Inverse Problems for the Diffusion–Drift Model of Charging of an Inhomogeneous Polar Dielectric

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The problems of reconstructing the unknown parameters of the model of electron-induced charging of an inhomogeneous polar dielectric from additional information about the volume charge density distribution and the electric field strength are studied. Within the optimization approach, these inverse problems are reduced to control problems and their solvability is proved. For extremum problems, optimality systems are derived and, based on their analysis, local uniqueness of the solution of one of the considered problems is proved. Taking into account the introduced characteristic of the inhomogeneity of the dielectric, auxiliary results on the solvability and properties of solutions of the boundary value problem, obtained earlier for the model of charging of a homogeneous dielectric, are corrected.

About the authors

R. V. Brizitskii

Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Email: mlnwizard@mail.ru
690041, Vladivostok, Russia

N. N. Maksimova

Amur State University

Email: maksimova.nn@amursu.ru
675000, Blagoveshchensk, Amur oblast, Russia

A. G. Maslovskaya

Amur State University

Author for correspondence.
Email: maslovskaya.ag@amursu.ru
675000, Blagoveshchensk, Amur oblast, Russia

References

  1. Chan D.S.H., Sim K.S., Phang J.C.H. A simulation model for electron irradiation induced specimen charging in a scanning electron microscope // Scanning Spectroscopy. 1993. V. 7. № 31. P. 847–859.
  2. Sessler G.M., Yang G.M. Charge dynamics in electron-irradiated polymers // Braz. J. Phys. 1999. V. 29. № 2. P. 233–240.
  3. Suga H., Tadokoro H., Kotera M. A simulation of electron beam induced charging-up of insulators // Electron Microscopy. 1998. V. 1. P. 177–178.
  4. Cazaux J. About the mechanisms of charging in EPMA, SEM, and ESEM with their time evolution // Microscopy and Microanalysis. 2004. V. 10. № 6. P. 670–680.
  5. Борисов С.С., Грачев Е.А., Зайцев С.И. Моделирование поляризации диэлектрика в процессе облучения электронным пучком // Прикладная физика. 2004. № 1. С. 118–124.
  6. Kotera M., Yamaguchi K., Suga H. Dynamic simulation of electron-beam-induced charging up of insulators // Japan J. Appl. Phys. 1999. V. 38. № 12 B. P. 7176–7179.
  7. Ohya K., Inai K., Kuwada H., Hauashi T., Saito M. Dynamic simulation of secondary electron emission and charging up of an insulting material // Surface and Coating Technology. 2008. V. 202. P. 5310–5313.
  8. Maslovskaya A.G. Physical and mathematical modeling of the electron-beam-induced charging of ferroelectrics during the process of domain structure switching // J. of Surface Investigation. 2013. V. 7. № 4. P. 680–684.
  9. Pavelchuk A.V., Maslovskaya A.G. Approach to numerical implementation of the drift-diffusion model of field effects induced by a moving source // Russ. Phys. J. 2020. V. 63. P. 105–112.
  10. Raftari B., Budko N.V., Vuik C. Self-consistence drift-diffusion-reaction model for the electron beam interaction with dielectric samples // J. Appl. Phys. 2015. V. 118. P. 204101 (17).
  11. Chezganov D.S., Kuznetsov D.K., Shur V.Ya. Simulation of spatial distribution of electric field after electron beam irradiation of -doped covered by resist layer // Ferroelectrics. 2016. V. 496. P. 70–78.
  12. Maslovskaya A., Pavelchuk A. Simulation of dynamic charging processes in ferroelectrics irradiated with SEM // Ferroelectrics. 2015. V. 476. P. 157–167.
  13. Maslovskaya A., Sivunov A.V. Simulation of electron injection and charging processes in ferroelectrics modified with SEM-techniques // Solid State Phenomena. 2014. V. 213. P. 119–124.
  14. Arat K.T., Klimpel T., Hagen C.W. Model improvements to simulate charging in scanning electron microscope // J. of Micro/ Nanolithography, MEMS, and MOEMS, 2019. V. 18. № 4. P. 04403 (13).
  15. Бризицкий Р.В., Максимова Н.Н., Масловская А.Г. Теоретический анализ и численная реализация стационарной диффузионно-дрейфовой модели зарядки полярных диэлектриков // Ж. вычисл. матем. и матем. физ. 2022. Т. 62. № 10. С. 1696–1706.
  16. Алексеев Г.В., Левин В.А., Терешко Д.А. Оптимизационный метод в задачах дизайна сферических слоистых тепловых оболочек // Докл. АН. 2017. Т. 476. № 5. С. 512–517.
  17. Brizitskii R.V., Saritskaya Zh.Yu. Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation // J. Inverse Ill-Posed Probl. 2018. V. 26. № 6. P. 821–833.
  18. Maksimova N.N., Brizitskii R.V. Inverse problem of recovering the electron diffusion coefficient // Дальневосточный матем. журн. 2022. Т. 22. № 2. С. 201–206.
  19. Алексеев Г.В. Оптимизация в стационарных задачах тепломассопереноса и магнитной гидродинамики. М.: Научный мир, 2010. 412 с.
  20. Buffa A. Some numerical and theoretical problems in computational electromagnetism. Thesis. 2000.
  21. Гилбарг Д., Трудингер М. Эллиптические дифференциальные уравнения с частными производными второго порядка. М.: Наука, 1989. 463 с.
  22. Berninger H. Non-overlapping domain decomposition for the Richards equation via superposition operators // Domain Decomposition Methods in Science and Engineering XVIII. Springer, 2009. P. 169–176.
  23. Фурсиков А.В. Оптимальное управление распределенными системами. Теория и приложения. Новосибирск: Научн. книга, 1999. 352 с.
  24. Алексеев Г.В., Бризицкий Р.В., Сарицкая Ж.Ю. Оценки устойчивости решений экстремальных задач для нелинейного уравнения конвекции–диффузии–реакции // Сиб. журн. индустр. матем. 2016. Т. 19. № 2. С. 3–16.
  25. Бризицкий Р.В., Сарицкая Ж.Ю. Обратные коэффициентные задачи для нелинейного уравнения конвекции–диффузии–реакции // Изв. РАН. Сер. матем. 2018. Т. 82. Вып. 1. С. 17–33.
  26. Бризицкий Р.В., Сарицкая Ж.Ю. Задача граничного управления для нелинейного уравнения конвекции–диффузии–реакции // Ж. вычисл. матем. и матем. физ. 2018. Т. 58. № 12. С. 2139–2152 .
  27. Алексеев Г.В. Коэффициентные обратные экстремальные задачи для стационарных уравнений тепломассопереноса // Ж. вычисл. матем. и матем. физ. 2007. Т. 47. № 6. С. 1055–1076.
  28. Chebotarev A.Yu., Grenkin G.V., Kovtanyuk A.E., Botkin N.D., Hoffmann K.-H. Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange // J. of Math. Analys. and Appl. 2018. V. 460. № 2. P. 737–744.
  29. Chebotarev A.Yu., Grenkin G.V., Kovtanyuk A.E., Botkin N.D., Hoffmann K.-H. Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions // Commun. Nonlinear Sci. Numer. Simulat. 2018. V. 57. P. 290–298.
  30. Chebotarev A.Y., Grenkin G.V., Kovtanyuk A.E. Inhomogeneous steady-state problem of complex heat transfer // ESAIM: Math. Model. and Numeric. Analys. 2017. V. 51. № 6. P. 2511–2519.
  31. Maslovskaya A.G., Moroz L.I., Chebotarev A.Y., Kovtanyuk A.E. Theoretical and numerical analysis of the Landau-Khalatnikov model of ferroelectric hysteresis // Commun. Nonlinear Sci. Numer. Simulat. 2021. V. 93. P. 105524.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 Р.В. Бризицкий, Н.Н. Максимова, А.Г. Масловская