Ellipsometry of substrate with nanoscale surface layer
https://doi.org/10.29235/1561-2430-2025-61-2-128-138
Abstract
An analytical solution of the inverse ellipsometry problem on determining the complex permittivity of a substrate in the presence of a nanosized surface layer with previously unknown characteristics is formulated. The layer is taken into account only by one integral parameter, which is restored simultaneously with the substrate permittivity. The solution uses ellipsometric parameters Δ and Ψ, measured at two angles of light incidence on the structure. The optimal values of the incident angles are established from the condition of the minimum of the error coefficient of the substrate permittivity reconstruction. The efficiency of the solution is checked in numerical simulations and real experiments on the ellipsometry of silicon substrates with various surface layers. In particular, the band gap of a silicon substrate doped with boron and subjected to a rapid heat treatment to stabilize the surface layer is determined.
Keywords
inverse ellipsometry problem,
nano-sized surface layer,
silicon substrate,
optimal angles of incidence,
band gap
Supporting agencies: This work was financially supported by the State Program of Scientific Research “Photonics and Electronics for Innovations”, subprogram “Photonics and its Applications” (1.1. “Advancement of Physical Principles and Development of Methods for Waveguide Spectroscopy of Thin-Film Structures and Media”).
About the Authors
D. V. Ponkratov
Mogilev State A. Kuleshov University
Belarus
Belarus
Dmitry V. Ponkratov – Postgraduate Student
1, Kosmonavtov Str., 212022, Mogilev
A. B. Sotsky
Mogilev State A. Kuleshov University
Belarus
Belarus
Alexander B. Sotsky – Dr. Sc. (Physics and Mathematics), Professor, Professor of the Department of Physics and Computer Technologies
1, Kosmonavtov Str., 212022, Mogilev
N. I. Staskov
Mogilev State A. Kuleshov University
Belarus
Belarus
Nikolay I. Staskov – Ph. D. (Physics and Mathematics), Professor of the Department of Physics and Computer Technologies
1, Kosmonavtov Str., 212022, Mogilev
H. A. Siarheichyk
State Center “Belmicroanalysis”, JSC “INTEGRAL”
Belarus
Belarus
Hanna A. Siarheichyk – Leading Engineer
121a, Kazintsa St., 220108, Minsk
References
1. Rauch N., Andersen E., Vicente-Gabás I. G., Duchoslav J., Minenkov A., Gasiorowski J., Flötgen C. [et al.]. A model for spectroscopic ellipsometry analysis of plasma-activated Si surfaces for direct wafer bonding. Applied Physics Letters, 2022, vol. 121, no. 8, pp. 081603-1–081603-6. https://doi.org/10.1063/5.0101633
2. Sotsky A. B., Chudakov E. A. Reciprocity relations for interference coatings. Vestsі Natsyyanalʼnaiakademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2023, vol. 59, no. 2, pp. 158–167 (in Russian). https://doi.org/10.29235/1561-2430-2023-59-2-158-167
3. Sotsky A. B., Chudakov E. A., Sotskaya L. I. The anomalous skin effect in metallic films. Journal of Applied Spectroscopy, 2024, vol. 91, no. 4, pp. 812–825. https://doi.org/10.1007/s10812-024-01789-7
4. Tompkins H. G., Irene E. A. (eds.). Handbook of Ellipsometry. New York, William Andrew, Inc., 2005. 891 p. https:// doi.org/10.1007/3-540-27488-x
5. Hiroyuki Fujiwara. Spectroscopic Ellipsometry: Principles and Applications. John Wiley & Sons, 2007, 388 p. https:// doi.org/10.1002/9780470060193
6. Aspnes D. E., Studna A. A. Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Physical Review B, 1983, vol. 27, no. 2, pp. 985–1009. https://doi.org/10.1103/physrevb.27.985
7. Jellison, G. E. Spectroscopic ellipsometry data analysis: measured versus calculated quantities. Thin Solid Films, 1998, vol. 313–314, pp. 33–39. https://doi.org/10.1016/s0040-6090(97)00765-7
8. Stas’kov N. I., Sotskij A. B., Sotskaya L. I., Ivashkevich I. V., Krekoten’ N. A., Bujko L. D. Optical characteristics of a natural surface layer on a silicon substrate. Izvestiya Gomel’skogo gosudarstvennogo universiteta imeni F. Skoriny = Proceedings Francisk Skorina Gomel State University, 2006, no. 6 (39), pp. 60–62 (in Russian).
9. Staskov N. I., Sotskaya L. I. Three-Component Model of an Effective Medium for Determining the Composition of Layers on Silicon Wafers. Journal of Applied Spectroscopy, 2017, vol. 84, no. 5, pp. 764–769. https://doi.org/10.1007/s10812017-0542-z
10. Sotskij A. B. Theory of Optical Waveguide Elements. Mogilev, Mogilev State A. Kuleshov University, 2011. 455 p. (in Russian).
11. Nayfeh Ali H. Introduction to Perturbation Techniques. Wiley-VCH, 1993. 536 p.
12. Sotsky A. B., Steingart L. M., Parashkov S. O., Sotskaya L. I. Choosing the ranges for measuring the reflectivity of a prism coupler in the waveguide spectroscopy of thin films. Izvestiya RAN. Seriya fizicheskaya = Bulletin of the Russian Academy of Sciences: Physics, 2016, vol. 80, no. 4, pp. 465–469 (in Russian). https://doi.org/10.7868/s036767651604030x
13. Adams M. J. An Introduction to Optical Waveguide. John Wiley & Sons Inc, 1981. 401 p.
14. Palik E. D. Handbook of Optical Constants of Solids. Orlando, Academic Press., 1985. 1086 p. https://doi.org/10.1016/b978-0-08-054721-3.50005-8
15. Anishchik V. M., Harushka V. A., Pilipenka U. A., Ponariadov V. V., Saladukha V. A., Omelchenko A. A. Variation of the silicon optical parameters after rapid heat treatment. Zhurnal Belorusskogo gosudarstvennogo universiteta. Fizika = Journal of the Belarusian State University. Physics, 2021, no. 3, pp. 81–85 (in Russian). https://doi.org/10.33581/2520-22432021-3-81-85
16. Rudy A. S., Churilov A. B., Kurbatov S. V., Mironrenko A. A., Naumov V. V., Kozlov E. A. Determination of the band structure and conductivity of a nanocomposite Si@O@Al. Technical Physics, 2024, vol. 69, pp. 1753–1764. https://doi.org/10.1134/s1063784224060379
17. Tan W. C., Koughia K., Singh J., Kasap S. O. Fundamental Optical Properties of Materials I. Optical Properties of Condensed Matter and Applications. John Wiley & Sons, Ltd, 2006. 25 p.
18. Kocevski V., Eriksson O., Rusz J. Transition between direct and indirect band gap in silicon nanocrystals. Physical Review B, 2013, vol. 87, pр. 245401-1–245401-9. https://doi.org/10.1103/PhysRevB.87.245401
Review
Views:
9
Email this article 