短時間低溫顯影之電子束微影與鄰近效應修正演算法

Short-Time and Low-Temperature Development for Electron-Beam Lithography and the Algorithms of Proximity Effect Correction

10.6342/NTU201704286

粘群

電子束微影 ； 鄰近效應修正 ； 顯影模型 ； 次十奈米微影 ； 關鍵顯影路徑 ； 群體智能 ； 圖形演算法 ； electron-beam lithography ； proximity effect correction ； development model ； sub-10 nm lithography ； critical-development path ； swarm intelligence ； graph algorithm

臺灣大學電子工程學研究所學位論文

2017年

博士

管傑雄

英文

電子束微影為高解析度奈米結構之無光罩製造技術中最為廣泛使用與重要的一項技術，也提供了電子與光子元件之高速發展的條件。在電子束微影中最關鍵的一項問題是電子散射造成之鄰近效應，使得製造之元件結構失真並嚴重影響元件性能與應用。大多數嘗試修正鄰近效應的研究視顯影圖樣為電子束曝光造成之靜態結果，聚焦於調控電子劑量之空間分佈。事實上，顯影為一動態的過程，並為顯影時間與溫度的函數，而其不斷變動的性質，可能造成顯影圖樣偏離預期。此效應將隨著元件設計圖案尺寸微縮化越為顯著。近來，少數研究開始考慮將顯影的模擬計算加入鄰近效應修正法中，但顯影本為一複雜過程，傳統計算方法需耗用大量計算資源且計算時間相當冗長。 本論文聚焦於改善使用正型電子阻劑之高加速電壓電子束微影中的鄰近效應。我們利用一系列單點曝光實驗探討顯影過程，建立一可用於描述入射電子劑量、電子阻劑、以及顯影時間與溫度等顯影條件之間關係之綜合微分模型。由此模型可發現曝光位置為一具有超高顯影速率之奇異點，並因此可將其視為顯影過程之起始點。此外，我們藉由曝光之電子劑量點散布函數檢視其引致之特徵區域性質，並更進一步發展可有效降低鄰近效應之低溫短時間顯影法，以該法製造線寬僅8奈米之獨立線或週期30奈米線寬9奈米之高密度線陣列。 從單點實驗研究中對於顯影過程的理解，引領我們發明創新之短距離鄰近效應修正方法。我們基於二維顯影模型提出關鍵顯影路徑概念，並以之作為評估電子束微影顯影圖樣適合度之指標。本論文將搜尋關鍵顯影路徑轉化為圖論之最短路徑問題，因此賦予顯影路徑之模擬能有更高效率之演算法之可能性。我們提出基於Dijkstra演算法之關鍵顯影路徑搜尋法，並使用優先佇列資料結構，以確保計算正確性與維持計算效率。此外，我們探討應用於鄰近效應修正問題中的最佳化策略。我們將具群體智慧之最佳化方法引入鄰近效應修正法，並與基於簡單形之最佳化方法比較。從數值分析顯示，在如逐像素式之精細鄰近效應修正法之較複雜適應度函數，選用適當之最佳化策略極為重要。以本論文提出之鄰近效應修正法應用於U形裂環共振器電子束微影圖樣之最佳化，可有效改善鄰近效應並製成與設計具高吻合度之顯影圖樣。我們提出之鄰近效應修正策略，可顯著降低計算成本並適用於具有多重設計限制條件之複雜圖樣。

Electron-beam lithography (EBL) is one of the most popular and important techniques in manufacturing high-resolution nanopatterns without masks and enabling the fast development of electronic and photonic devices. The proximity effect is one of the most critical issue in EBL, as it can degrade the pattern quality and, thus, impact the performance of the applications greatly. Regarding the development as a static result of electron-beam exposure, most studies solving the proximity effect by focusing on the spatial distribution of electron intensity. In fact, the development is a dynamic process as a function of the development duration and temperature. The continually changing nature of development may lead to pattern deviation. This effect becomes more noticeable as the required feature size continually shrinks. Recently, some of the researches start to consider integrating the development simulation into the proximity effect correction (PEC). However, the EBL development is a complicated process, and the conventional methods are very computationally intensive and lengthy. This dissertation focuses on solving the proximity effect of the high-voltage EBL using the positive-tone resist. We first use a set of single-spot experiments to categorize the development process and establish a comprehensive differential model of EBL to describe the relation among the incident electrons, resist, and the development conditions such as durations and temperatures. This model identifies the location of exposure point as a singular point of ultra-high development rate, which, thus, can be considered as the beginning point of the development. Further, we verify the characteristic region of each incident spot induced by the point spread function of the electron-beam system. Eliminating the proximity effect effectively, we further achieve the pattern of isolated line with the line width of 8 nm and dense line array with the line width of 9 nm with the pitch size of 30 nm by utilizing the results from single-spot experiments at low development temperatures. The insights from the study of the single-spot experiments lead to the innovation of a novel short-range PEC method. Based on the 2-D development model, we propose a novel concept of the critical-development path and its usage in the evaluation of the fitness of EBL patterns. For the first time, we also transform the searching of the critical-development path into the shortest-path problem of graph theory, which enables the potential of using a more efficient algorithm in the simulation of the development path. We propose a Dijkstra-based algorithm with the data structure of priority queue to guarantee the correctness and to maintain the efficiency. Also, we investigate the optimization strategies in the PEC problems. The algorithm of swarm intelligence is introduced to the PEC and is compared with the simplex-based method. From the numerical analysis, we demonstrate that choosing of a suitable optimization scheme is important especially in minimizing a complicated function like the fitness function of EBL with pixel-based fine tuning. The PEC algorithm is applied to the fabrication of an U-shaped split-ring resonators and produces an optimized exposure pattern that shows excellent agreement with the targeted design objectives. Our work on the PEC strategy reduces the computational cost significantly and is particularly suitable for the design of complex pattern with various constraints.

1. [1] J. Joo, B. Y. Chow, and J. M. Jacobson, “Nanoscale patterning on insulating substrates by critical energy electron beam lithography,” Nano Letters, vol. 6, no. 9, pp. 2021–2025, 2006.
   連結：
2. [3] H. Duan, A. I. Fernández-Domínguez, M. Bosman, S. A. Maier, and J. K. W. Yang,“Nanoplasmonics: Classical down to the nanometer scale,” Nano Letters, vol. 12, no. 3, pp. 1683–1689, 2012.
   連結：
3. [4] M. Ieong, B. Doris, J. Kedzierski, K. Rim, and M. Yang, “Silicon device scaling to the sub-10-nm regime,” Science, vol. 306, no. 5704, pp. 2057–2060, 2004.
   連結：
4. [5] R. Near, C. Tabor, J. Duan, R. Pachter, and M. El-Sayed, “Pronounced effects of anisotropy on plasmonic properties of nanorings fabricated by electron beam lithography,”Nano Letters, vol. 12, no. 4, pp. 2158–64, 2012.
   連結：
5. [6] D. R. Ward, F. Huser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nature nanotechnology, vol. 5, no. 10, pp. 732–736, 2010.
   連結：
6. [7] U. Y. Lau, S. S. Saxer, J. Lee, E. Bat, and H. D. Maynard, “Direct write protein patterns for multiplexed cytokine detection from live cells using electron beam lithography,”ACS Nano, vol. 10, no. 1, pp. 723–9, 2016.
   連結：
7. [9] T. H. P. Chang, “Proximity effect in electron‐beam lithography,” Journal of Vacuum Science and Technology, vol. 12, no. 6, pp. 1271–1275, 1975.
   連結：
8. [10] R. J. Bojko and B. J. Hughes, “Quantitative lithographic performance of proximity correction for electron beam lithography,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 8, no. 6, p. 1909, Nov. 1990.
   連結：
9. [12] L. Stevens, R. Jonckheere, E. Froyen, S. Decoutere, and D. Lanneer, “Determination of the proximity parameters in electron beam lithography using doughnut-structures,”Microelectronic Engineering, vol. 5, no. 1-4, pp. 141–150, Dec. 1986.
   連結：
10. [13] W. Patrick and P. Vettiger, “Optimization of the proximity parameters for the electron beam exposure of nanometer gate-length GaAs metal–semiconductor field effect transistors,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 6, no. 6, p. 2037, Nov. 1988.
    連結：
11. [14] E. Boere, E. van der Drift, J. Romijn, and B. Rousseeuw, “Experimental study on proximity effects in high voltage e-beam lithography,” Microelectronic Engineering, vol. 11, no. 1-4, pp. 351–354, Apr. 1990.
    連結：
12. [15] Z. Cui, “Monte carlo simulation of electron beam lithography on topographical substrates,” Microelectronic Engineering, vol. 41-42, pp. 175–178, Mar. 1998.
    連結：
13. [16] J. Zhou and X. Yang, “Monte carlo simulation of process parameters in electron beam lithography for thick resist patterning,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 24, no. 3, p. 1202, 2006.
    連結：
14. [17] C. A. Mack, “Three-dimensional electron-beam lithography simulation,” in Emerging Lithographic Technologies, D. E. Seeger, Ed., SPIE, Jul. 1997.
    連結：
15. [18] P. Vermeulen, R. Jonckheere, and L. Vandenhove, “Proximity-effect correction in electron-beam lithography,” Journal of Vacuum Science & Technology B, vol. 7, no. 6, pp. 1556–1560, 1989.
    連結：
16. [19] M. Osawa, K. Takahashi, M. Sato, and H. Arimoto, “Proximity effect correction using pattern shape modification and area density map for electron-beam projection lithography,” Journal of Vacuum Science & Technology B, vol. 19, no. 6, pp. 2483–2487, 2001.
    連結：
17. [20] L. E. Ocola, D. J. Gosztola, and D. Rosenmann, “Automated geometry assisted proximity effect correction for electron beam direct write nanolithography,” Journal of Vacuum Science & Technology B, vol. 33, no. 6, 06FD02–06FD02, 2015.
    連結：
18. [21] L. E. Ocola and A. Stein, “Effect of cold development on improvement in electron-beam nanopatterning resolution and line roughness,” Journal of Vacuum Science & Technology B, vol. 24, no. 6, pp. 3061–3065, 2006.
    連結：
19. [22] M. A. Mohammad, T. Fito, J. Chen, S. Buswell, M. Aktary, M. Stepanova, and S. K. Dew, “Systematic study of the interdependence of exposure and development conditions and kinetic modelling for optimizing low-energy electron beam nanolithography,”Microelectronic Engineering, vol. 87, no. 5-8, pp. 1104–1107, 2010.
    連結：
20. [23] M. A. Mohammad, T. Fito, J. Chen, M. Aktary, M. Stepanova, and S. K. Dew, “Interdependence of optimum exposure dose regimes and the kinetics of resist dissolution for electron beam nanolithography of polymethylmethacrylate,” Journal of Vacuum Science & Technology B, vol. 28, no. 1, pp. L1–L4, 2010.
    連結：
21. [24] F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Transactions on Electron Devices, vol. 22, no. 7, pp. 456–464, 1975.
    連結：
22. [25] Y. Hirai, S. Tomida, K. Ikeda, M. Sasago, M. Endo, S. Hayama, and N. Nomura, “Three-dimensional resist process simulator peace (photo and electron beam lithography analyzing computer engineering system),” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 10, no. 6, pp. 802–807, 1991.
    連結：
23. [26] M. Kotera, K. Yagura, and H. Niu, “Dependence of linewidth and its edge roughness on electron beam exposure dose,” Journal of Vacuum Science & Technology B, vol. 23, no. 6, pp. 2775–2779, 2005.
    連結：
24. [27] Q. Dai, R. Guo, S. Y. Lee, J. Choi, S. H. Lee, I. K. Shin, C. U. Jeon, B. G. Kim, and H. K. Cho, “A fast path-based method for 3-d resist development simulation,”Microelectronic Engineering, vol. 127, pp. 86–96, 2014.
    連結：
25. [29] S. A. Rishton and D. P. Kern, “Point exposure distribution measurements for proximity correction in electron beam lithography on a sub-100 nm scale,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 5, no. 1, p. 135, Jan. 1987.
    連結：
26. [32] T. Nishida, M. Notomi, R. Iga, and T. Tamamura, “Quantum wire fabrication by e-beam elithography using high-resolution and high-sensitivity e-beam resist ZEP-520,” Japanese Journal of Applied Physics, vol. 31, no. Part 1, No. 12B, pp. 4508–4514, Dec. 1992.
    連結：
27. [33] K. Koshelev, M. A. Mohammad, T. Fito, K. L. Westra, S. K. Dew, and M. Stepanova,“Comparison between ZEP and PMMA resists for nanoscale electron beam lithography experimentally and by numerical modeling,” Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, vol. 29, no. 6, 06F306, Nov. 2011.
    連結：
28. [35] W. Hu, G. Bernstein, K. Sarveswaran, and M. Lieberman, “Low temperature development of PMMA for sub-10-nm electron beam lithography,” in 2003 Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003., IEEE, 2003.
    連結：
29. [36] A. E. Grigorescu and C. W. Hagen, “Resists for sub-20-nm electron beam lithography with a focus on HSQ: State of the art,” Nanotechnology, vol. 20, no. 29, p. 292 001, Jul. 2009.
    連結：
30. [39] M. A. Mohammad, M. Muhammad, S. K. Dew, and M. Stepanova, “Fundamentals of electron beam exposure and development,” in Nanofabrication, Springer Vienna, Oct. 2011, pp. 11–41.
    連結：
31. [40] J. S. Greeneich, “Time evolution of developed contours in poly-(methyl methacrylate) electron resist,” Journal of Applied Physics, vol. 45, no. 12, pp. 5264–5268, Dec. 1974.
    連結：
32. [41] L. Masaro and X. X. Zhu, “Physical models of diffusion for polymer solutions, gels and solids,” Progress in Polymer Science, vol. 24, no. 5, pp. 731–775, Aug. 1999.
    連結：
33. [43] T. Okada, J. Fujimori, M. Aida, M. Fujimura, T. Yoshizawa, M. Katsumura, and T. Iida, “Enhanced resolution and groove-width simulation in cold development of zep520a,” Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, vol. 29, no. 2, p. 021 604, Mar. 2011.
    連結：
34. [44] P. G. De Gennes, “Dynamics of entangled polymer solutions. i. the rouse model,”Macromolecules, vol. 9, no. 4, pp. 587–593, 1976.
    連結：
35. [46] N. Nemoto, T. Kojima, T. Inoue, M. Kishine, T. Hirayama, and M. Kurata, “Self diffusion of polymers in the concentrated regime. part 2. self diffusion and tracerdiffusion coefficient and viscosity of concentrated solutions of linear polystyrenes in dibutyl phthalate,” Macromolecules, vol. 22, no. 9, pp. 3793–3798, 1989.
    連結：
36. [48] I. Nakanishi and K. Yamaguchi, “A numerical experiment on nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure,” Journal of Physics of the Earth, vol. 34, no. 2, pp. 195–201, 1986.
    連結：
37. [49] T. J. Moser, “Shortest path calculation of seismic rays,” Geophysics, vol. 56, no. 1, pp. 59–67, 1991.
    連結：
38. [50] M. A. Finney, “Fire growth using minimum travel time methods,” Canadian Journal of Forest Research, vol. 32, no. 8, pp. 1420–1424, 2002.
    連結：
39. [51] E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, 1959.
    連結：
40. [52] M. L. Fredman and R. E. Tarjan, “Fibonacci heaps and their uses in improved network optimization algorithms,” Journal of the ACM, vol. 34, no. 3, pp. 596–615, 1987.
    連結：
41. [53] M. Barbehenn, “A note on the complexity of dijkstra's algorithm for graphs with weighted vertices,” IEEE Transactions on Computers, vol. 47, no. 2, pp. 263–263, 1998.
    連結：
42. [54] B. V. Cherkassky, A. V. Goldberg, and T. Radzik, “Shortest paths algorithms: Theory and experimental evaluation,” Mathematical Programming, vol. 73, no. 2, pp. 129–174, 1996.
    連結：
43. [57] Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” in 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), IEEE, 1998.
    連結：
44. [58] T. Huang and A. S. Mohan, “A hybrid boundary condition for robust particle swarm optimization,” IEEE Antennas and Wireless Propagation Letters, vol. 4, pp. 112–117, 2005.
    連結：
45. [59] K. E. Parsopoulos and M. N. Vrahatis, “Particle swarm optimization method for constrained optimization problems,” Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies, vol. 76, no. 1, pp. 214–220, 2002.
    連結：
46. [60] M. J. D. Powell, “On trust region methods for unconstrained minimization without derivatives,” Mathematical Programming, vol. 97, no. 3, pp. 605–623, Aug. 2003.
    連結：
47. [61] M. J. D. Powell, A view of algorithms for optimization without derivatives, 5. 2007, vol. 43, pp. 1–12.
    連結：
48. [62] M. J. D. Powell, A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation. Springer Netherlands, 1994, pp. 51–67.
    連結：
49. [63] R. C. Eberhart and Y. Shi, “Comparing inertia weights and constriction factors in particle swarm optimization,” in Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512), IEEE, 2000.
    連結：
50. [65] M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nature Photonics, vol. 6,no. 11, pp. 737–748, 2012.
    連結：
51. [66] S. A. Schulz, J. Upham, F. Bouchard, I. De Leon, E. Karimi, and R. W. Boyd,“Quantifying the impact of proximity error correction on plasmonic metasurfaces,”Optical Materials Express, vol. 5, no. 12, pp. 2798–2803, 2015.
    連結：
52. [67] P. G. de Gennes, “Reptation of a polymer chain in the presence of fixed obstacles,”The Journal of Chemical Physics, vol. 55, no. 2, pp. 572–579, Jul. 1971.
    連結：
53. [68] K. Kremer and G. S. Grest, “Dynamics of entangled linear polymer melts: A molecular-dynamics simulation,” Journal of Chemical Physics, vol. 92, no. 8, pp. 5057–5057, 1990.
    連結：
54. [69] T. Yamaguchi, H. Namatsu, M. Nagase, K. Yamazaki, and K. Kurihara, “Nanometerscale linewidth fluctuations caused by polymer aggregates in resist films,” Applied Physics Letters, vol. 71, no. 16, pp. 2388–2390, Oct. 1997.
    連結：
55. [70] L. E. Ocola, “Nanoscale geometry assisted proximity effect correction for electron beam direct write nanolithography,” Journal of Vacuum Science & Technology B, vol. 27, no. 6, pp. 2569–2571, 2009.
    連結：
56. [71] A. Starikov, “Use of a single size square serif for variable print bias compensation in microlithography: Method, design, and practice,” Proc. SPIE, vol. 1088, 1989.
    連結：
57. [72] M. Parikh, “Self‐consistent proximity effect correction technique for resist exposure (spectre),” Journal of Vacuum Science and Technology, vol. 15, no. 3, pp. 931–933, 1978.
    連結：
58. [74] E. Jones, T. Oliphant, P. Peterson, et al., SciPy: Open source scientific tools for Python, http://www.scipy.org/, 2001.
    連結：
59. [2] J. C. van Oven, F. Berwald, K. K. Berggren, P. Kruit, and C. W. Hagen, “Electron-beam induced deposition of 3-nm-half-pitch patterns on bulk si,” Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, vol. 29, no. 6, 06F305–06F305, Nov. 2011.
60. [8] B. Wu and A. R. Neureuther, “Energy deposition and transfer in electron-beam lithography,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 19, no. 6, p. 2508, 2001.
61. [11] X. Huang, G. Bazán, and G. H. Bernstein, “New technique for computation and challenges for electron-beam lithography,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 11, no. 6, p. 2565, Nov. 1993.
62. [28] A. Hasegawa, R.-I. Kang, and K. Shono, “Electron beam direct lithography system using the SEM,” Electronics and Communications in Japan (Part II: Electronics), vol. 75, no. 11, pp. 51–61, 1992.
63. [30] H. Yang, L. Fan, A. Jin, Q. Luo, C. Gu, and Z. Cui, “Low-energy electron-beam lithography of ZEP-520 positive resist,” in 2006 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems, IEEE, Jan. 2006.
64. [31] Y. H. Lee, R. Browning, N. Maluf, G. Owen, and R. F. W. Pease, “Low voltage alternative for electron beam lithography,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 10, no. 6, p. 3094, Nov. 1992.
65. [34] W. ( Hu, K. Sarveswaran, M. Lieberman, and G. H. Bernstein, “Sub-10 nm electron-beam lithography using cold development of poly(methylmethacrylate),” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 22, no. 4, p. 1711, 2004.
66. [37] M. J. Rooks, E. Kratschmer, R. Viswanathan, J. Katine, R. E. Fontana, and S. A. MacDonald, “Low stress development of poly(methylmethacrylate) for high aspect ratio structures,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 20, no. 6, p. 2937, 2002.
67. [38] M. Stepanova, T. Fito, Z. Szabo, K. Alti, A. P. Adeyenuwo, K. Koshelev, M. Aktary, and S. K. Dew, “Simulation of electron beam lithography of nanostructures,”Journal of Vacuum Science & Technology B, vol. 28, no. 6, pp. C6c48–C6c57, 2010.
68. [42] B. A. Miller-Chou and J. L. Koenig, “A review of polymer dissolution,” Progress in Polymer Science, vol. 28, no. 8, pp. 1223–1270, Aug. 2003.
69. [45] F. Lange, P. Judeinstein, C. Franz, B. Hartmann-Azanza, S. Ok, M. Steinhart, and K. Saalwächter, “Large-scale diffusion of entangled polymers along nanochannels,”ACS Macro Letters, vol. 4, no. 5, pp. 561–565, 2015.
70. [47] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in 1995 IEEE International Conference on Neural Networks: Proceedings, vol. 4, IEEE, 1995, pp. 1942–1948.
71. [55] O. Kramer, D. E. Ciaurri, and S. Koziel, “Derivative-free optimization,” in Computational Optimization, Methods and Algorithms, S. Koziel and X.-S. Yang, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011, pp. 61–83.
72. [56] A. R. Conn, K. Scheinberg, and L. N. Vicente, Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics, Jan. 2009, pp. 276–276.
73. [64] C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Applied Physics B, vol. 84, no. 1, pp. 219–227, 2006.
74. [73] M. J. D. Powell, Advances in Optimization and Numerical Analysis, S. Gomez and J.-P. Hennart, Eds. Dordrecht: Springer Netherlands, 1994, ch. 51-67, pp. 51–67.
75. [75] S.-Y. Lee, J. C. Jacob, C. Chen, J. A. McMillan, and N. C. MacDonald, “Proximity effect correction in electron‐beam lithography: A hierarchical rule‐based scheme—pyramid,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, vol. 9, no. 6, pp. 3048–3053, 1991.
76. [76] S.-Y. Lee and J. Laddha, “Adaptive selection of control points for improving accuracy and speed of proximity effect correction,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, vol. 16, no. 6, pp. 3269–3274, 1998.