Abstract
A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.
Similar content being viewed by others
References
D. Roy Mahapatra, N. Sinha, J. T. W. Yeow, and R. Melnik, Appl. Surf. Sci. 255, 1959 (2008).
Seong Chu Lim, Dae Sik Lee, Ha Kyu Choi, Il Ha Lee, and Young Hee Lee, Diamond Relat. Mater. 18, 1435 (2009).
Marwan S. Mousa, Surf. Interface Anal. 39, 102 (2007).
Ya. S. Uflyand, Method of Paired Equations in Problems of Mathematical Physics (Nauka, Leningrad, 1977) [in Russian].
N. V. Egorov and E. M. Vinogradova, Vacuum 72, 103 (2004).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic, New York, 1980).
H. Bateman and A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, New York, 1954; Nauka, Moscow, 1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.M. Vinogradova, N.V. Egorov, 2011, published in Zhurnal Tekhnicheskoĭ Fiziki, 2011, Vol. 81, No. 9, pp. 1–5.
Rights and permissions
About this article
Cite this article
Vinogradova, E.M., Egorov, N.V. Mathematical modeling of a diode system based on a field emitter. Tech. Phys. 56, 1219–1224 (2011). https://doi.org/10.1134/S1063784211090295
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063784211090295