In this chapter, the types of electron emissions from the surface of a metal, which are thermionic emission, field-enhanced thermionic emission, field emission and thermo-field emission, are introduced. While cathode is emitting electrons, anode collects electrons passively and this process simply determines the roles of anode and cathode in gas discharges. The electric current is mostly carried by electrons because of their lower mass and higher energy compared to ions. Also, current density is critical to evaluate power density distribution and energy balance which are responsible for all the processes such as electron emission, phase transition and plasma production.
Electrons move from the cathode to the anode conduction band by transferring energy in the form of heat to the anode surface. This energy level corresponds to the anode work function. On the other side, cathode applies a potential barrier to the electrons which is the cathode work function. On both sides, there are potential falls seen in the potential distribution between cathode and anode but the cathode side is more important because the way of releasing electrons from the surface characterizes the electron emission. In glow discharges, the accelerated ions from the bulk plasma cause secondary electron emission from the surface and this process depends on the plasma density, the negative voltage results from the accumulated electrons on the surface and the corresponding electron energy leaving the surface to heat the plasma. So, this process is self-sustaining. For arc discharges, electrons are emitted by thermionic emission at very high temperature or determined by electric field. For some plasmas, both are effective and this process is called thermo-field emission.
The current density in thermionic emission is governed by Richardson-Dushman equation which is obtained by converting Fermi distribution to Boltzmann distribution. The free electrons are considered as electron gas. Fermi-Dirac distribution describes energy states occupied by electrons while electron energy is higher than Fermi energy level and some non-occupied states while the energy is below the Fermi energy level for the temperatures greater than zero. The energy difference between the vacuum and Fermi level is defined the work function. The electrons with sufficient energy can pass this energy barrier but only a small fraction of electrons is thermally excited. For example, most of the electrons are still bounded after the boiling temperature. Consequently, Fermi distribution shows that less electrons can gain energy above the Fermi energy level which is the highest energy of occupied states and only depends on the density.
In the field-enhanced thermionic emission, electric field causes an image effect which is explained as if there is an electron outside of the metal, it can influence free electrons creating Coulomb force. Therefore, the potential barrier is reduced and the emission current is increased by Schottky effect. For the strong electric field case, the potential barrier reduced further to let electrons can tunnel quantum-mechanically and the probability of tunneling is calculated by Schrödinger’s equation. If both temperature and electric field are high as in arc discharges, Murphy and Good come up with a good approximation to calculate the current density with some constants.
As a result, electron emission mechanisms are investigated in this part. The different processes are governed by the different current density equations because the emission processes depend on temperature and electric field levels. The cathode work potential is a barrier for electrons; however, electrons can jump from this barrier with increased temperatures or they can directly tunnel with high electric strength. The electric current between the anode and cathode is determined by those mechanisms.
Reference: Anders, André. “Some applications of cathodic arc coatings.” In Cathodic Arcs, pp. 1-62. Springer New York, 2008.
Course: AME 60637