Geodesic
On the well-posedness of mathematical models of diffusion due to a sharply focused electron probe in a homogeneous semiconductor material
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 122-129.

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In this paper, we compare qualitative properties of two- and three-dimensional mathematical models of the diffusion of particles (nonequilibrium minority charge carriers, excitons) generated by a sharply focused electron probe in a homogeneous semiconductor material. We show that the mathematical models considered are well posed and can be used for estimating electrophysical parameters of homogeneous semiconductor targets based on the results of experimental measurements.
Keywords: mathematical model, differential equation, partial derivative, Cauchy problem, electron probe, semiconductor, well-posedness, uniqueness, continuous dependence on data
Mots-clés : identification. 
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M. A. Stepovich; D. V. Turtin; E. V. Seregina. On the well-posedness of mathematical models of diffusion due to a sharply focused electron probe in a homogeneous semiconductor material. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 122-129. http://geodesic.mathdoc.fr/item/INTO_2021_193_a12/

[1] Bonch-Bruevich V. L., Kalashnikov S. G., Fizika poluprovodnikov, Nauka, M., 1990

[2] Vladimirov V. S., Zharinov V. V., Uravneniya matematicheskoi fiziki, Fizmatlit, M., 2004

[3] Mikheev N. N., Nikonorov I. M., Petrov V. I., Stepovich M. A., “Opredelenie elektrofizicheskikh parametrov poluprovodnikov v rastrovom elektronnom mikroskope metodami navedennogo toka i katodolyuminestsentsii”, Izv. AN SSSR. Ser. fiz., 54:2 (1990), 274–280

[4] Mikheev N. N., Petrov V. I., Stepovich M. A., “Kolichestvennyi analiz materialov poluprovodnikovoi optoelektroniki metodami rastrovoi elektronnoi mikroskopii”, Izv. RAN. Ser. fiz., 55:8 (1991), 1474–1482

[5] Mikheev N. N., Stepovich M. A., “Raspredelenie energeticheskikh poter pri vzaimodeistvii elektronnogo zonda s veschestvom”, Zavodskaya laboratoriya. Diagnostika materialov., 62:4 (1996), 20–25

[6] Pankov Zh., Opticheskie protsessy v poluprovodnikakh, Mir, M., 1973

[7] Polyakov A. N., Stepovich M. A., Turtin D. V., “Matematicheskoe modelirovanie katodolyuminestsentsii eksitonov, generirovannykh uzkim elektronnym puchkom v poluprovodnikovom materiale”, Izv. RAN. Ser. fiz., 80:12 (2016), 1629–1633

[8] Polyakov A. N., Stepovich M. A., Turtin D. V., “Trekhmernaya diffuziya eksitonov, generirovannykh elektronnym puchkom v poluprovodnikovom materiale: rezultaty matematicheskogo modelirovaniya”, Poverkhnost. Rentgen. sinkhrotron. neitron. issled., 12 (2015), 48–52

[9] Polyakov A. N., Noltemeyer M., Hempel T., Christen J., Stepovich M. A., “Dvumernaya diffuziya i katodolyuminestsentsiya eksitonov, generirovannykh elektronnym puchkom v poluprovodnikovom materiale: rezultaty matematicheskogo modelirovaniya”, Poverkhnost. Rentgen. sinkhrotron. neitron. issled., 11 (2012), 35–40

[10] Polyakov A. N., Noltemeyer M., Hempel T., Christen J., Stepovich M. A., “Katodolyuminestsentnye eksperimentalnye issledovaniya transporta eksitonov v nitride galliya”, Izv. RAN. Ser. fiz., 76:9 (2012), 1082–1085

[11] Polyakov A. N., Noltemeyer M., Hempel T., Christen J., Stepovich M. A., “Otsenka znachenii elektrofizicheskikh parametrov poluprovodnikovykh materialov po rezultatam izmerenii katodolyuminestsentsii eksitonov”, Prikl. fiz., 6 (2012), 41–46

[12] Stepovich M. A., Turtin D. V., Seregina E. V., Polyakov A. N., “O kachestvennykh kharakteristikakh dvumernoi matematicheskoi modeli diffuzii neosnovnykh nositelei zaryada, generirovannykh nizkoenergeticheskim elektronnym zondom v odnorodnom poluprovodnikovom materiale”, Sb. tr. mezhdunar. nauch. konf. «Aktualnye problemy prikladnoi matematiki, informatiki i mekhaniki» (17–19 dekabrya 2018 g., Voronezh), Voronezh. gos. un-t, Voronezh, 2019, 127–133

[13] Turtin D. V., Teoremy edinstvennosti resheniya zadachi Koshi dlya evolyutsionnykh uravnenii i sistem s rastuschimi koeffitsientami, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, VGU, Vladimir, 2012

[14] Noltemeyer M., Bertram F., Hempel T., Bastek B., Polyakov A. N., Christen J., Brandt M., Lorenz M., Grundmann M., “Excitonic transport in ZnO”, J. Mater. Res., 27:17 (2012), 2225–2231 | DOI

[15] Polyakov A. N., Smirnova A. N., Stepovich M. A., Turtin D. V., “Qualitative properties of a mathematical model of the diffusion of excitons generated by electron probe in a homogeneous semiconductor material”, Lobachevskii J. Math., 39:2 (2018), 259–262 | DOI | MR | Zbl

[16] Stepovich M. A., Turtin D. V., Seregina E. V. and Polyakov A. N., “On the qualitative characteristics of a two–dimensional mathematical model of diffusion of minority charge carriers generated by a low–energy electron beam in a homogeneous semiconductor material”, J. Phys. Conf. Ser., 1203 (2019), 012095-1–012095-8 | DOI