Geodesic
Mathematical modeling of a field emitter with a hyperbolic shape
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 3, pp. 238-248
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This article is devoted to modeling a field emission diode system. The emitter surface is a hyperboloid of rotation. The anode surface is a part of the hyperboloid of rotation, in a particular case, a circular diaphragm. A boundary value problem is formulated for the Laplace equation with non-axisymmetric boundary conditions of the first kind. A 3D solution was found by the variable separation method in the prolate spheroidal coordinates. The electrostatic potential distribution is presented in the form of the Legendre functions expansions. The calculation of the expansion coefficients is reduced to solving a system of linear equations with constant coefficients. All geometric dimensions of the system are the parameters of the problem.
Keywords: micro and nanoelectronics, field emitter, field emission, mathematical modeling, electrostatic potential, boundary-value problem, Legendre functions. 
@article{VSPUI_2020_16_3_a1,
     author = {N. V. Egorov and E. M. Vinogradova},
     title = {Mathematical modeling of a field emitter with a hyperbolic shape},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {238--248},
     year = {2020},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a1/}
}
TY  - JOUR
AU  - N. V. Egorov
AU  - E. M. Vinogradova
TI  - Mathematical modeling of a field emitter with a hyperbolic shape
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 238
EP  - 248
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a1/
LA  - ru
ID  - VSPUI_2020_16_3_a1
ER  - 
%0 Journal Article
%A N. V. Egorov
%A E. M. Vinogradova
%T Mathematical modeling of a field emitter with a hyperbolic shape
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2020
%P 238-248
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a1/
%G ru
%F VSPUI_2020_16_3_a1
N. V. Egorov; E. M. Vinogradova. Mathematical modeling of a field emitter with a hyperbolic shape. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 3, pp. 238-248. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a1/

[1] Y. Li, Y. Sun, J. T. W. Yeow, “Nanotube field electron emission: Principles, development, and applications”, Nanotechnology, 26:24 (2015), 23 pp.

[2] G. Kaur, N. V. Pulagara, R. Kumar, I. Lahiri, “Metal foam-carbon nanotube-reduced graphene oxide hierarchical structures for efficient field emission”, Diamond and Related Materials, 106 (2020), 107847, 8 pp. | DOI

[3] A. Grillo, F. Giubileo, L. Iemmo, G. Luongo, F. Urban, M. Passacantando, A. Di Bartolomeo, “Field emission from mono and two-dimensional nanostructures”, Materials Today: Proceedings, 20 (2020), 64–68 | DOI

[4] J. Lim, A. P. Gupta, S. J. Yeo, M. Kong, C. G. Cho, S. H. Kim, J. S. Ahn, M. Mativenga, J. Ryu, “Design and fabrication of CNT-based e-gun using stripe-patterned alloy substrate for X-ray applications”, IEEE Transactions on Electron Devices, 66:12 (2019), 8874963, 5301–5304 | DOI

[5] V. Filip, L. D. Filip, H. Wong, “Review on peculiar issues of field emission in vacuum nanoelectronic devices”, Solid-State Electronics, 138 (2017), 3–15 | DOI

[6] G. G. Sominskii, V. E. Sezonov, E. P. Taradaev, T. A. Tumareva, S. P. Taradaev, A. A. Rukavitsyna, M. E. Givargizov, A. N. Stepanova, “Field emitters for miniature high-voltage electronic devices operating in technical vacuum”, Radiophysics and Quantum Electronics, 62:7-8 (2019), 539–546 | DOI

[7] Bugaev A. S., Vinogradova E. M., Egorov N. V., Sheshin E. P., Field-electron cathodes and guns, ID Intellect Publ., Dolgoprudny, 2017, 288 pp. (In Russian)

[8] Uflyand Ya. S., Method of paired equations in problems of mathematical physics, Nauka Publ., L., 1977, 220 pp. (In Russian)

[9] N. N. Lebedev, I. P. Skal'skaya, “Electrostatic distribution over a thin segment of a hyperboloid”, USSR Computational Mathematics and Mathematical Physics, 7:2 (1967), 137–148 | DOI

[10] E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge University Press, Cambridge, 1931, 500 pp. | MR

[11] E. M. Vinogradova, N. V. Egorov, “Mathematical modeling of a diode system based on a field emitter”, Technical Physics, 56:9 (2011), 1219–1224 | DOI

[12] N. V. Egorov, E. M. Vinogradova, “Mathematical modeling of the electron beam formatting systems on the basis of field emission cathodes with various shapes”, User Modeling and User-Adapted Interaction, 72:2 (2003), 103–111

[13] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Applied Mathematics Series, 55, NBS, Washington, DC, 1964, 1046 pp. | MR

[14] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, products, 7th ed., Academic Press, Amsterdam–Boston–Heidelberg–London–New York–Oxford–Paris–San Diego–San Francisco–Singapore–Sydney–Tokyo, 2007, 1171 pp. | MR | Zbl

[15] H. Bateman, A. Erdelyi, Higher transcendental functions, In 2 vol., v. 1, McGraw-Hill Book Company Inc., New York–Toronto–London, 1953, 302 pp. | MR