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.
Similar content being viewed by others
References
K. Kanaya and S. Okayama, “Penetration and energy-loss theory of electrons in solid targets,” J. Phys. D 5, No. 1, 43–58 (1972).
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).
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).
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).
C. J. Wu, “Investigation of minority–carrier diffusion lengths by electron bombardment of Shottky barriers,” J. Appl. Phys. 49, No. 5, 2827–2836 (1978).
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).
E. V. Seregina, M. A. Stepovich, and V. V. Kalmanovich, “Modeling of heating in the epitaxial structure CdxHg1−xTe/CdTe with the projection least squares method,” J. Phys., Conf. Ser. 1163, Paper No. 12013 (2019).
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).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 104, 2020, pp. 149-156.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-020-05008-4