Field emission in diode and triode vacuum nanostructures

Abstract

To determine the emission characteristics of diode structures we use multiple images relative to the plane of the anode and cathode. And for triode structures such procedure was made for cathode -grid and grid -anode regions. In order to avoid singularity we move these planes from the boundary of atomic layers for a half-period of the lattice a. The tunnel current density have been calculated for diod and triode structures which are with a good agreement with experiment.To determine the emission characteristics of diode structures we use multiple images relative to the plane of the anode and cathode. And for triode structures such procedure was made for cathode-grid and grid-anode regions. In order to avoid singularity we move these planes from the boundary of atomic layers for a half-period of the lattice a. If there is a dielectric film on the cathode, you must enter another plane of images [1]. To determine barrier we are not doing a quantum-mechanical consideration, and believe electrons in periodic potential free. In this case, the periodic potential of the wire electrode can be considered as constant, and the electrons as free. It is enough to find the shape of two barriers: cathodegrid and grid-anode. The multiple images give to the value W = e 2 (16πε 0 ) −1 a −1 − 2.77/d for barrier height. The electron energy at each of the electrons is distributed from zero to the Fermi energy E F . But the anode V A and grid V G potentials displace its start of the countdown. When the quadratic approximation of the potential [2, 3], for diode we have:works for small d. But the most simple and sufficiently precise formula for all d follows from the image theory, if we keep the only first terms:Denoting E kz and E kr as kinetic energy of the electrons associated with longitudinal and transverse velocities and Fermi-Dirac distribution f , we write the density of the tunnel current in the form [2, 3];We count the potential in (2) from zero. The total current is the difference between the current cathode-anode and the reverse one from the anode to the cathode. So we haveHere D(E kz ) is the coefficient of tunneling, E − k = E F , E + k = E F + eV A and E + 0 = eV A are the maximal and minimal kinetic energy at cathode. To obtain it, we solve the Schrodinger equation for a complicated potential barrier. It can be quasiperiodic (Fig. 1, left), if the grid has several periodically located electrodes. This case may lead to resonant tunneling. Such potential U is calculated and presented for three periods. It is counted from zero electron energy at the anode when E F = 5 eV, Va = 8 V. Fig. 1 (right) presents the tunnel current density (A/m 2 ).We used the value E F = 3 eV and the work of electron exit 3.6 V (a = 0.1 nm) for all electrodes. The solid curves 1, 2, 3, 4, 5 belong to the diode structure with lengths d equal to 300, 100, 50, 20 and 10 nm, respectively. The curves 6-9 refer to the triode structure with length of 300 nm, two (6, 7, 8) and one (9) electrode at the grid. All grid electrodes (curves 6-8) were under the s...

Автоэмиссионная Шахматрая Структура На Основе Алмазографитовых Кластеров

“…Пусть заряд находится в точке ρ ′ = 0, z ′ цилиндрической системы координат. Решение задачи методом бесконеч-ных изображений имеет вид [13,14] …”

“…В работе [10] указанный эффект объяснен резонансным туннелированием в результате размерного квантования при образовании уровней размерного квантования, сов-падающих с уровнем Ферми. В работах [12][13][14][15][16][17][18][19] приме-нен классический подход на основе многократных элек-трических изображений и вычисления профиля барьера, а усиление эмиссии объяснено на основе размерного эффекта уменьшения толщины потенциального барьера примерно на толщину пленки, а также и его высоты. …”