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Mathematical Modeling of Heat and Mass Transfer Phenomena Caused by Interaction between Electron Beams and Planar Semiconductor Multilayers

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Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

An analytical matrix method is proposed for the mathematical modeling of heat and mass transfer caused by the interaction between broad electron beams and planar semiconductor multilayers. Some possibilities of using this approach to estimating the excess minority carrier distributions in planar semiconductor multilayers are discussed. It is shown that the proposed matrix method allows calculation of the excess minority carrier distributions in a relatively short time with an accuracy sufficient for use in electron probe techniques.

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REFERENCES

  1. Scanning Microscopy for Nanotechnology: Techniques and Applications, Zhou, W. and Wang, Z.L., Eds., New York: Springer, 2007.

    Google Scholar 

  2. Stepovich, M.A., Doctoral (Phys.–Math.) Dissertation, Moscow: Bauman Moscow State Tech. Univ., 2003.

  3. Everhart, T.E., J. Appl. Phys., 1960, vol. 31, no. 10, p. 1483.

    Article  ADS  Google Scholar 

  4. Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford: Clarendon, 1959, 2nd ed.

    MATH  Google Scholar 

  5. Afanasenkova, Yu.V. and Gladyshev, Yu.A., Izv. Saratov. Gos. Univ.,Nov. Ser. Ser. Mat. Mekh. Inf., 2013, vol. 13, nos. 1–2, p. 11.

    Google Scholar 

  6. Ginzgeimer, S.A., Cand. Sci. (Phys.–Math.) Dissertation, Kaluga: Kaluga State Pedagog. Univ., 2006.

  7. Bers, L. and Gelbart, A., Trans. Am. Math. Soc., 1944, vol. 56, p. 67.

    Article  Google Scholar 

  8. Gladyshev, Yu.A., Mat. Zametki, 1994, vol. 55, no. 3, p. 21.

    MathSciNet  Google Scholar 

  9. Gladyshev, Yu.A., Metod obobshchennykh stepenei Bersa i ego prilozheniya v matematicheskoi fizike (Method of the Generalized Powers of Bers and Its Applications in Mathematical Physics), Kaluga: Kaluzh. Gos. Univ., 2011.

  10. Gladyshev, Yu.A., Kalmanovich, V.V., and Stepovich, M.A., J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech., 2017, vol. 11, no. 5, p. 1096.

    Article  Google Scholar 

  11. Kalmanovich, V.V. and Stepovich, M.A., in Problemy razrabotki perspektivnykh mikro- i nanoelektronnykh sistem-2018 (Problems of Developing Promising Micro- and Nanoelectronic Systems 2018), Moscow: Inst. Probl. Proektirovania Mikroelektron. Ross. Akad. Nauk, 2018, p. 194.

  12. Gladyshev, Yu.A., Kalmanovich, V.V., Seregina, E.V., and Stepovich, M.A., Vopr. At. Nauki Tekh., Ser.:Yad.‑Reakt. Konstanty, 2018, no. 3, p. 158.

  13. Kalmanovich, V.V., Seregina, E.V., and Stepovich, M.A., J. Phys.: Conf. Ser, 2019, vol. 1163, 012012.

    Google Scholar 

  14. Stepovich, M.A., Snopova, M.G., and Khokhlov, A.G., Prikl. Fiz., 2004, no. 3, p. 61.

  15. Stepovich, M.A., Khokhlov, A.G., and Snopova, M.G., Proc. SPIE, 2004, vol. 5398, p. 159.

    Article  ADS  Google Scholar 

  16. Burylova, I.V., Petrov, V.I., Snopova, M.G., and Stepovich, M.A., Semiconductors, 2007, vol. 41, no. 4, p. 444.

    Article  ADS  Google Scholar 

  17. Snopova, M.G., Burylova, I.V., Petrov, V.I., and Stepovich, M.A., J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech., 2007, vol. 1, no. 4, p. 406.

    Article  Google Scholar 

  18. Filachev, A.M., Taubkin, I.I., and Trishenkov, M.A., Tverdotel’naya fotoelektronika. Fotodiody (Solid State Photoelectronics: Photodiodes), Moscow: Fizmatkniga, 2011.

  19. Filachev, A.M., Taubkin, I.I., and Trishenkov, M.A., Tverdotel’naya fotoelektronika. Fotorezistory i fotopriemnye ustroistva (Solid State Photoelectronics: Photoresistors and Photodetectors), Moscow: Fizmatkniga, 2012.

  20. Mikheev, N.N., Nikonorov, I.M., Petrov, V.I., and Stepovich, M.A., Bull. Acad. Sci. USSR,Phys., 1990, vol. 54, no. 2, p. 82.

    Google Scholar 

  21. Mikheev, N.N., Petrov, V.I., and Stepovich, M.A., Bull. Acad. Sci. USSR,Phys., 1991, vol. 55, no. 8, p. 1.

    Google Scholar 

  22. Mikheev, N.N. and Stepovich, M.A., Zavod. Lab.,Diagn. Mater., 1996, vol. 62, no. 4, p. 20.

    Google Scholar 

  23. Kanaya, K. and Okayama, S., J. Phys. D: Appl. Phys., 1972, vol. 5, no. 1, p. 43.

    Article  ADS  Google Scholar 

  24. Kalmanovich, V.V., in Sovremennye metody prikladnoi matematiki, teorii upravleniya i komp’yuternykh tekhnologii (Modern Methods of Applied Mathematics, Control Theory, and Computer Technology), Voronezh: Nauchnaya Kniga, 2015, p. 166.

  25. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1977.

  26. Amrastanov, A.N., Seregina, E.V., and Stepovich, M.A., Bull. Russ. Acad. Sci.: Phys., 2018, vol. 82, no. 9, p. 1187.

    Article  Google Scholar 

  27. Stepovich, M.A., Amrastanov, A.N., Seregina, E.V., and Filippov, M.N., J. Phys.: Conf. Ser., 2018, vol. 955, 012049.

    Google Scholar 

  28. Stepovich, M.A., Amrastanov, A.N., Seregina, E.V., and Filippov, M.N., J. Phys.: Conf. Ser., 2019, vol. 1163, 012014.

    Google Scholar 

  29. Mikheev, N.N., Stepovich, M.A., and Petrov, V.I., Bull. Russ. Acad. Sci.: Phys., 1993, vol. 57, no. 9, p. 1494.

    Google Scholar 

  30. Mikheev, N.N. and Stepovich, M.A., Mater. Sci. Eng., B, 1995, vol. 32, nos. 1–4, p. 11.

    Article  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-03-00271, and by the Russian Foundation for Basic Research and the government of Kaluga oblast, project no. 18-41-400001.

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Correspondence to V. V. Kalmanovich.

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Translated by E. Bondareva

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Kalmanovich, V.V., Seregina, E.V. & Stepovich, M.A. Mathematical Modeling of Heat and Mass Transfer Phenomena Caused by Interaction between Electron Beams and Planar Semiconductor Multilayers. Bull. Russ. Acad. Sci. Phys. 84, 844–850 (2020). https://doi.org/10.3103/S1062873820070138

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  • DOI: https://doi.org/10.3103/S1062873820070138

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