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Qualitative Analysis of a Class of Differential Equations of Heat and Mass Transfer in a Condensed Material

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We propose a mathematical model of three-dimensional diffusion of nonequilibrium minority charge carries caused by a pulsating sharply focused electron beam in a homogeneous semiconductor material and show the correctness of the model. We establish the continuous dependence of the solution on the data and obtain estimates for influence of data errors on the distribution of diffusing impurity. Bibliography: 9 titles.

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References

  1. K. Kanaya and S. Okayama, “Penetration and energy-loss theory of electrons in solid targets,” J. Phys. D 5, No. 1, 43–58 (1972).

    Article  Google Scholar 

  2. M. A. Stepovich, A. N. Amrastanov, E. V. Seregina, and M. N. Filippov, “On one peculiarity of the model describing the interaction of the electron beam with the semiconductor surface,” J. Phys., Conf. Ser. 955, Paper No. 12040 (2018).

  3. A. N. Polyakov, M. A. Stepovich, and D. V. Turtin, “Three-dimensional diffusion of excitons generated by an electron beam in a semiconductor material: Results of mathematical modeling.” J. Surface Invest. 9, No. 6, 1251–1255 (2015).

    Article  Google Scholar 

  4. D. B. Wittry, D. F. Kyser, “Measurements of diffusion lengths in direct–gap semiconductors by electron beam excitation,” J. Appl. Phys. 38, No. 1, 375–381 (1967).

    Article  Google Scholar 

  5. C. J. Wu, “Investigation of minority–carrier diffusion lengths by electron bombardment of Shottky barriers,” J. Appl. Phys. 49, No. 5, 2827–2836 (1978).

    Article  Google Scholar 

  6. V. V. Kalmanovich, E. V. Seregina, and M. A. Stepovich, “On the possibility of a numerical solution of the heat and mass transfer problem with the combined matrix&generalized powers of Bers method,” J. Phys., Conf. Ser. 1163, Paper No. 12012 (2019).

  7. E. V. Seregina, M. A. Stepovich, and V. V. Kalmanovich, “Modeling of heating in the epitaxial structure CdxHg1xTe/CdTe with the projection least squares method,” J. Phys., Conf. Ser. 1163, Paper No. 12013 (2019).

  8. E. V. Seregina, A. M. Makarenkov, and M. A. Stepovich, “Statistical analysis of a model of collective motion of minority charge carries using the projection method,” J. Surface Invest. 6, No. 2, 330–337 (2012).

    Article  Google Scholar 

  9. A. N. Polyakov, M. A. Stepovich, and D. V. Turtin, “Mathematical modeling of the cathodoluminescence of excitons generated by a narrow electron beam in a semiconductor material,” Bull. Russ. Acad. Sci., Phys. 80, No. 12, 1436–1440 (2016).

    Article  Google Scholar 

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Correspondence to M. A. Stepovich.

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Translated from Problemy Matematicheskogo Analiza 104, 2020, pp. 149-156.

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Turtin, D.V., Seregina, E.V. & Stepovich, M.A. Qualitative Analysis of a Class of Differential Equations of Heat and Mass Transfer in a Condensed Material. J Math Sci 250, 166–174 (2020). https://doi.org/10.1007/s10958-020-05008-4

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  • DOI: https://doi.org/10.1007/s10958-020-05008-4

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