Computer science

Mathematical modeling of a field emitter with a hyperbolic shape

N. V. Egorov, E. M. Vinogradova

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: 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.

UDC: 51-73, 537.2

MSC: 35J05

Received: January 21, 2020
Accepted: August 13, 2020

DOI: 10.21638/11701/spbu10.2020.302