Mathematical modeling of a field emitter with a hyperbolic shape

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.

Математическое моделирование двумерной диодной системы с полевым эмиттером лезвийной формы

In this paper the calculation of the electrostatic potential distribution for a two-dimensional diode emission system with a blade-shaped field emitter on a plane substrate is presented. The anode is a plane parallel to the substrate. To calculate the potential distribution, the effect of the emitter is simulated as the effect of a charged line, so that the emitter surface is zero equipotential. To solve the boundary problem, the method of separation of variables in Cartesian coordinates is used. All geometrical sizes of the diode system are parameters of the problem.

Effect of Point Defect in Carbon Nanotube (8.0) on the Molecular Electrostatic Potential distribution Near it Edge

The influence of point defect on the electronic and spatial structure of carbon nanotubes (8.0) have been studied depending on the placement vacancies in the structure of nanotubes. On the basis of quantum-chemical calculations and using semi-empirical and ab initio approaches the maps of the distribution of molecular electrostatic potential were builds in the planes which are perpendicular to the main axis of the nanotubes. It is shown that defects such as vacancy, are placed outside the first hexagonal carbon belt no effect on the topology of the distribution of molecular electrostatic potential in the vicinity of the entrance to the carbon nanotube. Instead, reactivity of port’s atoms such nanotubes may determinated point defects of the vacancy type to be placed in first hexagonal belt.