Abstract

Mask topography effects need to be taken into consideration for a more accurate solution of source mask optimization (SMO) in advanced optical lithography. However, rigorous 3D mask models generally involve intensive computation and conventional SMO fails to manipulate the mask-induced undesired phase errors that degrade the usable depth of focus (uDOF) and process yield. In this work, an optimization approach incorporating pupil wavefront aberrations into SMO procedure is developed as an alternative to maximize the uDOF. We first design the pupil wavefront function by adding primary and secondary spherical aberrations through the coefficients of the Zernike polynomials, and then apply the conjugate gradient method to achieve an optimal source-mask pair under the condition of aberrated pupil. We also use a statistical model to determine the Zernike coefficients for the phase control and adjustment. Rigorous simulations of thick masks show that this approach provides compensation for mask topography effects by improving the pattern fidelity and increasing uDOF.

© 2014 Optical Society of America

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2014 (2)

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

X. Wu, S. Liu, J. Li, E. Y. Lam, “Efficient source mask optimization with Zernike polynomial functions for source representation,” Opt. Express 22, 3924–3937 (2014).
[CrossRef] [PubMed]

2013 (5)

2012 (1)

2011 (2)

2010 (3)

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

E. Y. Lam, A. K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/Nanolith. MEMS MOEMS 9, 033002 (2010).
[CrossRef]

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

2009 (1)

2007 (1)

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

1995 (1)

1994 (1)

A. K. Wong, A. R. Neureuther, “Mask topography effects in projection printing of phase phifting masks,” IEEE Trans. on Electron Devices 41, 895–902 (1994).
[CrossRef]

Adam, K.

M. Fakhry, Y. Granik, K. Adam, K. Lai, “Total source mask optimization: High-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer, F. E. Abboud, eds. (2011), vol. 8166 of Proc. SPIE, p. 81663M.
[CrossRef]

Agudelo, V.

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, “Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 832609.
[CrossRef]

Aoyama, H.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Arce, G. R.

Baik, K.-H.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Bekaert, J.

Capodieci, L.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Chao, H.-Y.

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

Choi, J.

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

Choi, S.-W.

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

Coskun, T. H.

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

Dai, H.

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

Dam, T.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Demmerle, W.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Deng, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Dong, L.

Erdmann, A.

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

T. Fühner, P. Evanschitzky, A. Erdmann, “Mutual source, mask and projector pupil optimization,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 83260I.
[CrossRef]

F. Shao, P. Evanschitzky, D. Reibold, A. Erdmann, “Fast rigorous simulation of mask diffraction using the waveguide method with parallelized decomposition technique,” in 24th European Mask and Lithography Conference, U. F. W. Behringer, ed. (2008), vol. 6792 of Proc. SPIE, p. 679206.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, “Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 832609.
[CrossRef]

P. Evanschitzky, F. Shao, T. Fühner, A. Erdmann, “Compensation of mask induced aberrations by projector wavefront control,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 797329.
[CrossRef]

Evanschitzky, P.

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

T. Fühner, P. Evanschitzky, A. Erdmann, “Mutual source, mask and projector pupil optimization,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 83260I.
[CrossRef]

F. Shao, P. Evanschitzky, D. Reibold, A. Erdmann, “Fast rigorous simulation of mask diffraction using the waveguide method with parallelized decomposition technique,” in 24th European Mask and Lithography Conference, U. F. W. Behringer, ed. (2008), vol. 6792 of Proc. SPIE, p. 679206.
[CrossRef]

P. Evanschitzky, F. Shao, T. Fühner, A. Erdmann, “Compensation of mask induced aberrations by projector wavefront control,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 797329.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, “Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 832609.
[CrossRef]

Fakhry, M.

M. Fakhry, Y. Granik, K. Adam, K. Lai, “Total source mask optimization: High-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer, F. E. Abboud, eds. (2011), vol. 8166 of Proc. SPIE, p. 81663M.
[CrossRef]

Fenger, G.

M. K. Sears, G. Fenger, J. Mailfert, B. Smith, “Extending SMO into the lens pupil domain,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79731B.
[CrossRef]

Fey, D.

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

Finders, J.

J. Finders, T. Hollink, “Mask 3D effects: Impact on imaging and placement,” in 27th European Mask and Lithography Conference, U. F. Behringer, ed. (2011), vol. 7985 of Proc. SPIE, p. 79850I.
[CrossRef]

Fühner, T.

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

T. Fühner, P. Evanschitzky, A. Erdmann, “Mutual source, mask and projector pupil optimization,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 83260I.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, “Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 832609.
[CrossRef]

P. Evanschitzky, F. Shao, T. Fühner, A. Erdmann, “Compensation of mask induced aberrations by projector wavefront control,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 797329.
[CrossRef]

Gleason, B.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Gram, E. B.

Granik, Y.

M. Fakhry, Y. Granik, K. Adam, K. Lai, “Total source mask optimization: High-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer, F. E. Abboud, eds. (2011), vol. 8166 of Proc. SPIE, p. 81663M.
[CrossRef]

Han, C.

Han, W.-S.

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

Hirayanagi, N.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Hollink, T.

J. Finders, T. Hollink, “Mask 3D effects: Impact on imaging and placement,” in 27th European Mask and Lithography Conference, U. F. Behringer, ed. (2011), vol. 7985 of Proc. SPIE, p. 79850I.
[CrossRef]

Hu, P.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Huang, H.-T.

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

Izumi, H.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Jeon, C.-U.

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

Jia, N.

Kamat, V.

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

Kang, I.-Y.

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

Kim, H.-B.

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

Kita, N.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Kye, J.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Lai, K.

M. Fakhry, Y. Granik, K. Adam, K. Lai, “Total source mask optimization: High-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer, F. E. Abboud, eds. (2011), vol. 8166 of Proc. SPIE, p. 81663M.
[CrossRef]

Lam, E. Y.

Lee, J.-W.

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

Levinson, H. J.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Li, J.

Li, Y.

Limmer, S.

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

Liu, S.

Ma, X.

Ma, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Mack, C.

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007, Chap. 3).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, Aberration Theory Made Simple, 2 (SPIE, 2011, Chap. 1).

Mailfert, J.

M. K. Sears, G. Fenger, J. Mailfert, B. Smith, “Extending SMO into the lens pupil domain,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79731B.
[CrossRef]

Matsui, R.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Matsuyama, T.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Milanfar, P.

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

Mizuno, Y.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Moharam, M. G.

Neureuther, A. R.

A. K. Wong, A. R. Neureuther, “Mask topography effects in projection printing of phase phifting masks,” IEEE Trans. on Electron Devices 41, 895–902 (1994).
[CrossRef]

Ngai, C.

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

Nocedal, J.

J. Nocedal, S. J. Wright, Numerical Optimization, 2 (Springer, 2006, Chap. 5).

Pang, L.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Park, J. S.

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

Pommet, D. A.

Poonawala, A.

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

Reibold, D.

F. Shao, P. Evanschitzky, D. Reibold, A. Erdmann, “Fast rigorous simulation of mask diffraction using the waveguide method with parallelized decomposition technique,” in 24th European Mask and Lithography Conference, U. F. W. Behringer, ed. (2008), vol. 6792 of Proc. SPIE, p. 679206.
[CrossRef]

Sears, M. K.

M. K. Sears, B. Smith, “Modeling the effects of pupil-manipulated spherical aberration in optical nanolithography,” J. Micro/Nanolith., MEMS, MOEMS 12, 013008 (2013).
[CrossRef]

M. K. Sears, J. Bekaert, B. W. Smith, “Lens wavefront compensation for 3D photomask effects in subwavelength optical lithography,” Appl. Opt. 52, 314–322 (2013).
[CrossRef] [PubMed]

M. K. Sears, G. Fenger, J. Mailfert, B. Smith, “Extending SMO into the lens pupil domain,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79731B.
[CrossRef]

Shao, F.

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

F. Shao, P. Evanschitzky, D. Reibold, A. Erdmann, “Fast rigorous simulation of mask diffraction using the waveguide method with parallelized decomposition technique,” in 24th European Mask and Lithography Conference, U. F. W. Behringer, ed. (2008), vol. 6792 of Proc. SPIE, p. 679206.
[CrossRef]

P. Evanschitzky, F. Shao, T. Fühner, A. Erdmann, “Compensation of mask induced aberrations by projector wavefront control,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 797329.
[CrossRef]

Shen, Y.

Shin, I. K.

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

Siebert, J.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Slonaker, S. D.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Smith, B.

M. K. Sears, B. Smith, “Modeling the effects of pupil-manipulated spherical aberration in optical nanolithography,” J. Micro/Nanolith., MEMS, MOEMS 12, 013008 (2013).
[CrossRef]

M. K. Sears, G. Fenger, J. Mailfert, B. Smith, “Extending SMO into the lens pupil domain,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79731B.
[CrossRef]

Smith, B. W.

Tabery, C. E.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Tajima, K.

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

Tolani, V.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Tyminski, J. K.

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

Wong, A. K.

E. Y. Lam, A. K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/Nanolith. MEMS MOEMS 9, 033002 (2010).
[CrossRef]

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

A. K. Wong, A. R. Neureuther, “Mask topography effects in projection printing of phase phifting masks,” IEEE Trans. on Electron Devices 41, 895–902 (1994).
[CrossRef]

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005, Chap. 2).
[CrossRef]

Wong, N.

Wright, S. J.

J. Nocedal, S. J. Wright, Numerical Optimization, 2 (Springer, 2006, Chap. 5).

Wu, X.

Yoon, G.-S.

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

Yoshimoto, K.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Yu, J.-C.

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

Yu, P.

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

Zou, Y.

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Image Process. (2)

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

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

IEEE Trans. on Electron Devices (1)

A. K. Wong, A. R. Neureuther, “Mask topography effects in projection printing of phase phifting masks,” IEEE Trans. on Electron Devices 41, 895–902 (1994).
[CrossRef]

J. Micro/Nanolith. MEMS MOEMS (2)

E. Y. Lam, A. K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” J. Micro/Nanolith. MEMS MOEMS 9, 033002 (2010).
[CrossRef]

H. Aoyama, Y. Mizuno, N. Hirayanagi, N. Kita, R. Matsui, H. Izumi, K. Tajima, J. Siebert, W. Demmerle, T. Matsuyama, “Impact of realistic source shape and flexibility on source mask optimization,” J. Micro/Nanolith. MEMS MOEMS 13, 011005 (2014).
[CrossRef]

J. Micro/Nanolith., MEMS, MOEMS (1)

M. K. Sears, B. Smith, “Modeling the effects of pupil-manipulated spherical aberration in optical nanolithography,” J. Micro/Nanolith., MEMS, MOEMS 12, 013008 (2013).
[CrossRef]

J. Opt. (1)

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

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

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

A. Erdmann, F. Shao, P. Evanschitzky, T. Fühner, “Mask-topography-induced phase effects and wave aberrations in optical and extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 28, C6J1–C6J7 (2010).
[CrossRef]

Opt. Express (6)

Other (17)

J. Nocedal, S. J. Wright, Numerical Optimization, 2 (Springer, 2006, Chap. 5).

Y. Deng, Y. Zou, K. Yoshimoto, Y. Ma, C. E. Tabery, J. Kye, L. Capodieci, H. J. Levinson, “Considerations in source-mask optimization for logic applications,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 76401J.
[CrossRef]

V. N. Mahajan, Aberration Theory Made Simple, 2 (SPIE, 2011, Chap. 1).

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007, Chap. 3).
[CrossRef]

P. Evanschitzky, F. Shao, T. Fühner, A. Erdmann, “Compensation of mask induced aberrations by projector wavefront control,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 797329.
[CrossRef]

M. Fakhry, Y. Granik, K. Adam, K. Lai, “Total source mask optimization: High-capacity, resist modeling, and production-ready mask solution,” in Photomask Technology 2011, W. Maurer, F. E. Abboud, eds. (2011), vol. 8166 of Proc. SPIE, p. 81663M.
[CrossRef]

T. Dam, V. Tolani, P. Hu, K.-H. Baik, L. Pang, B. Gleason, S. D. Slonaker, J. K. Tyminski, “Source-mask optimization (SMO): from theory to practice,” in Optical Microlithography XXIII, M. V. Dusa, W. Conley, eds. (2010), vol. 7640 of Proc. SPIE, p. 764028.
[CrossRef]

M. K. Sears, G. Fenger, J. Mailfert, B. Smith, “Extending SMO into the lens pupil domain,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79731B.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, “Evaluation of various compact mask and imaging models for the efficient simulation of mask topography effects in immersion lithography,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 832609.
[CrossRef]

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005, Chap. 2).
[CrossRef]

G.-S. Yoon, H.-B. Kim, J.-W. Lee, S.-W. Choi, W.-S. Han, “Phase-shifted assist feature OPC for sub-45nm node optical lithography,” in Optical Microlithography XX, D. G. Flagello, ed. (2007), vol. 6520 of Proc. SPIE, p. 65201A.
[CrossRef]

T. Fühner, P. Evanschitzky, A. Erdmann, “Mutual source, mask and projector pupil optimization,” in Optical Microlithography XXV, W. Conley, ed. (2012), vol. 8326 of Proc. SPIE, p. 83260I.
[CrossRef]

J. Choi, I.-Y. Kang, J. S. Park, I. K. Shin, C.-U. Jeon, “Manufacurability of computation lithography mask: Current limit and requirements for sub-20nm node,” in Optical Microlithography XXVI, W. Conley, ed. (2013), vol. 8683 of Proc. SPIE, p. 86830L.
[CrossRef]

V. Agudelo, P. Evanschitzky, A. Erdmann, T. Fühner, F. Shao, S. Limmer, D. Fey, “Accuracy and performance of 3D mask models in optical projection lithography,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730O.
[CrossRef]

J. Finders, T. Hollink, “Mask 3D effects: Impact on imaging and placement,” in 27th European Mask and Lithography Conference, U. F. Behringer, ed. (2011), vol. 7985 of Proc. SPIE, p. 79850I.
[CrossRef]

F. Shao, P. Evanschitzky, D. Reibold, A. Erdmann, “Fast rigorous simulation of mask diffraction using the waveguide method with parallelized decomposition technique,” in 24th European Mask and Lithography Conference, U. F. W. Behringer, ed. (2008), vol. 6792 of Proc. SPIE, p. 679206.
[CrossRef]

T. H. Coskun, H. Dai, H.-T. Huang, V. Kamat, C. Ngai, “Accounting for mask topography effects in source-mask optimization for advanced nodes,” in Optical Microlithography XXIV, M. V. Dusa, ed. (2011), vol. 7973 of Proc. SPIE, p. 79730P.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Pupil wavefront distribution: a combination of primary and secondary spherical aberration.

Fig. 2
Fig. 2

Two kinds of test patterns used in simulation: (a)–(c) vertical line/space design with different pitches and (d) brick poly array. Red lines mark the critical locations for measuring the process window.

Fig. 3
Fig. 3

Simulation results of 32nm vertical lines at 112nm pitch.

Fig. 4
Fig. 4

Simulation results of brick poly array pattern.

Fig. 5
Fig. 5

Simulated aerial image of 32nm vertical lines at 96nm pitch.

Fig. 6
Fig. 6

Simulated pattern errors at different primary spherical aberration values (z9) for: (a) vertical line/space with different pitches and (b) brick poly array.

Fig. 7
Fig. 7

Simulated process window of vertical line/space with different pitches with (a) conventional SMO without pupil aberration and (b) mask-topography-aware SMO.

Fig. 8
Fig. 8

Simulated process window of brick poly array with (a) conventional SMO without pupil aberration and (b) mask-topography-aware SMO.

Tables (1)

Tables Icon

Table 1 Comparison of performance with different models and methods.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

I a ( x , y ) = J ( f , g ) | H ^ ( f + f 1 , g + g 1 ) e i 2 π W ( ρ , θ ) M ^ ( f 1 , g 1 ) e i 2 π ( f 1 x + g 1 y ) d f 1 d g 1 | 2 d f d g .
J ( f , g ) = J ( f , g ) J ( f , g ) d f d g ,
I a ( x , y ) f , g { J ( f , g ) | M ( x , y ) * H ( x , y ) | 2 } f , g J ( f , g ) .
H ( x , y ) = 1 { H ^ ( f , g ) e i 2 π W ( ρ , θ ) } .
I ( x , y ) = sig { I a ( x , y ) } = 1 1 + e α [ I a ( x , y ) t r ] ,
W ( ρ , θ ) = i = z i F i ( ρ , θ ) ,
W ( ρ , θ ) = z 9 ( 6 ρ 4 6 ρ 2 + 1 ) + z 16 ( 20 ρ 6 30 ρ 4 + 12 ρ 2 1 ) .
H ( x , y ; z 9 , z 16 ) = 1 { H ^ ( f , g ) e i 2 π [ z 9 ( 6 ρ 4 6 ρ 2 + 1 ) + z 16 ( 20 ρ 6 30 ρ 4 + 12 ρ 2 1 ) ] } .
minimize m { I ( x , y ; z 9 , z 16 ) I 0 ( x , y ) 2 2 } subject to M ( x , y ) { 0 , 1 } , J ( f , g ) 0 ,
{ I ( x , y ; z 9 , z 16 ) I 0 ( x , y ) 2 2 } m , n p ( z 9 m ) p ( z 16 n ) { I ( x , y ; z 9 m , z 16 n ) I 0 ( x , y ) 2 2 }
m , n ( M ) = f , g J ( f , g ) Re { [ 2 α ( I I 0 ) I ( 1 I ) ( M * H ( x , y ; z 9 m , z 16 n ) ) ] * H ˜ } ,
m , n ( J ) = x , y 2 α ( I I 0 ) I ( 1 I ) | M * H ( x , y ; z 9 m , z 16 n ) | 2 I a f , g J ( f , g ) ,
m , n ( M ) = m , n p ( z 9 m ) p ( z 16 n ) m , n ( M ) ,
m , n ( J ) = m , n p ( z 9 m ) p ( z 16 n ) m , n ( J ) .
α m ( k ) = m , n ( M ) ( k ) ( m , n ( M ) ( k ) m , n ( M ) ( k 1 ) ) ( m , n ( M ) ( k ) m , n ( M ) ( k 1 ) ) r m ( k 1 ) ,
r m ( k ) = m , n ( M ) ( k ) + α m ( k ) r m ( k 1 ) ,
M ( k + 1 ) = M ( k ) + s 1 r m ( k ) ,
α s ( k ) = m , n ( J ) ( k ) ( m , n ( J ) ( k ) m , n ( J ) ( k 1 ) ) ( m , n ( J ) ( k ) m , n ( J ) ( k 1 ) ) r s ( k 1 ) ,
r s ( k ) = m , n ( J ) ( k ) + α s ( k ) r s ( k 1 ) ,
J ( k + 1 ) = J ( k ) + s 2 r s ( k ) .
m , n ( M ) = x , y I I 0 2 2 M = [ 2 α ( I I 0 ) I ( 1 I ) I a M ] = f , g J ( f , g ) Re { [ 2 α ( I I 0 ) I ( 1 I ) ( M * H ( x , y ; z 9 m , z 16 n ) ) ] * H ˜ } .
m , n ( J ) = x , y I I 0 2 2 J = x , y 2 α ( I I 0 ) I ( 1 I ) I a J = x , y 2 α ( I I 0 ) I ( 1 I ) | M * H ( x , y ; z 9 m , z 16 n ) | 2 f , g J ( f , g ) f , g J ( f , g ) | M * H ( x , y ; z 9 m , z 16 n ) | 2 [ f , g J ( f , g ) ] 2 = x , y 2 α ( I I 0 ) I ( 1 I ) | M * H ( x , y ; z 9 m , z 16 n ) | 2 I a f , g J ( f , g ) .

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