Application of the transferred matrix method to a unified evaluation of the cathodic electron emission
Date
Authors
Volume
Issue
Journal
Series Titel
Book Title
Publisher
Link to publishers version
Abstract
The work is concerned with the Transfer Matrix Method for solving the steady-state Schrödinger equation applied for a unified evaluation of the emission current density from non-refractory cathodes. The method is applicable to arbitrary shapes of the potential barrier and its transmission probability is obtained without any analytical approximations. The Fermi-Dirac distribution for the free electrons in the metal is considered as a supply function. The results, obtained for a work function of the cathode material of 4.5 eV over a wide range of values of the surface temperature and the electric field strength, clearly show a growing deviation from those obtained by the classical Jeffreys-Wentzel-Kramers-Brillouin approximation with the increase of the electric field strength. Preliminary results are obtained to demonstrate the applicability of the Transfer Matrix method to the evaluation of the ion-assisted electron emission. A significant local enhancement of the emission current density is obtained as a result of the presence of an ion at a fixed position near the metal surface. The effect becomes very strongly pronounced at an appropriate value of the electric field strength, for which a resonant ion contribution appears.