography XXIII*, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).

10. Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys. **3**, 509–522 (2004). [CrossRef]

19. 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]

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

21. S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences **5**, 625–651 (2012). [CrossRef]

## 2. Forward imaging model

*I*(

_{a}*x*,

*y*) can be described as [22

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

*M*(

*x*,

*y*) is the input mask pattern, with its spectrum denoted by

*M*̂. The pupil function

*Ĥ*, where its inverse Fourier transform is

*H*(

*x*,

*y*), is called the point spread function. The symbol † and * are complex conjugate and convolution operators, respectively. The function

*J*(

*f*,

*g*) ≥ 0 represents the effective source, which is normalized by its total energy [23

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

24. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process. **20**, 2856–2864 (2011). [CrossRef] [PubMed]

*J*′(

*f*,

*g*) is an arbitrary source point.

*I*(

_{a}*x*,

*y*) then goes through the photoresist development to form the printed image

*I*(

*x*,

*y*). Approximating the resist effect with a sigmoid function due to its differentiability [25

25. A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. **16**, 774–788 (2007). [CrossRef] [PubMed]

*I*(

*x*,

*y*) is given by in which

*t*is the threshold and

_{r}*α*indicates the steepness of the sigmoid function.

## 3. Weighted source mask optimization algorithm

### 3.1. Hotspots selection and weight matrix formation

27. M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys. **8**, 043001 (2009). [CrossRef]

*I*

_{0}(

*x*,

*y*) and

*I*(

_{s}*x*,

*y*) is the smallest image, the difference image, denoted Δ

*I*(

*x*,

*y*), is therefore

*I*(

*x*,

*y*) take on larger values, showing greater sensitivity to focus and dose variations. They represent the critical locations that are often difficult to print, thus requiring more severe corrections in the inverse imaging process. To allow for a smooth transition from such hotspot regions to other areas, we convolve Δ

*I*(

*x*,

*y*) (at places where it is non-zero) with a lowpass filter

*G*(

*x*,

*y*), such as a 3 × 3 Gaussian kernel, i.e., we define

*W*(

*x*,

*y*) that corrects a certain location more severely when the corresponding

*I*(

_{m}*x*,

*y*) is large. When

*I*(

_{m}*x*,

*y*) is small compared with a threshold

*t*, empirically set to be half of the maximum value in

_{w}*I*, we put in 1 in the corresponding weight matrix position, which is to be the smallest value in the matrix. When it exceeds the threshold,

_{m}*W*(

*x*,

*y*) is set to be proportional to

*I*(

_{m}*x*,

*y*), with the constant of proportionality,

*λ*

_{1}, a user-defined parameter. Mathematically, we therefore have

*t*has an effect on the hotspot selection. Specifically, a larger

_{w}*t*will miss the detection of some potential hotspot regions, while a smaller

_{w}*t*will include extra pattern regions, in both cases leading to unnecessary computation. The parameter

_{w}*λ*

_{1}plays an important role in controlling the optimal step size. A smaller

*λ*

_{1}cannot sufficiently penalize the hotspot regions, while a larger one may exert excessive penalty. In our experiments,

*t*= 0.5 and

_{w}*λ*

_{1}= 3 are selected empirically.

### 3.2. The cost function

*W*(

*x*,

*y*) enters via a pixel-by-pixel multiplication with the difference between the simulated circuit image

*I*(

*x*,

*y*) and the desired image,

*I*

_{0}(

*x*,

*y*). In this work, such difference is measured by the

*ℓ*

_{2}norm. The weight matrix has the effect of varying the step length during the iteration process, resulting in faster convergence with fewer iterations. Mathematically, the pattern fidelity term is given by where ⊙ indicates pixel-by-pixel multiplication.

*J*′(

*f*,

*g*), and the other one is the derivative of ℱ with respect to the mask

*M*(

*x*,

*y*). Here we define the differential operator ∇

*F*(

*a*) to evaluate the gradient of a function

*F*with respect to its argument

*a*in the discrete domain, due to the discrete nature of the mask and source. As shown in the Appendix, these are given by

*t*as much as possible. To achieve this, we minimize

_{r}*I*≈ 0 at locations where the desired pattern

_{a}*I*

_{0}(

*x*,

*y*) = 0, and force

*I*≈ 2

_{a}*t*where

_{r}*I*

_{0}(

*x*,

*y*) = 1. This enables the intensity both above and below the nominal threshold

*t*to be equally penalized to reduce their sensitivity to dose changes [23

_{r}23. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express **19**, 19384–19398 (2011). [CrossRef] [PubMed]

29. 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. Manu, 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 22nm logic lithography process,” in *Optical Microlithography XXIV*, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

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

29. 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. Manu, 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 22nm logic lithography process,” in *Optical Microlithography XXIV*, H. J. Levinson and M. V. Dusa eds., Proc. SPIE 7274, 72740A (2009).

24. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process. **20**, 2856–2864 (2011). [CrossRef] [PubMed]

_{f}*J*(

*f*,

*g*) and ∇

_{g}*J*(

*f*,

*g*) are denotations of finite difference in numerical implementations, defined by

25. A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. **16**, 774–788 (2007). [CrossRef] [PubMed]

_{s}*J*(

*f*,

*g*) does not involve the mask, and ℛ

_{m}*M*(

*x*,

*y*) does not involve the source. Thus, the two gradients we need are and The derivations are detailed in the Appendix.

### 3.3. Optimization flow

*M*

_{opt}(

*x*,

*y*) and the corresponding source

*J*

_{opt}(

*f*,

*g*), i.e.

32. 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]

32. 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]

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

*t*, and then the cost function is optimized by a weighted sum of the nominal and the aberration terms, in which the weighting coefficients are determined by the variable probabilities. The mask and source updates are performed alternately until the termination criterion is reached. The gradients of the objective function with respect to the mask and source are given by and

_{r}*k*th iteration is denoted by the superscript

*k*with brackets.

## 4. Results

*σ*= 0.7 and

_{in}*σ*= 0.9 is adopted as the reference source, as well as the initial value for our source optimization. The parameters of the projection system are set to be

_{out}*λ*= 193nm and

*NA*= 1.35. In the sigmoid function,

*t*and

_{r}*α*are equal to 0.3 and 85, respectively. It is noted that effective source

*J*(

*f*,

*g*) is applied to aerial image computation throughout the optimization flow to normalize the aerial image in Eq.(4) such that in spite of changing source integration in the iterations, identical total source energy justifies a constant threshold

*t*in the photoresist approximation. In the hotspots selection step, the smallest image is generated at 70nm defocus and 10% dose increase.

_{r}## 5. Conclusions

## A. Appendix: Gradients derivation

*∂/∂M*and

*∂/∂J*′ are approximated by numerical differences.

## Acknowledgments

## References and links

1. | A. K. Wong, |

2. | S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express |

3. | S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process. |

4. | X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express |

5. | Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express |

6. | Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express |

7. | T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in |

8. | Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in |

9. | D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in |

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

11. | 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,” in |

12. | H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in |

13. | 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,” in |

14. | M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in |

15. | T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in |

16. | Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in |

17. | X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express |

18. | J.-C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” in |

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

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

21. | S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences |

22. | A. K. Wong, |

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

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

25. | A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process. |

26. | J. Kim and M. Fan, “Hotspot detection on post-OPC layout using full chip simulation based verification tool : a case study with aerial image simulation,” in |

27. | M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys. |

28. | J.-C. Yu and P. Yu, “Choosing objective functions for inverse lithography patterning,” in |

29. | 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. Manu, 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 22nm logic lithography process,” in |

30. | S. Hsu, Z. Li, L. Chen, K. Gronlund, H.-Y. Liu, and R. Socha, “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance,” in |

31. | J. Nocedal and S. J. Wright, |

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

33. | T. H. Coskun, H. Dai, V. Kamat, C.-M. Hsu, G. Santoro, C. Ngai, M. Reybrouck, G. Grozev, and H.-T. Huang, “Free form source and mask optimization for negative tone resist development for 22nm node contact holes,” in |

**OCIS Codes**

(110.3960) Imaging systems : Microlithography

(110.5220) Imaging systems : Photolithography

(110.1758) Imaging systems : Computational imaging

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: July 17, 2012

Revised Manuscript: September 2, 2012

Manuscript Accepted: September 3, 2012

Published: September 7, 2012

**Citation**

Jia Li, Yijiang Shen, and Edmund Y. Lam, "Hotspot-aware fast source and mask optimization," Opt. Express **20**, 21792-21804 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-19-21792

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### References

- A. K. Wong, Resolution Enhancement Techniques in Optical Lithography, (SPIE, Washington, 2001). [CrossRef]
- S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express16, 14746–14760 (2008). [CrossRef] [PubMed]
- S. Sherif, B. Saleh, and R. De Leone, “Binary images synthesis using mixed linear integar programming,” IEEE Trans. Image Process.4, 1252–1257 (1995). [CrossRef] [PubMed]
- X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express15, 15066–15079 (2007). [CrossRef] [PubMed]
- Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express17, 23690–23701 (2009). [CrossRef]
- Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express19, 5511–5521 (2011). [CrossRef] [PubMed]
- T. H. Dam, X. Zhou, D. Chen, A. Adamov, D. Peng, and B. Gleason, “Validation and application of a mask model for inverse lithography,” in Design for Manufacturability through Design-Process Integration II, V. K. Sing and M. L. Rieger eds., Proc. SPIE 6925, 69251J (2008).
- Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, and H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 76401J (2010).
- D. Melville, A. Rosenbluth, K. Tian, K. Lai, S. Bagheri, J. Tirapu-Azpiroz, J. Meiring, S. Halle, G. McIntyre, T. Faure, D. Corliss, A. Krasnoperova, L. Zhuang, P. Strenski, A. Waechter, L. Ladanyi, F. Barahona, D. Scarpazza, J. Lee, T. Inoue, M. Sakamoto, H. Muta, A. Wagner, G. Burr, Y. Kim, E. Gallagher, M. Hibbs, A. Tritchkov, Y. Granik, M. Fakhry, K. Adam, G. Berger, M. Lam, A. Dave, and N. Cobb, “Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).
- Y. Granik, “Source optimization for image fidelity and throughput,” J. Microlith. Microfab. Microsys.3, 509–522 (2004). [CrossRef]
- 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,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81662A (2011).
- H. Hu, Y. Zou, and Y. Deng, “Optimization on illumination source with design of experiments,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE7640, 764027 (2010).
- 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,” in Photomask Technology 2010, M. W. Montgomery and W. Maurer, eds., Proc. SPIE7823, 78233X (2010).
- M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer and F. E. Abboud, eds., Proc. SPIE8166, 81663M (2011).
- T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, and J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa and W. Conley, eds., Proc. SPIE 7640, 764006 (2010).
- Y. Deng, T. H. Coskun, J. Kye, and H. J. Levinson, “Lithography target optimization with source-mask optimization,” in Optical Microlithography XXV, W. Conley, ed., Proc. SPIE 8326, 83262P (2012).
- X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express17, 5783–5793 (2009). [CrossRef] [PubMed]
- J.-C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” in Optical Microlithography XXIV, M. V. Dusa, ed., Proc. SPIE 7973, 797320 (2011).
- J.-C. Yu, P. Yu, and H. Y. Chao, “Fast source optimization involving quadratic line-contour objectives for the resist image,” Opt. Express20, 8161–8174 (2012). [CrossRef] [PubMed]
- E. Y. Lam and A. K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Opt. Express17, 12259–12268 (2009). [CrossRef] [PubMed]
- S. K. Choy, N. Jia, C. S. Tong, M. L. Tang, and E. Y. Lam, “A robust computational algorithm for inverse photomask synthesis in optical projection lithography,” SIAM J. Imaging Sciences5, 625–651 (2012). [CrossRef]
- A. K. Wong, Optical Imaging in Projection Microlithography, (SPIE, Washington, 2005). [CrossRef]
- N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express19, 19384–19398 (2011). [CrossRef] [PubMed]
- Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical oithography,” IEEE Trans. Image Process.20, 2856–2864 (2011). [CrossRef] [PubMed]
- A. Poonawala and P. Milanfar, “Mask design for optical microlithography — an inverse imaging problem,” IEEE Trans. Image Process.16, 774–788 (2007). [CrossRef] [PubMed]
- J. Kim and M. Fan, “Hotspot detection on post-OPC layout using full chip simulation based verification tool : a case study with aerial image simulation,” in 23rd Annual BACUS Symposium on Photomask Technology, K. R. Kimmel and W. Staud, eds., Proc. SPIE 5256, 919–925 (2003).
- M. L. Kempsell, E. Hendrickx, A. Tritchkov, K. Sakajiri, K. Yasui, S. Yoshitake, Y. Granik, G. Vandenberghe, and B. W. Smith, “Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture,” J. Microlith. Microfab. Microsys.8, 043001 (2009). [CrossRef]
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