PIC/MC calculation of current–voltage characteristic of emissive probe

Abstract

Two numerical models were used to study the function of an emissive (electron-emitting) probe—the PIC/MC model and the thermal model. The PIC/MC model was used to calculate the I–V characteristics of the emissive probe. The calculations were focussed on the determination of the floating potential of the probe, which increases with increasing probe temperature. It was found that the floating potential can reach the value of the plasma potential, and it can even be higher than the plasma potential. The dependence of the floating potential on probe temperature is linear in the vicinity of the plasma potential, and the slope of this dependence changes when the floating potential equals the plasma potential. The potential profiles near the probe were also calculated and it was found that the space charge effects can be neglected for the plasma parameters studied (electron density 1014–1016 m−3, electron temperature 2500–40 000 K, probe temperature up to 2500 K). The thermal model was used for the calculation of the dependence of probe temperature and potential profiles on DC current passing through the probe (and heating the probe). The thermal model was based on the heat equation, which was solved using the finite element method. Finally, the results from both the above-mentioned models were combined to obtain the dependencies of floating potential on probe heating DC current.

Floating potential method using a thermionic emissive probe including an ionizing and collisional presheath

“…Recently, Jílek et al [48] published a particle-in-cell Monte Carlo (PIC-MC) model to determine the I -V curves and the floating potential of an emissive probe in a helium plasma considering ion-neutral collisions but neglecting ionization in the range of diffuse gas discharges, i.e., electron densities of 10 14 to 10 16 m −3 , electron temperatures of 0.2-3.5 eV and emissive probe temperatures lower than 2500 K. This model obtains floating potential values above the saturation value established by previous studies, reaching the plasma potential with values that coincide with the expressions proposed by Sheehan and Hershkowitz [2]. It also shows that the spacecharge effects are negligible due to the small size of the potential well associated with the formation of the virtual cathode in the SCL regime.…”

Determination of Plasma Potential Using an Emissive Probe with Floating Potential Method

“…V gradually increases against V , whereas V is saturated to the plasma potential. In [ 24 , 32 ], the floating potential approaches the plasma potential with the increase in the heating voltage (or filament temperature). This saturation trend against V is well reproduced in the circuit model, as shown in Figure 2 a.…”

“…Indeed, the filament of the negative terminal side was inserted into the ceramic tube for the length of a few millimeters. Furthermore, the space charge effect could have affected the difference, as mentioned in Section 1 , but it was negligible in this low-plasma-density region [ 32 ]; it was effectively larger than the electron density of 10 cm , which was much larger than that in this ICP source, as shown in Figure 5 c.…”

“…In 1966, Kemp et al [ 24 ] introduced the floating potential method with an emissive probe and proved that the floating potential approaches the plasma potential with the increase in filament temperature, which leads to greater emission from the filament. After that, most studies have focused on the space charge effect on the emissive probe and plasma [ 20 , 31 , 32 ]. A strong emission flux larger than the electron flux from plasma forms extra space charges, and a virtual cathode forms in front of the emitting surface [ 20 ], which deteriorates the accuracy of the emissive probe measurement.…”

“…In addition to the space charge limit condition, another factor that affects the accuracy has been recently reported. Jílek et al reported a computational study of the voltage distribution on the filament surface along with the filament temperature distribution [ 32 ]. They found that the floating voltage on the filament differs from the plasma potential due to the voltage distribution induced by temperature, which might decrease the measurement accuracy.…”