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Fast source optimization involving quadratic line-contour objectives for the resist imageJue-Chin Yu, Peichen Yu, and Hsueh-Yung Chao »View Author Affiliations
Jue-Chin Yu,1
Peichen Yu,1,*
and Hsueh-Yung Chao2
1Department of Photonics and Institute of Electro-Optical Engineering, National Chiao-Tung University, Hsinchu, Taiwan 2ANSYS, Inc., Pittsburgh, Pennsylvania, USA *Corresponding author: yup@faculty.nctu.edu.tw |
Optics Express, Vol. 20, Issue 7, pp. 8161-8174 (2012)
http://dx.doi.org/10.1364/OE.20.008161
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Abstract
In Abbe’s formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.
© 2012 OSA
OCIS Codes
(100.3190) Image processing : Inverse problems
(110.3960) Imaging systems : Microlithography
(110.1758) Imaging systems : Computational imaging
(110.3010) Imaging systems : Image reconstruction techniques
ToC Category:
Imaging Systems
History
Original Manuscript: January 19, 2012
Revised Manuscript: March 16, 2012
Manuscript Accepted: March 16, 2012
Published: March 23, 2012
Citation
Jue-Chin Yu, Peichen Yu, and Hsueh-Yung Chao, "Fast source optimization involving quadratic line-contour objectives for the resist image," Opt. Express 20, 8161-8174 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-8161
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- T. Cecil, C. Ashton, D. Irby, L. Luan, D. H. Son, G. Xiao, X. Zhou, D. Kim, B. Gleason, H. J. Lee, W. J. Sim, M. J. Hong, S. G. Jung, S. S. Suh, and S. W. Lee, “Enhancing fullchip ILT mask synthesis capability for IC manufacturability,” Proc. SPIE7973, 79731C (2011). [CrossRef]
- 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. SPIE7823, 78233X (2010). [CrossRef]
- 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. SPIE7823, 78233X (2010). [CrossRef]
- K. Lai, M. Gabrani, D. Demaris, N. Casati, A. Torres, S. Sarkar, P. Strenski, S. Bagheri, D. Scarpazza, A. E. Rosenbluth, D. O. Melville, A. Wächter, J. Lee, V. Austel, M. Szeto-Millstone, K. Tian, F. Barahona, T. Inoue, and M. Sakamoto, “Design specific joint optimization of masks and sources on a very large scale,” Proc. SPIE7973, 797308 (2011). [CrossRef]
- 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,” Proc. SPIE7640, 764006 (2010). [CrossRef]
- T. Cecil, C. Ashton, D. Irby, L. Luan, D. H. Son, G. Xiao, X. Zhou, D. Kim, B. Gleason, H. J. Lee, W. J. Sim, M. J. Hong, S. G. Jung, S. S. Suh, and S. W. Lee, “Enhancing fullchip ILT mask synthesis capability for IC manufacturability,” Proc. SPIE7973, 79731C (2011). [CrossRef]
- K. Lai, M. Gabrani, D. Demaris, N. Casati, A. Torres, S. Sarkar, P. Strenski, S. Bagheri, D. Scarpazza, A. E. Rosenbluth, D. O. Melville, A. Wächter, J. Lee, V. Austel, M. Szeto-Millstone, K. Tian, F. Barahona, T. Inoue, and M. Sakamoto, “Design specific joint optimization of masks and sources on a very large scale,” Proc. SPIE7973, 797308 (2011). [CrossRef]
- 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,” Proc. SPIE7640, 76401J (2010). [CrossRef]
- S. Tamulevicius, A. Guobiene, G. Janusas, A. Palevicius, V. Ostasevicius, and M. Andrulevicius, “Optical characterization of diffractive optical elements replicated in polymers,” J. Microlithor. Microfabrication. Microsyst.5, 013004 (2006).
- T. Matsuyama, N. Kita, T. Nakashima, O. Tanitsu, and S. Owa, “Tolerancing analysis of customized illumination for practical applications of source and mask optimization,” Proc. SPIE7640, 764007, 764007-10 (2010). [CrossRef]
- 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. SPIE7823, 78233X (2010). [CrossRef]
- C. Lim, V. Temchenko, and M. Niehoff, “Selective inverse lithography methodology,” Proc. SPIE7640, 764034 (2010). [CrossRef]
- K. Lai, M. Gabrani, D. Demaris, N. Casati, A. Torres, S. Sarkar, P. Strenski, S. Bagheri, D. Scarpazza, A. E. Rosenbluth, D. O. Melville, A. Wächter, J. Lee, V. Austel, M. Szeto-Millstone, K. Tian, F. Barahona, T. Inoue, and M. Sakamoto, “Design specific joint optimization of masks and sources on a very large scale,” Proc. SPIE7973, 797308 (2011). [CrossRef]
- 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,” Proc. SPIE7640, 764006 (2010). [CrossRef]
- 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. SPIE7274, 72740C, (2009). [CrossRef]
- 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,” Proc. SPIE7640, 764006 (2010). [CrossRef]
- 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. SPIE7274, 72740C, (2009). [CrossRef]
- L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K. H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” Proc. SPIE7520, 75200X (2009). [CrossRef]
- K. Lai, M. Gabrani, D. Demaris, N. Casati, A. Torres, S. Sarkar, P. Strenski, S. Bagheri, D. Scarpazza, A. E. Rosenbluth, D. O. Melville, A. Wächter, J. Lee, V. Austel, M. Szeto-Millstone, K. Tian, F. Barahona, T. Inoue, and M. Sakamoto, “Design specific joint optimization of masks and sources on a very large scale,” Proc. SPIE7973, 797308 (2011). [CrossRef]
- I. Torunoglu, E. Elsen, and A. Karakas, “A GPU-based full-chip source-mask optimization solution,” Proc. SPIE7640, 76401L (2010). [CrossRef]
- 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,” Proc. SPIE7640, 764006 (2010). [CrossRef]
- C. Alleaume, E. Yesilada, V. Farys, L. Depre, V. Arnoux, Z. Li, Y. Trouiller, and A. Serebriakov, “A systematic study of source error in source mask optimization,” Proc. SPIE7823, 782312, 782312-7 (2010). [CrossRef]
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- 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,” Proc. SPIE7640, 764006 (2010). [CrossRef]
- S. Geisler, J. Bauer, U. Haak, U. Jagdhold, R. Pliquett, E. Matthus, R. Schrader, H. Wolf, U. Baetz, H. Beyer, and M. Niehoff, “Optical proximity correction for 0.13 μm SiGe:C BiCMOS,” Proc. SPIE6792, 679210(2008). [CrossRef]
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- Y. Cao, Y. W. Lu, L. Chen, and J. Ye, “Optimized hardware and software for fast, full chip simulation,” Proc. SPIE5754, 407–414 (2004). [CrossRef]
- C. Alleaume, E. Yesilada, V. Farys, L. Depre, V. Arnoux, Z. Li, Y. Trouiller, and A. Serebriakov, “A systematic study of source error in source mask optimization,” Proc. SPIE7823, 782312, 782312-7 (2010). [CrossRef]
- 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,” Proc. SPIE7640, 76401J (2010). [CrossRef]
- J. C. Yu, P. Yu, and H. Y. Chao, “Wavefront-based pixel inversion algorithm for generation of subresolution assist features,” J. Micro./Nanolith. MEMS MOEMS.10, 043014 (2011).
- J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE7973, 787320 (2011).
- J. C. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express18(22), 23331–23342 (2010). [CrossRef] [PubMed]
- J. C. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE7973, 787320 (2011).
- J. C. Yu, P. Yu, and H. Y. Chao, “Wavefront-based pixel inversion algorithm for generation of subresolution assist features,” J. Micro./Nanolith. MEMS MOEMS.10, 043014 (2011).
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Opt. Express
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Proc. SPIE
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- L. Pang, P. Hu, D. Peng, D. Chen, T. Cecil, L. He, G. Xiao, V. Tolani, T. Dam, K. H. Baik, and B. Gleason, “Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods,” Proc. SPIE7520, 75200X (2009). [CrossRef]
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- S. Jung, W. Sim, M. Jeong, J. Ser, S. Lee, S. W. Choi, X. Zhou, L. Luan, T. Cecil, D. Son, R. Gleason, and D. Kim, “Improving model prediction accuracy for ILT with aggressive SRAFs,” Proc. SPIE7823, 782311(2010). [CrossRef]
- C. Lim, V. Temchenko, and M. Niehoff, “Selective inverse lithography methodology,” Proc. SPIE7640, 764034 (2010). [CrossRef]
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- 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,” Proc. SPIE7640, 76401J (2010). [CrossRef]
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- M. Fakhry, Y. Granik, K. Adam, and K. Lai, “Total source mask optimization: high-capacity, resist modeling, and production-ready mask solution,” Proc. SPIE8166, 81663M (2011). [CrossRef]
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