Light & Engineering 27 (2)

Volume 27
Date of publication 04/22/2019

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Application Of The Photometric Theory Of The Radiance Field In The Problems Of Electron Scattering. L&E 27 (2) 2019

Articles authors:

Victor P. Afanas’ev, Vladimir P. Budak, Dmitry S. Efremenko, Pavel S. Kaplya

Viktor P. Afanas’ev, Dr. of Phys. and Math. Science, graduated from the Moscow Power Engineering Institute (MPEI) in 1970. He works as a professor at the MPEI. In addition, he is a member of three dissertation councils and an expert of the Russian Academy of Science and the Federal Agency for Scientific Organizations

Vladimir P. Budak, Professor, Doctor of Technical Sciences. In 1981, he graduated from the Moscow Power Engineering Institute (MPEI). At present, he is the Editor-in-Chief of the Svetotekhnika / Light & Engineering journals, Professor of the Subdepartment of Light and Engineering in NRU “MPEI”. Full member of the Academy of Electrotechnical Sciences of Russia

Dmitry S. Efremenko, Ph. D. He graduated from the Moscow Power Engineering institute (MPEI) in 2009. He received his Ph. D. degree from the Moscow State University in 2011 and the habilitation degree from MPEI in 2017. Since 2011 he works as a Research Scientist at the German Aerospace Centre (DLR). He is a docent at the Technical University of Munich. He has over 70 peer-reviewed publications. His scientific interests include radiate transfer, remote sensing, and machine learning

Pavel S. Kaplya, Ph.D. in Phys. And Math. Science, graduated from the Moscow Power Engineering Institute (MPEI) in 2012. He works by Yandex LLC

Abstract:

The physical model of the radiance field is similar in some aspects to the elementary particle transport theory under the assumptions of the classical mechanics. Disregarding the differences in the used nomenclatures, it can be shown that the transport equations for the radiance field are identical to those for the particle flux density. Since the end of the 19th century, both theories have been developing in parallel, thereby enriching each other. In other words, a breakthrough, which has been made in one theory, readily contributes to the significant progress in another one. Nowadays the accuracy achieved in the experiments with particles is close to the limit, which allows validating the relationships derived within the light scattering theory. Besides, the experiments with particles are free from uncertainties in the scattering medium, which are typical for atmospheric remote sensing applications. In this paper, a new algorithm is described, which is derived by analogies between these theories. It is applied for calculating the electron flux elastically scattered by plane-parallel layers of a solid with the strongly forward peaked phase functions. The calculations are compared against the experimental angular distributions of electrons, which are elastically reflected by the two-layer solid samples.

References:

1. Veklenko B.A. The nature of the photon and quantum optics // Light & Engineering, 2018, Vol. 26, # 2, pp. 4–13.
2. Beer A. Bestimmung der Absorption des rothen Lichts in farbigen Flussigkeiten // Annal. Phys. Chem., 1852, Vol. 86, pp. 78–88.
3. Dashen R.F. Theory of electron backscattering // Phys. Rev., 1964, V.134, pp.1025–1032.
4. Afanas’ev V.P., Naujoks D. Backscattering of fast electrons // Phys. Stat. Sol., 1990, Vol. 164, pp. 133–140.
5. Borodyansky S. Effects of elastic scattering on energy spectra of emitted and backscattered electrons // Surf. Interface. Anal., 1993, Vol. 84, pp. 811–814.
6. Hofmann S. Auger- and X-Ray Photoelectron Spectroscopy in Materials Science // Springer, Berlin/Heidelberg, 2013, 528 p.
7. Powell C.J., Jablonski A. Progress in quantitative surface analysis by X-ray photoelectron spectroscopy: Current status and perspectives // J. of Electron Spectros. Relat. Phenom, 2010, Vol. 178–179, pp. 331–346.
8. Kaplya P.S. Sozdanie vy`sokotochny`x metodov analiza tvyordy`x tel na osnove rasshifrovki danny`x e`lektronnoj spektroskopii metodami invariantnogo pogruzheniya [Creating high-precision methods for analyzing solids on the basis of decoding electronic spectroscopic data by invariant imbedding methods] // Thesis for the degree of candidate physical and mathematical of sciences, 2016.
9. Bronstein I.M., Vasilyev A.A., Pronin V.P., Khinich I.I. Uprugoe otrazhenie e`lektronov srednix e`nergij ot neuporyadochenny`x metallicheskix poverxnostej [Elastic reflection of medium-energy electrons from disordered metal surfaces] // Izvestiya AN SSSR, Ser. Fizicheskaya, 1985, Vol. 49, # 9, pp. 1755–1759.
10. Bronstein I.M., Pronin V.P. Uprugoe rasseyanie e`lektronov srednix e`nergij metallicheskimi plyonkami [Elastic Scattering of Medium-Energy Electrons by Metal Films] // Fizika tvyordogo tela, 1975, Vol. 17, pp. 2431–2433.
11. Gergely G. Elastic backscattering of electrons: determination of physical parameters of electron transport processes by elastic peak electron spectroscopy // Prog. Surf. Sci., 2002, Vol.71, pp. 31–88.
12. Doicu A., Trautmann T. Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case // J. Quant. Spectrosc. Radiat. Transfer, 2009, Vol. 110, pp. 146–158.
13. Spurr R.J.D., Kurosu T.P., Chance K.V. A linearized discrete ordinate radiative transfer model for atmospheric remote-sensing retrieval // J. Quant. Spectrosc. Radiat. Transfer, 2001, Vol. 68, #6, pp. 689–735.
14. Stamnes K., Tsay S.,C., Wiscombe W., Jayaweera K. Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media // Appl. Opt., 1988, Vol. 27, pp. 2502–2509.
15. Budak V.P., Korkin S.V. Complete matrix solution of radiative transfer equation for pile of horizontally homogeneous slabs // J. Quant. Spectrosc. Radiat. Transfer, 2011, Vol. 112, pp. 1141–1148.
16. Afanas’ev V.P., Budak V.P., Efremenko D.S., Lubenchenko A.V. Uglovy`e raspredeleniya e`lektronov i lyogkix ionov, uprugo otrazhyonny`x ot poverxnosti tvyordogo tela [Angular Distributions of Electrons and Light Ions Elastically Reflected from a Solid Surface] // Poverxnost`. Rentgenovskie, sinxrotronny`e i nejtronny`e issledovaniya, 2010, Vol. 4, #3, pp. 488–493.
17. Ambartsumyan V.A. Novy`j sposob raschyota rasseyaniya sveta v mutnoj srede [New method for calculating the scattering of light in a turbid medium] // Izv. AN Arm. SSR. Ser. geogr. i geofiz., 1942, #3, pp. 97–106.
18. Ambartsumyan V.A. K zadache o diffuznom otrazhenii sveta [To the problem of diffuse reflection of light] // Zhurnal e`ksperimental`noj i teoreticheskoj fiziki, 1943, Vol. 13, #9–10, pp. 323–334.
19. Chandrasekhar S. Radiative transfer // Oxford University Press, London, UK, 1950, 405 p.
20. Sobolev V.V. Rasseyanie sveta v atmosferax planet [The scattering of light in the atmospheres of the planets] // Nauka Publ., Moscow, 1972, 335 p.
21. Goudsmit S., Saunderson J.L. Multiple scattering of electrons // Phys. Rev., 1940, Vol. 57, pp. 24–29.
22. Goudsmit S., Saunderson J.L. Multiple scattering of electrons. II // Phys. Rev., 1940, Vol. 58, pp. 36–42.
23. Scott W. Theory of Small-Angle Multiple Scattering of Fast Charged Particles // Rev. of Modern Phys., 1963, Vol. 35, pp. 231–313.
24. Afanas’ev V.P. E`lementarny`e processy` i kinetika vy`sokotemperaturnoj neravnovesnoj plazmy` [Elementary processes and kinetics of high-temperature non-equilibrium plasma] // MPEI Publ., Moscow, 1988, 84 p.
25. Ambartsumyan V.A. K voprosu o diffuznom otrazhenii sveta mutnoj sredoj [On the diffuse reflection of light by a turbid medium] // Reports of the USSR Academy of Sciences, 1943, Vol. 38, #8, pp. 257–261.
26. Afanas’ev V.P., Golovina O.Yu., Gryazev A.S., Efremenko D.S., Kaplya P.S. Photoelectron spectra of finite-thickness layers // Journal of Vacuum Science & Technology B., 2015, Vol. 33, #3, 7 p.
27. Afanas’ev V.P., Gryazev A.S., Efremenko D.S., Kaplya P.S. Differential inverse inelastic mean free path and differential surface excitation probability retrieval from electron energy loss spectra // Vacuum, 2017, Vol. 136, pp. 146–155.
28. Werner W.S.M. Differential probability for surface adn volume electronic excitations in Fe, Pd and Pt // Surface Science, 2005, Vol. 588, pp. 26–40.
29. Werner W.S.M. Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni // Surface Science, 2007, Vol. 601, #10, pp. 2125–2138.
30. Bellman R, Kalaba R, Wing G. Invariant imbedding and mathematical physics. I. Particle processes // J. Math. Phys., 1960, Vol. 1, pp. 280–308.
31. Flatau PJ, Stephens GL. On the fundamental solution of the radiative transfer equation // J. Geophys. Res, 1988, Vol. 93(D9), pp. 11037–11050.
32. Waterman P.C. Matrix-exponential description of radiative transfer // J. Opt. Soc. Am., 1981, Vol. 71, #4, pp. 410–422.
33. Efremenko D.S., Molina Garcia V., Gimeno Garsia S., Doicu A. A review of the matrix-exponential formalism in radiative transfer // J. Quant. Spectrosc. Radiat. Transfer., 2017, Vol. 196, pp. 17–45.
34. Pienado J., Ibanez J., Hernandez V., Arias E. A family of BDF algorithms for solving Differential Matrix Riccati Equations using adaptive techniques // Procedia Computer Science, 2010, Vol. 1, pp. 2569–2577.
35. Afanas’ev V.P., Efremenko D.S., Kaplya P.S. Analytical and numerical methods for computing electron partial intensities in the case of multilayer systems // Journal of Electron Spectroscopy and Related Phenomena, 2016, Vol. 210, pp. 16–29.
36. Afanasyev V.P., Kaplya P.S., Lisitsyna E.Yu. Malouglovoe priblizhenie i model` Os`val`da-Kaspera-Gauklera v zadachax otrazheniya e`lektronov ot tvyordy`x tel [Small-Angle Approximation and the Osvald-Kasper-Gaukler Model in the Problems of Electron Reflection from Solids] // Poverxnost`. Rentgenovskie sinxrotronny`e i nejtronny`e issledovaniya, 2016, #3, pp. 66–71.
37. Jablonski A., Hansen H.S., Jansson C., Tougaard S. Elastic electron backscattering from surfaces with overlayers // Phys. Rev.B., 1992, Vol. 45, pp. 3694–3702. 38. Jablonski A. Elastic electron backscattering from gold // Phys. Rev.B., 1991, Vol. 43, pp. 7546–7554.
39. Jablonski A., Jansson C., Tougaard S. Elastic electron backscattering from surfaces: Prediction of maximum intensity // Phys. Rev. B, 1993, Vol. 47, pp. 7420–7430. 40. Zommer L., Lesiak B., Jablonski A. Energy dependence of elastic electron backscattering from solids // Phys. Rev.B., 1993, Vol. 47, pp. 13759–13762.
41. Kuzovlev A.I., Kurnaev V.A., Remizovich V.S., Trifonov N.N. Refraction of the beam of charged particles during inclined transmission through a thin target // Nucl. Instrum. and Methods. Research Section B: Beam Interactions with Materials and Atoms, 1998, Vol. 135, pp. 477–481.
42. Bronstein I.M., Pronin V.P. Uprugoe otrazhenie e`lektronov srednix e`nergij pri napy`lenii Be na Au [Elastic reflection of medium-energy electrons during the deposition of Be on Au], XXVIII Herzen Readings. Physical and semiconductor electronics // LGPI of A.I. Herzen Publ. House, Leningrad, 1975, pp. 18–20.
43. Afanas’ev V.P., Gryazev A.S., Kaplya P.S., Koppen M., Ridzel O. Y., Subbotin N.Y., Hansen P. Investigation of Deuterium Implantation into Beryllium Sample by Electron Energy Loss Spectroscopy // IOP Conf. Series: Journal of Physics: Conf. Series, 2017, Vol. 891, 6 p.
44. Afanasyev V.P., Kaplya P.S. Funkciya propuskaniya. E`ffekt «povorota tela yarkosti» [Transmission function. The effect of “turning the body of brightness”] // Poverxnost`. Rentgenovskie, sinxrotronny`e i nejtronny`e issledovaniya, 2017, #12, pp. 66–75.

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