danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2026-70-5-415-423dan-1335Research ArticleТЕХНИЧЕСКИЕ НАУКИTECHNICAL SCIENCESОптимизация p–i–n структуры на основе GaN для бетавольтаического преобразования энергииOptimization of GaN-based p–i–n structure for betavoltaic energy conversionШипицаТ. Д.ShipitsaT. D.

Шипица Тимофей Дмитриевич – мл. науч. сотрудник 

ул. Академическая, 15/2, 220072, Минск 

Shipitsa Timophey D. – Junior Researcher 

15/2, Akademicheskaya Str., 220072, Minsk 

timopheyshipitsa@gmail.comhttps://orcid.org/0000-0002-4725-0969МазаникА. В.MazanikA. V.

Мазаник Александр Васильевич – д-р физ.-мат. наук, вед. науч. сотрудник

ул. Академическая, 15/2, 220072, Минск 

Mazanik Alexander V. – D. Sc. (Physics and Mathematics), Leading Researcher

15/2, Akademicheskaya Str., 220072, Minsk 

mazanikalexander@gmail.comАфанасьевК. Г.AfanacievK. G.

Афанасьев Константин Геннадьевич – ст. науч. сотрудник

ул. Академическая, 15/2, 220072, Минск 

Afanaciev Konstantin G. – Senior Research 

15/2, Akademicheskaya Str., 220072, Minsk 

K.afanaciev@gmail.comБаевВ. Г.BayevV. G.

Баев Вадим Геннадьевич – канд. физ.-мат. наук, заведующий лабораторией

ул. Академическая, 15/2, 220072, Минск 

Bayev Vadim G. – Ph. D. (Physics and Mathematics), Head of the Laboratory

15/2, Akademicheskaya Str., 220072, Minsk 

vadim.gh.bayev@gmail.comБриньА. А.BrinA. A.

Бринь Антон Анатольевич – канд. физ.-мат. наук, вед. науч. сотрудник

ул. Академическая, 15/2, 220072, Минск 

Brin Anton A. – Ph. D. (Physics and Mathematics), Leading Researcher

15/2, Akademicheskaya Str., 220072, Minsk 

brin2026@yandex.byhttps://orcid.org/0000-0002-4510-0190СвитоИ. А.SvitoI. A.

Свито Иван Антонович – канд. физ.-мат. наук, доцент, вед. науч. сотрудник

ул. Академическая, 15/2, 220072, Минск 

Svito Ivan A. – Ph. D. (Physics and Mathematics), Leading Researcher

15/2, Akademicheskaya Str., 220072, Minsk 

ivansvito184@gmail.comВолковА. А.VolkovA. A.

Волков Александр Александрович – мл. науч. сотрудник 

ул. Академическая, 15/2, 220072, Минск 

Volkov Alexander A. – Junior Researcher 

15/2, Akademicheskaya Str., 220072, Minsk 

alksndr.volkov@gmail.comВойтеховскийТ. Д.VoytehovskyT. D.

Войтеховский Тимофей Дмитриевич – мл. науч. сотрудник

ул. Академическая, 15/2, 220072, Минск 

Voytehovsky Timophey D. – Junior Researcher 

15/2, Akademicheskaya Str., 220072, Minsk 

voytehovsky_t@outlook.comИнститут энергетики Национальной академии наук БеларусиБеларусьInstitute of Power Engineering of the National Academy of Science of BelarusBelarus202613112026705415423Copyright © Шипица Т.Д., Мазаник А.В., Афанасьев К.Г., Баев В.Г., Бринь А.А., Свито И.А., Волков А.А., Войтеховский Т.Д., 20262026Шипица Т.Д., Мазаник А.В., Афанасьев К.Г., Баев В.Г., Бринь А.А., Свито И.А., Волков А.А., Войтеховский Т.Д.Shipitsa T.D., Mazanik A.V., Afanaciev K.G., Bayev V.G., Brin A.A., Svito I.A., Volkov A.A., Voytehovsky T.D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1335

Определены оптимальные значения толщины бета-источника 63Ni для бетавольтаического преобразователя энергии с помощью программного пакета Geant4, предназначенного для математического моделирования прохождения частиц через вещество методом Монте-Карло, c учетом эффекта самопоглощения. Так, при толщине 2 мкм поверхностная активность достигает 90 % от насыщения и составляет 4,6 ‧108 Бк‧см–2. Рассчитаны энергетические спектры электронов на поверхности источника в зависимости от его толщины, на их основании оптимизированы параметры барьерной p–i–n структуры на основе нитрида галлия GaN, в которой происходит поглощение бета-частиц, генерация электронно-дырочных пар и их разделение встроенным электрическим полем. Как показали расчеты, максимальная электрическая мощность, генерируемая бетавольтаическим преобразователем, составляет 0,12 мкВт‧см–2, что соответствует КПД бетавольтаического преобразования 6,7 %. Полученные результаты в дальнейшем будут использованы для создания прототипа бетавольтаического преобразователя энергии на основе нитрида галлия GaN.

Using mathematical modeling in the Geant4 software package designed for simulating particle transport through matter via the Monte Carlo method and taking into account the self-absorption effect, the optimal thickness of the 63Ni beta source for a betavoltaic energy converter was determined. The surface activity reaches 90 % relative to the saturation value at a source thickness of 2 µm and is equal to 4.6‧108 Bq/cm2. The electron energy spectra on the source surface were calculated as a function of its thickness. These spectra were used for optimization of the parameters of a p-i-n barrier structure, in which beta-particles are absorbed, electron-hole pairs are generated and separated by a built-in electric field. According to the calculations, the maximum electric power generated by a GaN-based betavoltaic converter is equal to 0.12 μW‧cm–2, which corresponds to a betavoltaic conversion efficiency of 6.7 %. The results will be used in the design of a prototype of a gallium nitride betavoltaic energy converter.

p–i–n структуранитрид галлиябетавольтаическое преобразование энергииисточник 63Niмоделированиеоптимизацияp–i–n structuregallium nitridebetavoltaic energy conversion63Ni sourcemodellingoptimizationИсследования проводились в рамках отдельного проекта Национальной академии наук Беларуси «Бетавольтаические преобразователи энергии на основе широкозонных полупроводников». Авторы статьи выражают благодарность Лаборатории информационных технологий Объединенного института ядерных исследований за предоставленную возможность использовать ресурсы платформы HybriLIT для моделирования с помощью программного обеспечения COMSOL Multiphysics.The work was supported by the particular project of the National Academy of Science of Belarus “Betavoltaic energy converters based on wide-band-gap semiconductors” for financial support. The authors of the paper are grateful to JINR Laboratory of Information Technologies for the opportunity to use resources of the HybriLIT platform for simulations with the COMSOL Multiphysics software.ReferencesReview – Betavoltaic cell: the past, present, and future / C. Zhou, J. Zhang, X. Wang [et al.] // ECS Journal of Solid State Science and Technology. – 2021. – Vol. 10. – Art 027005. https://doi.org/10.1149/2162-8777/abe423Zhou C., Zhang J., Wang X., Yang Y., Xu P., Li P., Zhang L., Chen Z., Feng H., Wu W. Review – Betavoltaic cell: the past, present, and future. ECS Journal of Solid State Science and Technology, 2021, vol. 10, art. 027005. https://doi.org/10.1149/2162-8777/abe423Betavoltaic nuclear battery: a review of recent progress and challenges as an alternative energy source / M. B. Naseem, H. S. Kim, J. Lee [et al.] // Journal of Physical Chemistry C. – 2023. – Vol. 127, N 16. – P. 7565–7579. https://doi.org/10.1021/acs.jpcc.3c00684Naseem M. B., Kim H. S., Lee J., Kim C. H., In S. Betavoltaic nuclear battery: a review of recent progress and challenges as an alternative energy source. Journal of Physical Chemistry C, 2023, vol. 127, no. 16, pp. 7565–7579. https://doi.org/10.1021/acs.jpcc.3c00684Agyekum, E. B. Beta-voltaic nuclear batteries – review of recent developments, challenges and future research directions / E. B. Agyekum // Journal of Energy Storage. – 2025. – Vol. 122. – Art. 116701. https://doi.org/10.1016/j.est.2025.116701Agyekum E. B. Beta-voltaic nuclear batteries – review of recent developments, challenges and future research directions. Journal of Energy Storage, 2025, vol. 122, art. 116701. https://doi.org/10.1016/j.est.2025.116701Ji, W. Measurement of low energy beta radiation from Ni-63 by using peeled-off Gafchromic EBT3 film / W. Ji, J.-B. Kim, J.-J. Kim // Nuclear Engineering and Technology. – 2022. – Vol. 54, N 10. – P. 3811–3815. https://doi.org/10.1016/j.net.2022.05.009Ji W., Kim J.-B., Kim J.-J. Measurement of low energy beta radiation from Ni-63 by using peeled-off Gafchromic EBT3 film. Nuclear Engineering and Technology, 2022, vol. 54, no. 10, pp. 3811–3815. https://doi.org/10.1016/j.net.2022.05.009Properties and data of the isotope 63Ni // ChemLin. – URL: https://www.chemlin.org/isotope/nickel-63 (date of access: 28 July 2026).Properties and data of the isotope 63Ni. ChemLin. Available at: https://www.chemlin.org/isotope/nickel-63 (accessed 28 July 2026).ESTAR: Stopping Powers and Ranges for Electrons // NIST. – URL: https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html (date of access: 28 July 2026).ESTAR: Stopping Powers and Ranges for Electrons. NIST. Available at: https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html (accessed 28 July 2026).Kanaya, K. Penetration and energy-loss theory of electrons in solid targets / K. Kanaya, S. Okayama // Journal of Physics D: Applied Physics. – 1972. – Vol. 5. – Art. 43. https://doi.org/10.1088/0022-3727/5/1/308Kanaya K., Okayama S. Penetration and energy-loss theory of electrons in solid targets. Journal of Physics D: Applied Physics, 1972, vol. 5, art. 43. https://doi.org/10.1088/0022-3727/5/1/308Geant4 – a simulation toolkit / S. Agostinelli, J. Allison, K. Amako [et al.] // Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. – 2003. – Vol. 506, N 3. – P. 250–303. https://doi.org/10.1016/S0168-9002(03)01368-8Agostinelli S., Allison J., Amako K., Apostolakis J., Araujo H., Arce P., Asai M. [et al.]. Geant4 – a simulation toolkit. Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2003, vol. 506, no. 3, pp. 250–303. https://doi.org/10.1016/S0168-9002(03)01368-8Semiconductor Module // COMSOL. – URL: https://www.comsol.com/semiconductor-module (date of access: 22 July 2026).Semiconductor Module. COMSOL. Available at: https://www.comsol.com/semiconductor-module (accessed 22 July 2026).Defect-related optical transitions in GaN / W. Rieger, R. Dimitrov, D. Brunner [et al.] // Physical Review B. – 1996. – Vol. 54. – Art. 17596. https://doi.org/10.1103/PhysRevB.54.17596Rieger W., Dimitrov R., Brunner D., Rohrer E., Ambacher O., Stutzmann M. Defect-related optical transitions in GaN. Physical Review B, 1996, vol. 54, art. 17596. https://doi.org/10.1103/PhysRevB.54.17596Optical band gap dependence on composition and thickness of InxGa1−xN (0 < x < 0.25) grown on GaN / C. A. Parker, J. C. Roberts, S. M. Bedair [et al.] // Applied Physics Letters. – 1999. – Vol. 75, N 17. – P. 2566–2568. https://doi.org/10.1063/1.125079Parker C. A., Roberts J. C., Bedair S. M., Reed M. J., Liu S. X., El-Masry N. A., Robins L. H. Optical band gap dependence on composition and thickness of InxGa1−xN (0 < x < 0.25) grown on GaN. Applied Physics Letters, 1999, vol. 75, no. 17, pp. 2566–2568. https://doi.org/10.1063/1.125079First-principles calculations of indirect Auger recombination in nitride semiconductors / E. Kioupakis, D. Steiauf, P. Rinke [et al.] // Physical Review B. – 2015. – Vol. 92. – Art. 035207. https://doi.org/10.1103/PhysRevB.92.035207Kioupakis E., Steiauf D., Rinke P., Delaney K. T., Van de Walle C. G. First-principles calculations of indirect Auger recombination in nitride semiconductors. Physical Review B, 2015, vol. 92, art. 035207. https://doi.org/10.1103/PhysRevB.92.035207Modeling and simulation of bulk gallium nitride power semiconductor devices / G. Sabui, P. J. Parbrook, M. Arredondo-Arechavala, Z. J. Shen // AIP Advances. – 2016. – Vol. 6, N 5. – Art. 055006. https://doi.org/10.1063/1.4948794Sabui G., Parbrook P. J., Arredondo-Arechavala M., Shen Z. J. Modeling and simulation of bulk gallium nitride power semiconductor devices. AIP Advances, 2016, vol. 6, no. 5, art. 055006. https://doi.org/10.1063/1.4948794Carrier dynamics in bulk GaN / P. Ščajev, K. Jarašiūnas, S. Okur [et al.] // Journal of Applied Physics. – 2012. – Vol. 111, N 2. – Art. 023702. https://doi.org/10.1063/1.3673851Ščajev P., Jarašiūnas K., Okur S., Özgür Ü., Morkoç H. Carrier dynamics in bulk GaN. Journal of Applied Physics, 2012, vol. 111, no. 2, art. 023702. https://doi.org/10.1063/1.3673851Caughey, D. M. Carrier mobilities in silicon empirically related to doping and field / D. M. Caughey, R. E. Thomas // Proceedings of the IEEE. – 1967. – Vol. 55, N 12. – P. 2192–2193. https://doi.org/10.1109/PROC.1967.6123Caughey D., Thomas R. Carrier mobilities in silicon empirically related to doping and field. Proceedings of the IEEE, 1967, vol. 55, no. 12, pp. 2192–2193. https://doi.org/10.1109/PROC.1967.6123Vitanov, S. Simulation of high electron mobility transistors: Ph. D. thesis / S. Vitanov. – Wien, 2010.Vitanov S. Simulation of high electron mobility transistors, Ph. D. thesis. Wien, 2010.Sellin, P. J. New materials for radiation hard semiconductor detectors / P. J. Sellin, J. Vaitkus // Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. – 2006. – Vol. 557, N 2. – P. 479–489. https://doi.org/10.1016/j.nima.2005.10.128Sellin P. J., Vaitkus J. New materials for radiation hard semiconductor detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2006, vol. 557, no. 2, pp. 479–489. https://doi.org/10.1016/j.nima.2005.10.128A high open-circuit voltage gallium nitride betavoltaic microbattery / Z. Cheng, X. Chen, H. San [et al.] // Journal of Micromechanics and Microengineering. – 2012. – Vol. 22, N 7. – Art. 074011. https://doi.org/10.1088/0960-1317/22/7/074011Cheng Z., Chen X., San H., Feng Z., Liu B. A high open-circuit voltage gallium nitride betavoltaic microbattery. Journal of Micromechanics and Microengineering, 2012, vol. 22, no. 7, art. 074011. https://doi.org/10.1088/0960-1317/22/7/074011High open-circuit voltage betavoltaic cell based on GaN pin homojunction / Z. J. Cheng, H. S. San, Z. H. Feng [et al.] // Electronics Letters. – 2011. – Vol. 47, N 12. https://doi.org/10.1049/el.2011.1143Cheng Z. J., San H. S., Feng Z. H., Liu B., Chen X. Y. High open-circuit voltage betavoltaic cell based on GaN pin homojunction. Electronics Letters, 2011, vol. 47, no. 12. https://doi.org/10.1049/el.2011.1143

The authors declare that there are no conflicts of interest present.