RUPAC2012 - List of Authors (Vinogradova, E.M.)

Paper	Title	Page
TUPPB044	The Knife-Edged Field Emitter Mathematical Modeling	412
	E.M. Vinogradova, M.G. Fomenko Saint-Petersburg State University, Saint-Petersburg, Russia
	Numerous nano-scale electronic devices are based on the field emitters such as carbon nanotubes. The field emitters are extensively applied in the various domains of an instrument engineering. In the present work the problem of a field emission cathode as the knife-edged field emitter mathematical modeling is solved. The supposed shapes of the emission diode system with the field emitter are the lune's type (as a cathode) and the infinitely thin spherical segment (as an anode). The effect of the space charge is neglected. The boundary - value problem for the Laplace equation in the toroidal coordinate system is presented. To solve the electrostatic problem the variable separation method is used. The potential distribution is represented as the series with respect to Legendre functions. The boundary conditions and the normal derivative continuity conditions lead to the linear algebraic equations system relative to the series coefficients. In this way the distribution of the potentials for the whole region of the considered electro-optical systems was obtained.

TUPPB045	The Field Cathodes with the Effect of Space Charge Modeling	415
	M.A. Makarova, E.M. Vinogradova Saint-Petersburg State University, Saint-Petersburg, Russia
	This work is devoted to the question of the effect of space charge on the field electron emission. The electrostatic potential distributions for the diode emission systems are calculated. The diode systems, which can be readily constructed, is generally used for the characterization of field emission properties of novel materials. They have some effective applications in vacuum nano- and microelectronics. In this work the plane diode emission system and cylindrical diode emission system are investigated. The solutions of Poisson's equation for the electrostatic potential distribution are received for the boundary-value problems. The right side of Poisson's equation is assumed to be the piecewise constant function. The charge conservation law and the energy conservation law are used. One and two dimensional cases are investigated.

TUPPB047	The Triode-type System on the Basis of the Field Emitter Modeling	418
	D.S. Televnyi St. Petersburg State University, St. Petersburg, Russia E.M. Vinogradova Saint-Petersburg State University, Saint-Petersburg, Russia
	The mathematical model of a cylindrical triode-type system on the basis of the field emitter is under consideration. The internal area of the system is filled of two different dielectrics. Effect of space charge is not considered. The field emitter is modeled by a charged filament of finite length, which located on the system's axis. The modulator has a form of a circular diaphragm. The Poisson equation with the given values of potentials at the electrodes is solved. The variable separation method is used to determine distribution of electrostatic potential. An unknown function of the charge density is approximated by a piecewise constant linear function. The problem of finding unknown coefficients in the potential eigenfunction expansion is reduced to the linear algebraic equations system. Numerical calculations emitter's forms are represented.

TUPPB048	The Multi-Tip Field Emission Cathode Mathematical Modeling	421
	N.V. Egorov, E.M. Vinogradova Saint-Petersburg State University, Saint-Petersburg, Russia
	The multi-tip field cathode as the field emission cathode arrays for rectangular lattice is considered. The field emission cathodes are of interest for vacuum nano-scale electronic devices. The electrostatic potential distribution is presented for the periodic system of free-number thin tips on a plane substrate as a field emission cathode and a plane substrate as an anode. The tips shape may be various. The potential of the substrate and cathode is equal the zero, the anode's potential is equal a constant. The effect of space charge is neglected. The each tip is represented as a system of the point charges. The point charges are determined to the zero equipotential coincides with the cathode's shape. The potential distribution is found for whole region of the field emission cathode arrays. The exact three-dimensional solution to the Laplace/Poisson equation has been obtained in the Cartesian coordinate system. This solution has direct applications in three-dimensional calculations of electron trajectories in micron- and submicron-sized field-emitter arrays.

Paper

Title

Page

The Knife-Edged Field Emitter Mathematical Modeling

412

E.M. Vinogradova, M.G. Fomenko
Saint-Petersburg State University, Saint-Petersburg, Russia

Numerous nano-scale electronic devices are based on the field emitters such as carbon nanotubes. The field emitters are extensively applied in the various domains of an instrument engineering. In the present work the problem of a field emission cathode as the knife-edged field emitter mathematical modeling is solved. The supposed shapes of the emission diode system with the field emitter are the lune's type (as a cathode) and the infinitely thin spherical segment (as an anode). The effect of the space charge is neglected. The boundary - value problem for the Laplace equation in the toroidal coordinate system is presented. To solve the electrostatic problem the variable separation method is used. The potential distribution is represented as the series with respect to Legendre functions. The boundary conditions and the normal derivative continuity conditions lead to the linear algebraic equations system relative to the series coefficients. In this way the distribution of the potentials for the whole region of the considered electro-optical systems was obtained.

TUPPB045

The Field Cathodes with the Effect of Space Charge Modeling

415

M.A. Makarova, E.M. Vinogradova
Saint-Petersburg State University, Saint-Petersburg, Russia

This work is devoted to the question of the effect of space charge on the field electron emission. The electrostatic potential distributions for the diode emission systems are calculated. The diode systems, which can be readily constructed, is generally used for the characterization of field emission properties of novel materials. They have some effective applications in vacuum nano- and microelectronics. In this work the plane diode emission system and cylindrical diode emission system are investigated. The solutions of Poisson's equation for the electrostatic potential distribution are received for the boundary-value problems. The right side of Poisson's equation is assumed to be the piecewise constant function. The charge conservation law and the energy conservation law are used. One and two dimensional cases are investigated.

TUPPB047

The Triode-type System on the Basis of the Field Emitter Modeling

418

D.S. Televnyi
St. Petersburg State University, St. Petersburg, Russia
E.M. Vinogradova
Saint-Petersburg State University, Saint-Petersburg, Russia

The mathematical model of a cylindrical triode-type system on the basis of the field emitter is under consideration. The internal area of the system is filled of two different dielectrics. Effect of space charge is not considered. The field emitter is modeled by a charged filament of finite length, which located on the system's axis. The modulator has a form of a circular diaphragm. The Poisson equation with the given values of potentials at the electrodes is solved. The variable separation method is used to determine distribution of electrostatic potential. An unknown function of the charge density is approximated by a piecewise constant linear function. The problem of finding unknown coefficients in the potential eigenfunction expansion is reduced to the linear algebraic equations system. Numerical calculations emitter's forms are represented.

TUPPB048

The Multi-Tip Field Emission Cathode Mathematical Modeling

421

N.V. Egorov, E.M. Vinogradova
Saint-Petersburg State University, Saint-Petersburg, Russia

The multi-tip field cathode as the field emission cathode arrays for rectangular lattice is considered. The field emission cathodes are of interest for vacuum nano-scale electronic devices. The electrostatic potential distribution is presented for the periodic system of free-number thin tips on a plane substrate as a field emission cathode and a plane substrate as an anode. The tips shape may be various. The potential of the substrate and cathode is equal the zero, the anode's potential is equal a constant. The effect of space charge is neglected. The each tip is represented as a system of the point charges. The point charges are determined to the zero equipotential coincides with the cathode's shape. The potential distribution is found for whole region of the field emission cathode arrays. The exact three-dimensional solution to the Laplace/Poisson equation has been obtained in the Cartesian coordinate system. This solution has direct applications in three-dimensional calculations of electron trajectories in micron- and submicron-sized field-emitter arrays.