Skip to main content
SpringerLink
Log in

Designing a New Lattice Model to Simulate Low-molecular-weight Block Copolymers for Nanolithographic Applications

  • Research Article
  • Published:
Chinese Journal of Polymer Science Aims and scope Submit manuscript

Abstract

A new lattice model is designed to be suitable for simulating low-molecular-weight block copolymer (BCP) melts currently used in experiments to achieve sub-10 nm domain sizes (i.e., having an invariant degree of polymerization between 102 and 103). It gives an isothermal compressibility comparable to real polymers such as polystyrene and poly(methyl methacrylate), high Monte Carlo simulation efficiency, and the fluctuation effects important for the low-molecular-weight BCPs. With its high lattice coordination number, the model can also be readily used for branched chains such as star BCPs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. International Technology Roadmap for Semiconductors (ITRS) 2.0. http://www.itrs2.net/

  2. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 1980, 13, 1602–1617.

    Article  CAS  Google Scholar 

  3. Wan, L.; Ruiz, R.; Gao, H.; Patel, K. C.; Albrecht, T. R.; Yin, J.; Kim, J.; Cao, Y.; Lin, G. The limits of lamellae-forming PS-b-PMMA block copolymers for lithography. ACS Nano 2015, 9, 7506–7514.

    Article  CAS  Google Scholar 

  4. Kennemur, J. G.; Hillmyer, M. A.; Bates, F. S. Synthesis, thermodynamics, and dynamics of poly (4-tert-butylstyrene-b-methyl methacrylate). Macromolecules 2012, 45, 7228–7236.

    Article  CAS  Google Scholar 

  5. Kennemur, J. G.; Yao, L.; Bates, F. S.; Hillmyer, M. A. Sub-5 nm domains in ordered poly(cyclohexylethylene)-block-poly(methyl methacrylate) block polymers for lithography. Macromolecules 2014, 47, 1411–1418.

    Article  CAS  Google Scholar 

  6. Sweat, D. P.; Kim, M.; Larson, S. R.; Choi, J. W.; Choo, Y.; Osuji, C. O.; Gopalan, P. Rational design of a block copolymer with a high interaction parameter. Macromolecules 2014, 47, 6687–6696.

    Article  CAS  Google Scholar 

  7. Luo, Y.; Montarnal, D.; Kim, S.; Shi, W.; Barteau, K. P.; Pester, C. W.; Hustad, P. D.; Christianson, M. D.; Fredrickson, G. H.; Kramer, E. J. Poly(dimethylsiloxane-b-methyl methacrylate): a promising candidate for sub-10 nm patterning. Macromolecules 2015, 48, 3422–3430.

    Article  CAS  Google Scholar 

  8. Jeong, G.; Yu, D. M.; Mapas, J. K. D.; Sun, Z.; Rzayev, J.; Russell, T. P. Realizing 5. 4 nm full pitch lamellar microdomains by a solidstate transformation. Macromolecules 2017, 50, 7148–7154.

    Article  CAS  Google Scholar 

  9. Kwak, J.; Mishra, A. K.; Lee, J.; Lee, K. S.; Choi, C.; Maiti, S.; Kim, M.; Kim, J. K. Fabrication of sub-3 nm feature size based on block copolymer self-assembly for next-generation nanolithography. Macromolecules 2017, 50, 6813–6818.

    Article  CAS  Google Scholar 

  10. Albert, J. N.; Epps III, T. H. Self-assembly of block copolymer thin films. Materials Today 2010, 13, 24–33.

    Article  CAS  Google Scholar 

  11. Fredrickson, G. H.; Helfand, E.; Bates, F. S.; Leibler, L. Microphase separation in block copolymer: recent developments. Springer Series Chem. 1989, 51, 13–19.

    Article  CAS  Google Scholar 

  12. Bates, C. M.; Maher, M. J.; Janes, D. W.; Ellison, C. J.; Willson, C. G. Block copolymer lithography. Macromolecules 2014, 47, 2–12.

    Article  CAS  Google Scholar 

  13. Matsen, M. W.; Thompson, R. Equilibrium behavior of symmetric ABA triblock copolymer melts. J. Chem. Phys. 1999, 111, 7139–7146.

    Article  CAS  Google Scholar 

  14. Spontak, R. J.; Smith, S. D. Perfectly-alternating linear (AB)n multiblock copolymers: effect of molecular design on morphology and properties. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 947–955.

    Article  CAS  Google Scholar 

  15. Zhu, Y.; Gido, S. P.; Moshakou, M.; Iatrou, H.; Hadjichristidis, N.; Park, S.; Chang, T. Effect of junction point functionality on the lamellar spacing of symmetric (PS)n (Pl)n miktoarm star block copolymers. Macromolecules 2003, 36, 5719–5724.

    Article  CAS  Google Scholar 

  16. Zhang, G.; Fan, Z.; Yang, Y.; Qiu, F. Phase behaviors of cyclic diblock copolymers. J. Chem. Phys. 2011, 135, 174902.

    Article  Google Scholar 

  17. Zhang, J.; Wu, J.; Jiang, R.; Wang, Z.; Yin, Y.; Li, B.; Wang, Q. Lattice self-consistent field calculations of confined symmetric block copolymers of various chain architectures. Soft Matter 2020, 16, 4311–4323.

    Article  CAS  Google Scholar 

  18. Shi, W.; Tateishi, Y.; Li, W.; Hawker, C. J.; Fredrickson, G. H.; Kramer, E. J. Producing small domain features using miktoarm block copolymers with large interaction parameters. ACS Macro Lett. 2015, 4, 1287–1292.

    Article  CAS  Google Scholar 

  19. Gartner III, T. E.; Kubo, T.; Seo, Y.; Tansky, M.; Hall, L. M.; Sumerlin, B. S.; Epps III, T. H. Domain spacing and composition profile behavior in salt-doped cyclic vs linear block polymer thin films: a joint experimental and simulation study. Macromolecules 2017, 50, 7169–7176.

    Article  CAS  Google Scholar 

  20. Zong, J.; Wang, Q. Fluctuation/correlation effects in symmetric diblock copolymers: on the order-disorder transition. J. Chem. Phys. 2013, 139, 124907.

    Article  Google Scholar 

  21. Dai, K. H.; Norton, L. J.; Kramer, E. J. Equilibrium segment density distribution of a diblock copolymer segregated to the polymer/polymer interface. Macromolecules 1994, 27, 1949–1956.

    Article  CAS  Google Scholar 

  22. Fetters, L.; Lohse, D.; Richter, D.; Witten, T.; Zirkel, A. Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties. Macromolecules 1994, 27, 4639–4647.

    Article  CAS  Google Scholar 

  23. Cochran, E. W.; Bates, F. S. Thermodynamic behavior of poly(cyclohexylethylene) in polyolefin diblock copolymers. Macromolecules 2002, 35, 7368–7374.

    Article  CAS  Google Scholar 

  24. Carmesin, I.; Kremer, K. The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 1988, 21, 2819–2823.

    Article  CAS  Google Scholar 

  25. Deutsch, H.; Binder, K. Interdiffusion and self-diffusion in polymer mixtures: a Monte Carlo study. J. Chem. Phys. 1991, 94, 2294–2304.

    Article  CAS  Google Scholar 

  26. Larson, R. Monte Carlo lattice simulation of amphiphilic systems in two and three dimensions. J. Chem. Phys. 1988, 89, 1642–1650.

    Article  CAS  Google Scholar 

  27. Pakula, T. Cooperative relaxations in condensed macromolecular systems. 1. A model for computer simulation. Macromolecules 1987, 20, 679–682.

    Article  CAS  Google Scholar 

  28. Shaffer, J. S. Effects of chain topology on polymer dynamics: bulk melts. J. Chem. Phys. 1994, 101, 4205–4213.

    Article  CAS  Google Scholar 

  29. Wang, Q. Studying soft matter with “soft” potentials: fast lattice Monte Carlo simulations and corresponding lattice self-consistent field calculations. Soft Matter 2009, 5, 4564–4567.

    Article  CAS  Google Scholar 

  30. Reiter, J.; Edling, T.; Pakula, T. Monte Carlo simulation of lattice models for macromolecules at high densities. J. Chem. Phys. 1990, 93, 837–844.

    Article  CAS  Google Scholar 

  31. Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953, 21, 1087–1092.

    Article  CAS  Google Scholar 

  32. Jacucci, G.; Rahman, A. Comparing the efficiency of metropolis Monte Carlo and molecular-dynamics methods for configuration space sampling. Il Nuovo Cimento D 1984, 4, 341–356.

    Article  Google Scholar 

  33. Hubbard, J. Calculation of partition functions. Phys. Rev. Lett. 1959, 3, 77.

    Article  Google Scholar 

  34. Fredrickson, G. The equilibrium theory of inhomogeneous polymers. Oxford University Press on Demand: 2006.

  35. Vetterling, W. T.; Press, W. H.; Teukolsky, S. A.; Flannery, B. P. Numerical Recipes Example Book (C++): The Art of Scientific Computing. Cambridge University Press: 2002.

  36. Mark, J. E. Physical properties of polymers handbook. New York: Springer: 2007; Vol. 1076.

    Book  Google Scholar 

  37. Schelten, J.; Ballard, D.; Wignall, G.; Longman, G.; Schmatz, W. Small-angle neutron scattering studies of molten and crystalline polyethylene. Polymer 1976, 17, 751–757.

    Article  CAS  Google Scholar 

  38. Wang, Q.; Yan, Q.; Nealey, P. F.; de Pablo, J. J. Monte Carlo simulations of diblock copolymer thin films confined between two homogeneous surfaces. J. Chem. Phys. 2000, 112, 450–464.

    Article  CAS  Google Scholar 

  39. Wang, Q.; Nealey, P. F.; de Pablo, J. J. Lamellar structures of symmetric diblock copolymers: Comparisons between lattice Monte Carlo simulations and self-consistent mean-field calculations. Macromolecules 2002, 35, 9563–9573.

    Article  CAS  Google Scholar 

  40. Zimm, B. H.; Stockmayer, W. H. The dimensions of chain molecules containing branches and rings. J. Chem. Phys. 1949, 17, 1301–1314.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (No. 21829301) and by the 111 Project (No. B16027).

Author information

Authors and Affiliations

  1. School of Physics, Nankai University, Tianjin, 300071, China

    Jia-Ping Wu & Bao-Hui Li

  2. Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, CO, 80523-1370, USA

    Qiang Wang

Authors
  1. Jia-Ping Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bao-Hui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Bao-Hui Li or Qiang Wang.

Additional information

Notes

The authors declare no competing financial interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, JP., Li, BH. & Wang, Q. Designing a New Lattice Model to Simulate Low-molecular-weight Block Copolymers for Nanolithographic Applications. Chin J Polym Sci 40, 413–420 (2022). https://doi.org/10.1007/s10118-022-2677-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10118-022-2677-5

Keywords

Search

Navigation