Field emission

In field emission , a sufficiently strong electric field (more than 10 ⁹  V / m) releases electrons with a very small energy range from a (negatively charged) cathode . Classically it is considered for a particle with a certain average thermal energy that is smaller than the height of the work function , it is impossible to leave the cathode material. From a quantum mechanical point of view, however, there is a certain probability that individual electrons will escape from the solid . These are then sucked out by the high external field. This effect is generally called the tunnel effect . The electron tunnels through the potential wall, which was tilted by the external electric field - this special type of tunnel is also called Fowler-Nordheim tunnels (named after Ralph Howard Fowler and Lothar Nordheim ).

history

The leakage of electrons from a solid, which cannot be satisfactorily explained by the means of classical physics, was one of the first research subjects in quantum mechanics . Erwin Wilhelm Müller invented the field emission microscope , with which processes at the atomic level on metal surfaces could be examined for the first time. In terms of quantum mechanics, the tunnel effect is also based on similar models. It was first observed in a vacuum in 1897 during the field emission of electrons in an experiment by Robert Williams Wood , who, however, was not yet able to interpret this effect. In 1928 it was first described theoretically by Ralph H. Fowler and Lothar Nordheim .

Applications

In beam generation systems of modern electron microscopes , field emission cathodes are widely used, since the high spatial and temporary coherence of field-emitted electrons has advantages for electron-optical imaging. Field emission screens are a field emission application that was further developed and brought to market by the Japanese company (Field Emission Technologies Inc.). Also, vacuum fluorescent displays can be manufactured according to the principle of field emission, but are not widely used due to the high operating voltage. In contrast to the glow emission , the cathode remains cold with the field emission. It is therefore more energy efficient in certain applications.

In electron tubes for high voltages, field emission is undesirable and must be avoided by using smooth, pure and flawless electrode surfaces. It is essential to keep the radii of curvature at the edges as large as possible, because this is the only way to keep the field strength (at a given voltage) sufficiently small (see also corona ring ).

The free electrons generated by field emission in a vacuum are used directly in the field emission microscope, which has now largely been replaced by other electron microscopes , to create an image, for example a tungsten tip . Both unevenness (elevations lead to a stronger field) and regional, crystal structure-related differences in the work function are visible.

calculation

The current density of the field emission is generally calculated from (Fowler-Nordheim equation for field emission): ${\displaystyle j}$

${\displaystyle j(E)={\frac {q^{3}m^{*}}{8\pi mh\Phi }}\cdot {E^{2}}\exp {\left(-{\frac {4{\sqrt {2m\Phi ^{3}}}}{3\hbar qE}}\right)}=K_{1}{{|E|^{2}} \over \Phi }\cdot e^{-K_{2}\cdot \Phi ^{3 \over 2}/|E|}}$

With

• ${\displaystyle h}$: Planck's quantum of action
• ${\displaystyle q}$: Charge of the tunneling particle
• ${\displaystyle m}$: effective mass in the dielectric
• ${\displaystyle m^{*}}$: effective mass in the load carrier
• ${\displaystyle E}$: electric field strength
• ${\displaystyle K_{1}}$, : parameters that are weakly dependent on the material - "constants" ${\displaystyle K_{2}}$
• ${\displaystyle \Phi }$: Work job

The tunnel current density according to Fowler and Nordheim indicates the tunnel current caused by the external electric field per cross-sectional area in amperes per square meter (A / m²). To get the actual current in amps, one has to multiply the above expression by the cross-sectional area through which the current passes.

See also

• Peak discharge

Individual evidence

1. ^ ^{A b} R. H. Fowler, L. Nordheim: Electron Emission in Intense Electric Fields . In: Proceedings of the Royal Society of London. Series A . tape 119 , no. 781 , April 1, 1928, p. 173-181 , doi : 10.1098 / rspa.1928.0091 .
2. ↑ Erwin W. Müller: Electron microscopic observations of field cathodes . In: Journal of Physics . tape 106 , no. 9-10 , 1937, pp. 541-550 , doi : 10.1007 / BF01339895 .
3. ↑ OLED competition: The first FE displays will be available at the end of 2009 . prad.de