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Quantum electrodynamical formulation of photochemical acid generation and its implications on optical lithography

  • Seungjin Lee (Quantum Computing Research Section, Electronics and Telecommunications Research Institute)
  • 투고 : 2024.03.21
  • 심사 : 2024.08.14
  • 발행 : 2024.10.10

초록

The photochemical acid generation is refined from the first principles of quantum electrodynamics. First, we briefly review the formulation of the quantum theory of light based on the quantum electrodynamics framework to establish the probability of acid generation at a given spacetime point. The quantum mechanical acid generation is then combined with the deprotection mechanism to obtain a probabilistic description of the deprotection density directly related to feature formation in a photoresist. A statistical analysis of the random deprotection density is presented to reveal the leading characteristics of stochastic feature formation.

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과제정보

SL expresses gratitude to Dawoon Choi and Yunkyoung Song for their enlightening discussions during the initial phase of this work. This work was partly supported by the Institute for Information & Communications Technology Promotion (IITP) grant (no. 2019-0-00003, Research and Development of Core Technologies for Programming, Running, Implementing, and Validating of Fault-Tolerant Quantum Computing System) and the National Research Foundation of Korea (NRF) grants (nos. 2024M3K5A1004355, RS-2024-00432214, RS-2023-00281456, and RS-2023-00283771). It is worth noting that this work was partially completed at Samsung Electronics, one of the author's former affiliations.

참고문헌

  1. C. A. Mack, Line-edge roughness and the ultimate limits of lithography, Advances in Resist Materials and Processing Technology XXVII, Vol. 7639, SPIE, 2010, pp. 901-916.
  2. J. Schwinger, Quantum electrodynamics. I. A covariant formulation, Phys. Rev. 74 (1948), no. 10, 1439-1461.
  3. L. Mandel, E. C. G. Sudarshan, and E. Wolf, Theory of photoelectric detection of light fluctuations, Proc. Phys. Soc. 84 (1964), no. 3, 435.
  4. G. M. Gallatin, Resist blur and line edge roughness, Optical Microlithography XVIII, Vol. 5754, SPIE, 2005, pp. 38-52.
  5. A. Latypov, G. Khaira, G. Fenger, J. Sturtevant, C.-I. Wei, and P. D. Bisschop, Probability prediction of EUV process failure due to resist-exposure stochastic: applications of Gaussian random fields excursions and Rice's formula, Extreme Ultraviolet (EUV) Lithography XI, Vol. 11323, SPIE, 2020, pp. 140-164.
  6. S. Weinberg, The quantum theory of fields: volume 1, foundations, Cambridge University Press, 1995.
  7. A. Messiah, Quantum mechanics, Dover Publications, 2014.
  8. L. Mandel and E. Wolf, Optical coherence and quantum optics, Cambridge University Press, 1995.
  9. J. R. Klauder, Improved version of optical equivalence theorem, Phys. Rev. Lett. 16 (1966), no. 12, 534-536.
  10. E. C. G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams, Phys. Rev. Lett. 10 (1963), no. 7, 277-279.
  11. R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130 (1963), no. 6, 2529-2539.
  12. F. A. Houle, W. D. Hinsberg, M. Morrison, M. I. Sanchez, G. Wallraff, C. Larson, and J. Hoffnagle, Determination of coupled acid catalysis-diffusion processes in a positive-tone chemically amplified photoresist, J. Vac. Sci. Technol. B 18 (2000), no. 4, 1874-1885.
  13. C. W. Wang, C. Y. Chang, and Y. Ku, Photobase generator and photo decomposable quencher for high-resolution photoresist applications, Advances in resist materials and processing technology XXVII, R. D. Allen, (ed.), Vol. 7639, SPIE, 2010, pp. 76390W.
  14. R. J. Adler and J. E. Taylor, Random fields and geometry, Springer, 2009.
  15. P. D. Bisschop, Stochastic effects in EUV lithography: random, local CD variability, and printing failures, J. Micro/Nanolithography, MEMS, MOEMS 16 (2017), no. 4, 41013.
  16. A. Latypov, C.-I. Wei, P. D. Bisschop, G. Khaira, and G. Fenger, Calibration of Gaussian random field stochastic EUV models, Optical and EUV Nanolithography XXXV, Vol. 12051, SPIE, 2022, pp. 28-36.
  17. Z. Pan, A. Latypov, C.-I. Wei, P. D. Bisschop, G. Fenger, and J. Sturtevant, Importance sampling in Gaussian random field EUV stochastic model for quantification of stochastic variability of EUV vias, Optical and EUV Nanolithography XXXVI, Vol. 12494, SPIE, 2023, pp. 425-438.
  18. Y.-P. Tsai, C.-M. Chang, Y.-H. Chang, A. Oak, D. Trivkovic, and R.-H. Kim, Study of EUV stochastic defect on wafer yield, DTCO and computational patterning III, N. V. Lafferty, (ed.), Vol. 12954, SPIE, 2024, pp. 1295404.
  19. C.-I. Wei, A. Latypov, P. D. Bisschop, G. Khaira, and G. Fenger, Calibration and application of Gaussian random field models for exposure and resist stochastic in EUV lithography, Jpn. J. Appl. Phys. 61 (2022), no. SD, SD0806.
  20. J. G. Santaclara, B. Geh, A. Yen, T. A. Brunner, D. D. Simone, J. Severi, and G. Rispens, One metric to rule them all: new k4 definition for photoresist characterization, Extreme Ultraviolet (EUV) Lithography XI, Vol. 11323, SPIE, 2020, pp. 321-330.