Determination of the Electrical Material Thin Film Electromagnetic Characteristics Using the Percolation Theory
DOI:
https://doi.org/10.24160/0013-5380-2025-10-87-93Keywords:
thin film, fractal surface, percolation, conductivity, dielectric constant, inductance, film surface parameters, surface peaksAbstract
The surface of a thin film obtained by vacuum methods is a fractal structure consisting of a set of overlapping Gaussian surfaces (surface peaks). Effective kinetic coefficients for the conductivity, capacitance, and induction of a single element of the electrical material thin film surface have been calculated for such surfaces using the percolation theory. The bridge between two overlapping peaks of the film surface is taken in the analysis as a single surface element. The film surface geometry was not simplified during the calculations. The input data for the calculations are the surface statistical parameters obtained during its examination by atomic force microscopy. With a normal distribution of input parameters, the distribution of effective kinetic coefficients will be exponential in nature. The obtained effective kinetic coefficients make it possible to simulate, using a grid model, the electromagnetic properties of thin films such as conductivity, dielectric constant and magnetic permeability, depending on the film material. The maximum allowable distance between surface peaks, which corresponds to the thin film percolation thickness, is a limitation for using this method to calculate effective kinetic coefficients.
References
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19. Erkan S, Arpat E., Peters S. Investigation of Percolation Thickness of Sputter Coated Thin NiCr Films on Clear Float Glass. – Applied Surface Science, 2017, vol. 421, No. B, DOI: 10.1016/j.apsusc.2017.01.143.
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21. Тумаркин А.В. и др. Варьирование состава сегнетоэлектрических пленок при ионно-плазменном распылении: эксперимент и моделирование. – Известия РАН. Серия физическая, 2018, т. 82, № 3, c. 395–401.
#
1. Iudin D.I., Koposov E.V. Fraktaly: ot prostogo k slozhnomu (Fractals: from Simple to Complex). N. Novgorod: NNGASU, 2012, 200 p.
2. Panin A.V., Shugurov A.R., Puchkareva L.N. Fizicheskaya mezomekhanika – in Russ. (Physical Mesomechanics), 2000, vol. 3, No. 3, pp. 53–60.
3. Nosova Yu.M. et al. Vakuumnaya tekhnika i tekhnologiya – in Russ. (Vacuum Engineering and Technology), 2011, vol. 21, No. 2, c. 119–122.
4. Ko E.C., Kang W., Han J.H. Improved Dielectric Constant and Leakage Current Characteristics of BaTiO3 Thin Film on SrRuO3 Seed Layer. – Journal of Alloys and Compounds, 2022, vol. 895, No. 1, DOI: 10.1016/j.jallcom.2021.162579.
5. Ketov S.V. et al. Formation of Nanostructured Metallic Glass Thin Films Upon Sputtering. – Heliyon, 2017, vol. 3, No. 1, DOI: 10.1016/j.heliyon.2016.e00228.
6. Sharma V., Ghosh R.K., Kuanr B.K. Influence of Ferromagnetic Layer Thickness on the Gilbert Damping and Magnetocrystalline Anisotropy in PLD Grown Epitaxial Co2FeSi Heusler Alloy Thin Films. – Results in Surfaces and Interfaces, 2022, vol. 6, DOI: 10.1016/j.rsurfi.2022.100052.
7. Antonets I.V. et al. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2010, vol. 80, No. 9, c. 134–140.
8. Muhortov V.M., Yuzyuk Yu.I. Geterostruktury na osnove nanorazmernyh segnetoelektricheskih plenok (Heterostructures Based on Nanoscale Ferroelectric Films). Rostov n/D.: YuFU, 2007, 84 p.
9. Cicek Z. et al. Thickness Dependence of Dielectric Properties of TlGaS2 Thin Films. – Materials Science in Semiconductor Processing, 2023, vol. 166, DOI: 10.1016/j.mssp.2023.107733.
10. Giyon E. et al. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1991, vol. 161, No. 10, c. 121–128.
11. Balagurov B.Ya., Kashin V.A. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2002, vol. 72, No. 10, c. 1–9.
12. Emets Yu.P. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2003, vol. 73, No. 3, c. 42–53.
13. Shklovskiy B.I., Efros A.L. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1975, vol. 117, No. 3, c. 401–435.
14. Shklovskiy B.I., Efros A.L. Elektronnye svoystva legirovan-nyh poluprovodnikov (Electronic Properties of Doped Semiconductors). M.: Nauka, 1979, 416 p.
15. Haviar S. et al. Analysis and 3D Modelling of Percolated Conductive Networks in Nanoparticle-Based Thin Films. – Applied Surface Science Advances, 2025, vol. 25, DOI: 10.1016/j.apsadv.2024. 100689.
16. Wang Z., Zhang J., Weng G.J. Modeling the Percolation Behavior of Conductive Particles/Insulating Polymer-Based Composites with Equivalent Circuit of Resistance. – Polymer, 2025, vol. 324, DOI: 10.1016/j.polymer.2025.128262.
17. Snarskiy A.A., Slipchenko K.V., Bezsudnov I.V. Pis’ma v zhurnal tekhnicheskoy fiziki – in Russ. (Letters to the Journal of Technical Physics), 1997, vol. 23, No. 24, c. 35–39.
18. Fokin A.G. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1996, vol. 166, No. 10, c. 1069–1093.
19. Erkan S, Arpat E, Peters S. Investigation of Percolation Thickness of Sputter Coated Thin NiCr Films on Clear Float Glass. – Applied Surface Science, 2017, vol. 421, No. B, DOI: 10. 1016/j.apsusc.2017.01.143.
20. Ossi P.M. et al. Process Controlled Nanostructure and Superhydrophobicity of Thin Films Prepared Ablating Titanium in Mixed Argon/Nitrogen Atmospheres. – Applied Surface Science, 2025, vol. 693, DOI: 10.1016/j.apssusc.2025.162651.
21. Tumarkin A.V. et al. Izvestiya RAN. Seriya fizicheskaya – in Russ. (Bulletin of the Russian Academy of Sciences: Physics), 2018, vol. 82, No. 3, c. 395–401
2. Панин А.В., Шугуров А.Р., Пучкарева Л.Н. О природе шероховатости поверхности тонких диэлектрических пленок. – Физическая мезомеханика, 2000, т. 3, № 3, с. 53–60.
3. Носова Ю.М. и др. Исследование зависимости удельного сопротивления тонких пленок алюминия, нанесенных методом ВЧ распыления, от их фрактальной размерности. – Вакуумная техника и технология, 2011, т. 21, № 2, c. 119–122.
4. Ko E.C., Kang W., Han J.H. Improved Dielectric Constant and Leakage Current Characteristics of BaTiO3 Thin Film on SrRuO3 Seed Layer. – Journal of Alloys and Compounds, 2022, vol. 895, No. 1, DOI: 10.1016/j.jallcom.2021.162579.
5. Ketov S.V. et al. Formation of Nanostructured Metallic Glass Thin Films Upon Sputtering. – Heliyon, 2017, vol. 3, No. 1, DOI: 10.1016/j.heliyon.2016.e00228.
6. Sharma V., Ghosh R.K., Kuanr B.K. Influence of Ferromagnetic Layer Thickness on the Gilbert Damping and Magnetocrystalline Anisotropy in PLD Grown Epitaxial Co2FeSi Heusler Alloy Thin Films. – Results in Surfaces and Interfaces, 2022, vol. 6, DOI: 10.1016/j.rsurfi.2022.100052.
7. Антонец И.В. и др. Наноструктура, проводящие и отражающие свойства тонких пленок железа и (Fe)X(BaF2)Y. – Журнал технической физики, 2010, т. 80, № 9, c. 134–140.
8. Мухортов В.М., Юзюк Ю.И. Гетероструктуры на основе наноразмерных сегнетоэлектрических пленок. Ростов н/Д.: ЮФУ, 2007, 84 с.
9. Cicek Z. et al. Thickness Dependence of Dielectric Properties of TlGaS2 Thin Films. – Materials Science in Semiconductor Processing, 2023, vol. 166, DOI: 10.1016/j.mssp.2023.107733.
10. Гийон Э. и др. Фракталы и перколяция в пористой среде. – Успехи физических наук, 1991, т. 161, № 10, c. 121–128.
11. Балагуров Б.Я., Кашин В.А. Исследование электрофизических характеристик двумерных трехкомпонентных периодических моделей. – Журнал технической физики, 2002, т. 72, № 10, c. 1–9.
12. Емец Ю.П. Дисперсия диэлектрической проницаемости трех- и четырехкомпонентных матричных сред. – Журнал технической физики, 2003, т. 73, № 3, c. 42–53.
13. Шкловский Б.И., Эфрос А.Л. Теория протекания и проводимость сильно неоднородных сред. – Успехи физических наук, 1975, т. 117, № 3, c. 401–435.
14. Шкловский Б.И., Эфрос А.Л. Электронные свойства легированных полупроводников. М.: Наука, 1979, 416 с.
15. Haviar S. et al. Analysis and 3D Modelling of Percolated Conductive Networks in Nanoparticle-Based Thin Films. – Applied Sur-face Science Advances, 2025, vol. 25, DOI: 10.1016/j.apsadv.2024.100689.
16. Wang Z., Zhang J., Weng G.J. Modeling the Percolation Behavior of Conductive Particles/Insulating Polymer-Based Composites with Equivalent Circuit of Resistance. – Polymer, 2025, vol. 324, DOI: 10.1016/j.polymer.2025.128262.
17. Снарский А.А., Слипченко К.В., Безсуднов И.В. Соотношение взаимности для эффективной электропроводности случайно-неоднородной среды во фрактальной области. – Письма в журнал технической физики, 1997, т. 23, № 24, c. 35–39.
18. Фокин А.Г. Макроскопическая проводимость случайно-неоднородных сред. Методы расчета. – Успехи физических наук, 1996, т. 166, № 10, c. 1069–1093.
19. Erkan S, Arpat E., Peters S. Investigation of Percolation Thickness of Sputter Coated Thin NiCr Films on Clear Float Glass. – Applied Surface Science, 2017, vol. 421, No. B, DOI: 10.1016/j.apsusc.2017.01.143.
20. Ossi P.M. et al. Process Controlled Nanostructure and Superhydrophobicity of Thin Films Prepared Ablating Titanium in Mixed Argon/Nitrogen Atmospheres. – Applied Surface Science, 2025, vol. 693, DOI: 10.1016/j.apssusc.2025.162651.
21. Тумаркин А.В. и др. Варьирование состава сегнетоэлектрических пленок при ионно-плазменном распылении: эксперимент и моделирование. – Известия РАН. Серия физическая, 2018, т. 82, № 3, c. 395–401.
#
1. Iudin D.I., Koposov E.V. Fraktaly: ot prostogo k slozhnomu (Fractals: from Simple to Complex). N. Novgorod: NNGASU, 2012, 200 p.
2. Panin A.V., Shugurov A.R., Puchkareva L.N. Fizicheskaya mezomekhanika – in Russ. (Physical Mesomechanics), 2000, vol. 3, No. 3, pp. 53–60.
3. Nosova Yu.M. et al. Vakuumnaya tekhnika i tekhnologiya – in Russ. (Vacuum Engineering and Technology), 2011, vol. 21, No. 2, c. 119–122.
4. Ko E.C., Kang W., Han J.H. Improved Dielectric Constant and Leakage Current Characteristics of BaTiO3 Thin Film on SrRuO3 Seed Layer. – Journal of Alloys and Compounds, 2022, vol. 895, No. 1, DOI: 10.1016/j.jallcom.2021.162579.
5. Ketov S.V. et al. Formation of Nanostructured Metallic Glass Thin Films Upon Sputtering. – Heliyon, 2017, vol. 3, No. 1, DOI: 10.1016/j.heliyon.2016.e00228.
6. Sharma V., Ghosh R.K., Kuanr B.K. Influence of Ferromagnetic Layer Thickness on the Gilbert Damping and Magnetocrystalline Anisotropy in PLD Grown Epitaxial Co2FeSi Heusler Alloy Thin Films. – Results in Surfaces and Interfaces, 2022, vol. 6, DOI: 10.1016/j.rsurfi.2022.100052.
7. Antonets I.V. et al. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2010, vol. 80, No. 9, c. 134–140.
8. Muhortov V.M., Yuzyuk Yu.I. Geterostruktury na osnove nanorazmernyh segnetoelektricheskih plenok (Heterostructures Based on Nanoscale Ferroelectric Films). Rostov n/D.: YuFU, 2007, 84 p.
9. Cicek Z. et al. Thickness Dependence of Dielectric Properties of TlGaS2 Thin Films. – Materials Science in Semiconductor Processing, 2023, vol. 166, DOI: 10.1016/j.mssp.2023.107733.
10. Giyon E. et al. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1991, vol. 161, No. 10, c. 121–128.
11. Balagurov B.Ya., Kashin V.A. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2002, vol. 72, No. 10, c. 1–9.
12. Emets Yu.P. Zhurnal tekhnicheskoy fiziki – in Russ. (Journal of Technical Physics), 2003, vol. 73, No. 3, c. 42–53.
13. Shklovskiy B.I., Efros A.L. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1975, vol. 117, No. 3, c. 401–435.
14. Shklovskiy B.I., Efros A.L. Elektronnye svoystva legirovan-nyh poluprovodnikov (Electronic Properties of Doped Semiconductors). M.: Nauka, 1979, 416 p.
15. Haviar S. et al. Analysis and 3D Modelling of Percolated Conductive Networks in Nanoparticle-Based Thin Films. – Applied Surface Science Advances, 2025, vol. 25, DOI: 10.1016/j.apsadv.2024. 100689.
16. Wang Z., Zhang J., Weng G.J. Modeling the Percolation Behavior of Conductive Particles/Insulating Polymer-Based Composites with Equivalent Circuit of Resistance. – Polymer, 2025, vol. 324, DOI: 10.1016/j.polymer.2025.128262.
17. Snarskiy A.A., Slipchenko K.V., Bezsudnov I.V. Pis’ma v zhurnal tekhnicheskoy fiziki – in Russ. (Letters to the Journal of Technical Physics), 1997, vol. 23, No. 24, c. 35–39.
18. Fokin A.G. Uspekhi fizicheskih nauk – in Russ. (Achievements of Physical Sciences), 1996, vol. 166, No. 10, c. 1069–1093.
19. Erkan S, Arpat E, Peters S. Investigation of Percolation Thickness of Sputter Coated Thin NiCr Films on Clear Float Glass. – Applied Surface Science, 2017, vol. 421, No. B, DOI: 10. 1016/j.apsusc.2017.01.143.
20. Ossi P.M. et al. Process Controlled Nanostructure and Superhydrophobicity of Thin Films Prepared Ablating Titanium in Mixed Argon/Nitrogen Atmospheres. – Applied Surface Science, 2025, vol. 693, DOI: 10.1016/j.apssusc.2025.162651.
21. Tumarkin A.V. et al. Izvestiya RAN. Seriya fizicheskaya – in Russ. (Bulletin of the Russian Academy of Sciences: Physics), 2018, vol. 82, No. 3, c. 395–401
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2025-08-28
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