Application of Spectral Ellipsometry for Dielectric, Metal and Semiconductor Films in Microelectronics Technology

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Abstract

The article reviews model-based and model-free approaches to solving problems of spectral ellipsometry related to the measurement of thicknesses and optical parameters of thin layers of dielectrics, metals and semiconductors in microelectronics application. Model-based approaches employ a priori information about the dispersion relation in form of the Cauchy, Drude, Drude—Lorentz and Tautz—Lorentz. Model-free approaches can use any smooth multivariate functional dependence describing a smooth spectral curve. Also, machine learning can be used to implement the model-free approach, which is well suited for determining the thickness of multilayer structures and their optical characteristics and allows to significantly increase the speed of data processing.

About the authors

R. A. Gaidukasov

Valiev Institute of Physics and Technology of Russian Academy of Sciences

Author for correspondence.
Email: gaydukasov.r@gmail.com
Russian Federation, Moscow

A. V. Miakonkikh

Valiev Institute of Physics and Technology of Russian Academy of Sciences

Email: gaydukasov.r@gmail.com
Russian Federation, Moscow

References

  1. Drude P. Beobachtungen über die Reflexion des Lichtes am Antimonglanz // Annalen der Physik und Chemie. Wiley. 1888. V. 270(7). P. 489–531.
  2. Rothen A. The Ellipsometer, an Apparatus to Measure Thicknesses of Thin Surface Films // Review of Scientific Instruments. AIP Publishing. 1945. V. 16(2). P. 26–30.
  3. Chen S. et al. On the anomalous optical conductivity dispersion of electrically conducting polymers: ultra-wide spectral range ellipsometry combined with a Drude — Lorentz model // Journal of Materials Chemistry C. Royal Society of Chemistry (RSC). 2019. V. 7(15). P. 4350–4362.
  4. Miakonkikh A.V., Smirnova E.A., Clemente I.E. Application of the spectral ellipsometry method to study the processes of atomic layer deposition // Russian Microelectronics. 2021. V. 50(4). P. 230–238.
  5. Clemente I.E., Miakonkikh A.V. Application of spectral ellipsometry to in situ diagnostics of atomic layer deposition of dielectrics on Silicon and AlGaN // SPIE Proceedings / ed. V.F. Lukichev, K.V. Rudenko. SPIE, 2016.
  6. Langereis E. et al. In situspectroscopic ellipsometry as a versatile tool for studying atomic layer deposition // Journal of Physics D: Applied Physics. IOP Publishing. 2009. V. 42(7). P. 073001.
  7. Gaidukasov R.A., Myakon’kikh A.V., Rudenko K.V. Application of the Tikhonov Regularization Method in Problems of Ellipsometic Porometry of Low-K Dielectrics // Russian Microelectronics. Pleiades Publishing Ltd. 2022. V. 51(4). P. 199–209.
  8. Archer R.J. Determination of the Properties of Films on Silicon by the Method of Ellipsometry // Journal of the Optical Society of America. The Optical Society. 1962. V. 52(9). С. 970.
  9. Orlikovskii A.A., Rudenko K.V. In situ diagnostics of plasma processes in microelectronics: The current status and immediate prospect. Part III // Russian Microelectron. 2001. V. 30. P. 275–294.
  10. Polyak B.T. Introduction to optimization. 1983.
  11. Nelder J.A., Mead R.A Simplex Method for Function Minimization // Computer Journal. 1965. V. 7. P. 308–313.
  12. Liu J. et al. Machine learning powered ellipsometry // Light Sci Appl. 2021. V. 10(1). P. 55.
  13. Li Y. et al. Deep Learning for Rapid Analysis of Spectroscopic Ellipsometry Data // Advanced Photonics Research. 2021. V. 2(12). P. 2100147.
  14. Arunachalam A. et al. Machine learning approach to thickness prediction from in situ spectroscopic ellipsometry data for atomic layer deposition processes // Journal of Vacuum Science and Technology A. 2022. V. 40(1). P. 012405.
  15. Alcaire T. et al. Spectroscopic Ellipsometry Imaging for Process Deviation Detection via Machine Learning Approach // 2020 31st Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC). IEEE.
  16. Azzam R.M.A., Bashara N.M. Ellipsometry and polarized light // North Holland Personal Library. Amsterdam. 1977.
  17. Born M., Wolf E. Principles of Optics. 7th Edition. 1997.
  18. Jellison G.E., Modine F.A. Handbook of Ellipsometry ed. H.G. Tompkins and E.A. Irene // Springer. New York. 2005. Chap. 6.
  19. Woollam J.A. Complete EASE Software Manual for Spectroscopic Ellipsometer ver. 6.
  20. Fujiwara H., Collins R.W. Spectroscopic Ellipsometry for Photovoltaics. Volume 1. Fundamental Principles and Solar Cell Characterization-Springer.
  21. Cauchy L. Bull. Des. Sc. Math. 1830. V. 14(9).
  22. Urbach F. The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids // Phys. Rev. 1953. V. 92(5). P. 1324–1324.
  23. Sellmeier W. Ueber die durch die Aetherschwingungen erregten Mitschwingungen der Körpertheilchen und deren Rückwirkung auf die ersteren, besonders zur Erklärung der Dispersion und ihrer Anomalien // Ann. Phys. Chem. 1872. V. 223(11). P. 386–403.
  24. Lee H.W. The Hartmann formula for the dispersion of glass // Transactions of the Optical Society. IOP Publishing. 1926. V. 28(3). P. 161–167.
  25. Conrady A.E. Applied Optics and Optical Design. 1985.
  26. Briot M. Essai sur la théorie mathématique de la lumière // Paris, Mallet-Bachelier. Harvard University. 1864.
  27. Cardona M.P.Yu. Fundamentals of Semiconductors // Springer Berlin Heidelberg. 2005.
  28. Wooten F. Optical Properties of Solids // Academic Press. New York. 1972.
  29. Kittel C. Introduction to Solid State Physics, 5th ed. // Wiley. New York. 1976.
  30. Tiwald T.E. et al. Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles // Thin Solid Films. 1998. V. 313–314. P. 661–666.
  31. Tauc J. Amorphous and Liquid Semiconductors // Plenum. New York. 1974.
  32. Tauc J., Grigorovici R., Vancu A. Optical Properties and Electronic Structure of Amorphous Germanium // Phys. Stat. Sol. (b). 1966. V. 15(2). P. 627–637.
  33. Shvets V.A. et al. Uniformity of Optical Constants in Amorphous Ta2O5Thin Films as Measured by Spectroscopic Ellipsometry // Russian Microelectronics. 2004. V. 33(5). P. 285–291.
  34. Forouhi A.R., Bloomer I. Optical dispersion relations for amorphous semiconductors and amorphous dielectrics // Phys. Rev. B. 1986. V. 34(10). P. 7018–7026.
  35. McGahan W.A., Woollam J.A. Optical Characterization and Modeling of Amorphous Hydrogenated Carbon Films // MRS Proc. 1994. V. 349.
  36. Jellison G.E.Jr., Modine F.A. Parameterization of the optical functions of amorphous materials in the interband region // Appl. Phys. Lett. 1996. V. 69(3). P. 371–373.
  37. Kim I. et al. Optical spectrum augmentation for machine learning powered spectroscopic ellipsometry // Opt. Express. 2022. V. 30(10). P. 16909.
  38. Sarker I.H. Machine Learning: Algorithms, Real-World Applications and Research Directions // SN COMPUT. SCI. 2021. V. 2(3).
  39. Lussier F. et al. Deep learning and artificial intelligence methods for Raman and surface-enhanced Raman scattering // TrAC Trends in Analytical Chemistry. 2020. V. 124. P. 115796.
  40. Enders A.A. et al. Functional Group Identification for FTIR Spectra Using Image-Based Machine Learning Models // Anal. Chem. 2021. V. 93(28). P. 9711–9718.
  41. Park W.B. et al. Classification of crystal structure using a convolutional neural network // Int Union Crystallogr J. 2017. V. 4(4). P. 486–494.
  42. Yanguas-Gil A., Elam J.W. Machine learning and atomic layer deposition: Predicting saturation times from reactor growth profiles using artificial neural networks // Journal of Vacuum Science and Technology A. 2022. V. 40(6). P. 062408.
  43. LeCun Y. et al. Backpropagation Applied to Handwritten Zip Code Recognition // Neural Computation. MIT Press — Journals. 1989. V. 1(4). P. 541–551.
  44. Ivakhnenko A.G., Lapa V.G. Cybernetic predictive devices. 1965.
  45. Dechter R. Learning While Searching in Constraint-Satisfaction-Problems // Proceedings of the 5th National Conference on Artificial Intelligence. Philadelphia, PA, August 11–15, 1986. Volume 1: Science.
  46. Palik E.D. Handbook of Optical Constants of Solids. Academic Press. San Diego. 1985.
  47. Optical Data from Sopra SA. http://www.sspectra.com/sopra.htmlLangereis E. et al. In situspectroscopic ellipsometry as a versatile tool for studying atomic layer deposition // J. Phys. D: Appl. Phys. 2009. V. 42(7). P. 073001.
  48. Fix E., Hodges J.L. Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties International Statistical Review / Revue Internationale de Statistique. 1989. V. 57(3). P. 238.
  49. Cortes C., Vapnik V. Support-vector networks // Mach Learn. 1995. V. 20(3). P. 273–297.
  50. Tin Kam Ho. The random subspace method for constructing decision forests IEEE Trans. Pattern Anal. Machine Intell. 1998. V. 20(8). P. 832–844.
  51. Von Winterfeldt D., Edwards W. Decision Analysis and Behavioral Research // Cambridge University Press. 1986
  52. Tolles J., Meurer W.J. Logistic Regression // JAMA. 2016. V. 316(5). P. 533.
  53. Alcaire T. et al. On the Fly Ellipsometry Imaging for Process Deviation Detection // IEEE Trans. Semicond. Manufact. 2022. V. 35(3). P. 432–438.
  54. Sun Q. et al. Nondestructive monitoring of annealing and chemical-mechanical planarization behavior using ellipsometry and deep learning // Microsyst Nanoeng. 2023. V. 9(1).
  55. Kwak H. et al. Non-destructive thickness characterisation of 3D multilayer semiconductor devices using optical spectral measurements and machine learning // Light: Advanced Manufacturing. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. 2021. V. 2(1). P. 9.
  56. Kwak H., Kim J. Semiconductor Multilayer Nanometrology with Machine Learning // Nanomanufacturing and Metrology. Springer Science and Business Media LLC. 2023. V. 6(1).
  57. Tian S.I.P. et al. Rapid and Accurate Thin Film Thickness Extraction via UV–Vis and Machine Learning // 2020 47th IEEE Photovoltaic Specialists Conference (PVSC). IEEE. 2020.

Supplementary files

Supplementary Files
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1. JATS XML
2. Fig. 1. Schematic diagram of the experimental setup for spectral ellipsometry. Linearly polarized light falls on the sample with the angle of incidence φ

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3. Fig. 2. Real and imaginary parts of the Lorentz oscillator with center E0 = 3, width G = 0.5 and oscillator force A = 25

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4. Fig. 3. Real and imaginary parts of the Tautz-Lorentz oscillator with center E0 = 3, width G = 0.5, amplitude A = 25 and optical energy of the forbidden zone Eg = 2

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