RUPAC2012 - List of Authors (Fomenko, M.G.)

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.

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.