Machine Learning for Compact Lithographic Process Models

  • J. P. ShielyEmail author


This chapter described the motivations and requirements for compact patterning models, and the role of machine learning in constructing them. We start by defining patterning process models and their role in the IC fabrication process. We then describe the requirements of these models, in particular with regard to turn-around time in production high-volume manufacturing, which usually necessitates the use of compact patterning process models rather than rigorous models. We describe the stages into which the pattern process can be subdivided, and the challenges of modeling each stage. We then move to the discussion of supervised learning as it has been applied to the problem of training compact patterning process models. In the final section, we review some of recent results in applying deep learning to this domain.



Special thanks to Mike Rieger and John Stirniman for introducing me to this fascinating field.


  1. 1.
    E. Abbe, Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Arch. Mikrosk. Anat. 9, 413–418 (1873)CrossRefGoogle Scholar
  2. 2.
    Agudelo et al., Application of artificial neural networks to compact mask models in optical lithography simulation. J. Micro/Nanolith, MEMS MOEMS 13(1), 0110022-1–16, (2014)Google Scholar
  3. 3.
    J.T. Azpiroz, Analysis and modeling of photomask near-fields in sub-wavelength deep ultraviolet lithography with optical proximity correction, Dissertation, University of California, Los Angeles, 2004Google Scholar
  4. 4.
    S. Babin et al., Modeling of charge and discharge in scanning electron microscopy. Proc. SPIE 7378 (2009).
  5. 5.
    D. Beale et al., Etch modeling for accurate full-chip process proximity correction. Proc. SPIE 5754 (2004).
  6. 6.
    Å. Björk, Numerical Methods for Least Squares Problems (Society for Industrial and Applied Mathematics, Philadelphia, 1996). CrossRefGoogle Scholar
  7. 7.
    S.-Y. Chou et al., Study of mask corner rounding effects on lithographic patterning for 90-nm technology and beyond. Proc. SPIE 5446 (2004).
  8. 8.
    N. Cobb, Fast optical and process proximity correction algorithms for integrated circuit manufacturing, Dissertation, University of California, Berkeley, 1998Google Scholar
  9. 9.
    K. Cummings et al., Using a neural network to proximity correct patterns written with a Cambridge electron beam microfabricator 10.5 lithography system. Appl. Phys. Lett. 57, 1431 (1990)Google Scholar
  10. 10.
    R. Dennard et al., Design of ion-implanted MOSFET’s with very small physical dimensions. IEEE J. Solid State Circuits (1974).
  11. 11.
    F.H. Dill, Modeling projection printing of positive photoresists. IEEE Trans Electron Devices 22, 456–464 (1975)CrossRefGoogle Scholar
  12. 12.
    B. Efron et al., Least angle regression. Ann. Stat. 32, 407–499 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Fang et al., A physics-based model for negative tone development materials. J. Photopolym. Sci. Technol. 27, 53–59 (2014)CrossRefGoogle Scholar
  14. 14.
    R. Frye et al., Proximity effect corrections in electron beam lithography using a neural network, in IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings (1990).
  15. 15.
    H. Gamo, Matrix treatment of partial coherence, in Progress in Optics, ed. by E. Wolf (1964).
  16. 16.
    A. Garetto et al., Aerial imaging technology for photomask qualification: from a microscope to a metrology tool. Adv. Opt. Technol. (2012).
  17. 17.
    I. Goodfellow, Y. Bengio, A. Courville, Deep Learning (The MIT Press, Cambridge, 2016)zbMATHGoogle Scholar
  18. 18.
    T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. (Springer, New York, 2009)CrossRefGoogle Scholar
  19. 19.
    H. Hopkins, On the diffraction theory of optical images. Proc. Roy. Soc. A 217, 408 (1953)MathSciNetzbMATHGoogle Scholar
  20. 20.
    A. Isoyan, L. Melvin, Full-chip high resolution electron-beam lithography proximity effect correction modeling. Proc. SPIE 7637 (2010).
  21. 21.
    J. Kotani et al., Mask CD uniformity improvement by dry etching loading effect correction. Proc. SPIE 5256.
  22. 22.
    A. Krizhevsky, ImageNet classification with deep convolutional neural networks. Adv. Neural Inf. Proces. Syst. 25, 1097–1105 (2012)Google Scholar
  23. 23.
    S. Lan et al., Deep learning assisted fast mask optimization. Proc. SPIE 10587 (2018).
  24. 24.
    Y. LeCun et al., Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  25. 25.
    M. Levenson et al., Improving resolution in photolithography with a phase shifting mask. IEEE Trans. Electron Devices 29, 1828–1836 (1982)CrossRefGoogle Scholar
  26. 26.
    P. Liu et al., A full-chip 3D computational framework. Proc. SPIE 83260A (2012).
  27. 27.
    C. Mack, New kinetic model for resist dissolution. J. Electrochem. Soc. 139, L34–L39 (1992)CrossRefGoogle Scholar
  28. 28.
    C. Mack, Fundamental Principles of Optical Lithography (Wiley, Hoboken, 2007)CrossRefGoogle Scholar
  29. 29.
    V. Mardiris, Neural networks for the simulation of photoresist exposure process in integrated circuit fabrication. Model. Simul. Mater. Sci. Eng. 5, 439–450 (1997)CrossRefGoogle Scholar
  30. 30.
    D. Matiut et al., New models for the simulation of post-exposure bake of chemically amplified resists. Proc. SPIE 5039 (2003).
  31. 31.
    T. Mitchell, Machine Learning (McGraw-Hill, New York, 1997)zbMATHGoogle Scholar
  32. 32.
    M.G. Moharam et al., Rigorous coupled-wave analysis of planar-grating diffraction. J. Opt. Soc. Am. A 71 (1981).
  33. 33.
    G. Moore, Cramming more components onto integrated circuits. Electronics 38, 114–117 (1965)Google Scholar
  34. 34.
    N. Nakayamada et al., Modeling of resist surface charging effect on EBM-8000 and its comparison with EBM-6000. Proc. SPIE 8701 (2013).
  35. 35.
    N. Nakayamada et al., Electron beam lithography modeling assisted by artificial intelligence technology. Proc. SPIE 10454 (2017).
  36. 36.
    O. Otto et al., Automated optical proximity correction: a rules-based approach. Proc. SPIE 2197 (1994).
  37. 37.
    M. Rieger, Communication theory in optical lithography. J. Micro/Nanolithogr. MEMS MOEMS 11(1) (2012).
  38. 38.
    S. Robertson, Negative tone development: gaining insight through physical simulation. Proc. SPIE 7972 (2011).
  39. 39.
    D. Rumelhart, G. Hinton, R. Williams, Learning representations by backpropagating errors. Nature 323, 533 (1986)CrossRefGoogle Scholar
  40. 40.
    V. Rutigiliani et al., Setting up a proper power spectral density (PSD) and autocorrelation analysis for material and process characterization. Proc. SPIE 10585 (2018).
  41. 41.
    I. Santo et al., Accurate contour extraction from mask SEM image. Proc. SPIE 9050 (2014).
  42. 42.
    D. Shamiryan et al., Dry etching process for bulk finFET manufacturing. Microelectron. Eng. 86(1), 96–98 (2009)CrossRefGoogle Scholar
  43. 43.
    S. Shim et al., Etch proximity correction through machine-learning driven etch bias model. Proc. SPIE 9782 (2016).
  44. 44.
    S. Shim et al., Machine learning-based resist 3D model. Proc. SPIE 10147 (2017).
  45. 45.
    L. Stirniman, M. RIeger, Fast proximity correction with zone sampling. Proc. SPIE (1994). Google Scholar
  46. 46.
    I. Stobert et al., Etch correction and OPC: a look at the current and future of etch correction. 1493 Proc. SPIEE 8685 (2013).
  47. 47.
    L.F. Thompson et al. (eds.), Introduction to Microlithography, 2nd edn. (American Chemical Society, Washington, 1994)Google Scholar
  48. 48.
    Y. Watanabe et al., Accurate lithography simulation model based on convolutional neural networks. Proc. SPIE 10147 (2017).
  49. 49.
    F. Weisbuch, A.S. Naranaya, Assessing SEM contour based OPC models quality using rigorous simulation. Proc. SPIE 9051 (2014).
  50. 50.
    A.K. Wong et al., Massively parallel electromagnetic simulation for photolithographic applications. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 14 (1995).
  51. 51.
    C. Wu et al., Photoresist 3D profile related etch process simulation and its application to full chip etch compact modeling. Proc. SPIE 9426 (2015).
  52. 52.
    M. Young, Modeling high numerical aperture optical lithography. Proc. SPIE 922 (1988).
  53. 53.
    F. Zach, Neural network based approach to resist modeling and OPC. Proc. SPIE 5377 (2004).
  54. 54.
    H. Zhang et al., An accurate ILT-enabling full-chip mask 3d model for all-angle patterns (2013). Proc. SPIE 8880.
  55. 55.
    R. Zimmerman et al., Predictive modeling for EBPC in EBDW. Proc. SPIE 7488 (2009).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Synopsys, Inc.Mountain ViewUSA

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