3.4 Results and Discussion
3.4.2 Plasma Parameters Achieved, Scalings Measurements, and Energy
Qualitative scaling measurements made spectroscopically during experiments with the NIII antenna are shown in Figs. 3.14, 3.15, and 3.16. In the left panel of Fig. 3.14, the temperature-dependent [Ar I 703.0 nm] / [Ar I 696.5 nm] line intensity ratio decreases gradually with increasing RF power, in agreement with the prediction of the global dis- charge model (see Fig. 3.9). The [Ar II 434.8 nm] / [Ar I 696.5 nm] ratio shown in the right panel is roughly proportional to PRF, indicating that the ionization fraction increased at higher powers as expected.
The dependence of the line ratios onpAr, shown in Fig. 3.15, is also consistent with the
0 100 200 300 400 500 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Magnetic Field (G)
Line Intensity Ratio
[Ar I 703.0 nm] / [Ar I 696.5 nm]
0 100 200 300 400 500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Magnetic Field (G)
Line Intensity Ratio
[Ar II 434.8 nm] / [Ar I 696.5 nm]
Figure 3.16: Measured argon optical emission line ratios vs. axial magnetic field strength.
The NIII antenna was used, the gas pressure was 6 mTorr, and the RF power output was
∼2.11±0.27 kW.
model predictions11. The [Ar I 703.0 nm] / [Ar I 696.5 nm] ratio (left panel) shows that Te fell at higher pressures. The interpretation of variations in the [Ar II 434.8 nm] / [Ar I 696.5 nm] ratio (right panel) is ambiguous in this case. The observed decrease in the line ratio at high pressures could be due solely to the strong temperature dependence arising because of the 6.19 eV difference in the upper level energies for the two lines, or it might be partially explained by a decrease in the ionization fraction at largeng (the model predicts thatni will rise butni/ng will decrease as pAr is increased).
The scaling of the line ratios with the background magnetic field strength, shown in Fig.
3.16, was of particular interest, since our initial goal was to deliver power to the plasma via helicon waves. The measurements implied that the electron temperature was approximately constant as a function ofB(left panel), although it is possible that there was some variation inTe that could not be resolved by the [Ar I 703.0 nm] / [Ar I 696.5 nm] line ratio, which has relatively weak temperature dependence. WithTeheld constant, the [Ar II 434.8 nm] / [Ar I 696.5 nm] line ratio is proportional to the ionization fraction, so the right panel shows that as the field strength was increased, ni/ng ∝ni first decreased and then increased.
More precise scaling measurements were made for experiments with the HTH antenna
11For all argon gas pressure measurements in the range 1–1000 mTorr reported in this thesis, a gas species correction factor of 1.6 was applied to the thermocouple gauge measurement. For example, when the ther- mocouple read 10 mTorr, the true pressure waspAr ≈16 mTorr. The magnitude of this correction factor was chosen based on recommended values in the range 1.5–1.7 found in documentation for various thermo- couple and Pirani gauges manufactured by Duniway, Pfeiffer, Kurt J. Lesker, and Arun Microelectronics.
The factor 1.6 was also confirmed by direct calibration of the thermocouple on the main vacuum chamber using a capacitance manometer from the Caltech ice dusty plasma experiment [86].
0 500 1000 1500 2000 2500 0
5 10 15 20 25 30 35 40
RF Power (W)
Ion Saturation Current (mA)
Data, 30 mTorr Model, ICP Model, CCP
0 500 1000 1500 2000 2500
0 5 10 15 20 25 30 35 40
RF Power (W)
Ion Saturation Current (mA)
10 mTorr 30 mTorr
Figure 3.17: Langmuir probe ion saturation current vs. RF power with B = 0 G (left) and B = 340 G (right). The HTH antenna was used for both sets of measurements, and PRF and Isat. were measured at t = 100 µs, except in the lowest power cases, for which the discharge only reached a quasi-steady state at a later time. In panel (a), the solid and dotted lines show the model predictions for inductively coupled and capacitively coupled discharges, respectively, at 30 mTorr, assuming that 80% of the RF power delivered to the load was absorbed by the plasma.
using the Langmuir probe, which was also capable of measuring the magnitude ofni if the model prediction for Te was used along with the measured ion saturation current in Eq.
D.9. The measuredIsat.as a function of RF power and magnetic field is shown in Figs. 3.17 and 3.18. Data was taken at both 10 and 30 mTorr in the magnetized cases, while with B = 0, the discharge could only be initiated atpAr & 20 mTorr. Isat. ∝niTe1/2, so it was a good proxy for density given thatTe varied over a relatively narrow range asPRF and B were adjusted (see Figs. 3.9 and 3.12).
In the left panel of Fig. 3.17, the data is compared with model predictions for Isat.
(derived from the results shown in Fig. 3.9 using Eq. D.9) for discharges with low voltage (ICP) and high voltage (CCP) sheaths. We only measured the net RF power delivered to the load as a whole; the fraction of this power that was actually absorbed by the plasma (rather than dissipated in the impedance matching capacitors and antenna resistance) is not known, but adopting a reasonable value of 80% for the model calculation gives good agreement between the data and the ICP model. The Isat. values predicted by the CCP model, on the other hand, are far too low, indicating that the discharge could not have been primarily capacitively coupled.
Numerical values for the ion density in several representative cases are listed in Table 3.2
0 200 400 600 800 1000 1200 0
10 20 30 40 50 60
Magnetic Field (G)
Ion Saturation Current (mA)
10 mTorr 30 mTorr
5.2 ×1019m−3
5.9 ×1019m−3
3.3 ×1019m−3
Figure 3.18: Ion saturation current vs. axial magnetic field strength with PRF = 2.40± 0.20 kW. The HTH antenna was used andIsat.was measured att= 100µs. The calculated values ofni at several points are labeled for reference (also see Table 3.2).
and labeled on Fig. 3.18. The table also shows the corresponding model predictions for ICPs and CCPs; comparing the model and data confirms that the energy transfer mechanism in unmagnetized discharges using the HTH antenna was mostly inductive, while discharges that used the NIII antenna likely operated with a mix of capacitive and inductive coupling.
In discharges with an axial magnetic field applied, the additional possibility of wave heating by helicons existed. However, there were several pieces of indirect evidence that damping of these waves or the related Trivelpiece-Gould mode [77, 76] was not the primary mechanism for energy transfer to the plasma in our experiment:
• The plasma densities obtained with and without a magnetic field were similar (com- pare the 30 mTorr data between the left panel and the right panel of Fig. 3.17).
Helicon sources can typically create plasma more efficiently than unmagnetized ICPs;
this is thought to be because wave-particle interactions reduce the collisional energy loss per ionization event to near the ionization potential [56, 51]. However, we did not see the expected degree of improvement when the magnetic field was turned on, which should have increased the density both by improving confinement and by allowing for helicon wave propagation.
Antenna p B (G) Expt. ne ModelTe (ICP) Mod. ne (ICP) Mod. ne (CCP) NIII 11 0 8.3×1018 3.04 eV 2.2×1019 2.9×1018 NIII 11 470 2.1×1019 2.60 eV 5.4×1019 6.0×1018 HTH 30 0 5.2×1019 2.26 eV 6.2×1019 6.7×1018 HTH 10 470 3.3×1019 2.72 eV 8.6×1019 9.4×1018 HTH 30 470 5.9×1019 2.05 eV 1.5×1020 1.5×1019 Table 3.2: Comparison of measured densities with global discharge model predictions for inductively coupled (ICP) and capacitively coupled (CCP) discharges, assuming 80% of the RF power delivered to the load was absorbed by the plasma. All densities are given inm−3, and pressures are in mTorr. The experimental densities were calculated from the measured ion saturation currents using theTevalues predicted by the model, as discussed in Appendix D. As in Fig. 3.12, approximate model calculations for discharges with B = 470 G were carried out by assuming that the radial loss rate (parameterized by hR ≡ nsR/ni0) was a factor of 2 lower than in the unmagnetized case.
• In experiments with the HTH antenna,ne was nearly constant as a function ofB for B ≤500 G, and increased only gradually at higher fields (see Fig. 3.18). When the NIII antenna was used, the ionization fraction increased significantly at B &200 G, but ne was lower at B ∼ 100 G than at B = 0 (see Fig. 3.16). In contrast, a rough linear scaling of density with field strength has been observed in many helicon experiments [51, 87, 55] due to the proportionality betweenneandB0 in Eq. 3.7. The mode jumps that are often seen in plots ofne vs. B for helicon sources [80] were also absent in our experiments.
• As the RF power was increased in magnetized experiments with the HTH antenna (see the right panel of Fig. 3.17), no density jump indicating a transition from a CCP or ICP mode to the helicon mode was seen, unlike in other helicon sources [54, 88].
There was a notable jump in the [Ar II 434.8 nm] / [Ar I 696.5 nm] line ratio at PRF ∼ 1200 W in the experiments with the NIII antenna (see the right panel of Fig. 3.14), but this could not have been due to a helicon mode transition because no magnetic field was applied in this case.
• The effectiveness of the HTH antenna at producing plasma was unchanged when the direction of the magnetic field was reversed, in contrast to the behavior of other experiments in which helicon mode operation has been demonstrated [52, 79].
Evidence of helicon mode operation was likewise absent in a limited set of experiments
with the single-loop antenna (see Fig. 2.3). Therefore, we may conclude that inductive coupling rather than wave heating was the dominant energy transfer mechanism in our RF plasma source. It is natural to ask why helicon mode operation was not achieved, even though our source operated with values ofω,kz,B, and ne (see Eq. 3.7) typical of helicon sources, and three standard helicon antennas were tested. One possible explanation was that the RF pulse length was too short: other pulsed helicon experiments have found that it took anywhere from∼500µs [89] to >2 ms [90] for a steady state to be reached. In order to test this hypothesis, we increased the RF amplifier’s output stage capacitance from 47µF to 188µF; with this modification, >2 ms RF pulses were possible, and the output power declined by less than 15% over the first 1 ms of the pulse. However, no mode transitions were observed in experiments with longer RF pulses; the plasma density simply decreased in time as in the left panel of Fig. 3.13, but at a more gradual rate. Therefore, we concluded that the short pulse length was not to blame for the lack of helicon mode operation.
Even if our RF pulse length was in principle long enough, and the power high enough, for the source to transition to a helicon mode, there may not have been a path through parameter space to reach this mode of operation. Carter et al. [91] attributed the observed difficulty in achieving helicon source operation with light ions (H and He) to this practical constraint. In experiments with argon, Boswell’s group [54, 92] observed density jumps when the magnetic field was increased only after dramatically adjusting the matching network tuning, as the radiation resistance of the antenna was lower in the helicon mode than in an inductively coupled mode. However, in many of Boswell’s experiments the RF supply was pulsed on a ms timescale [51, 93], implying that the impedance matching did not have to be adjusted while the plasma was present in order to achieve helicon mode jumps. An extensive effort was made to explore different tunings and find a helicon mode of operation in our pre-ionization source, but no efficiency improvement over the typical ICP mode of operation was observed.
A third possibility is that our discharge tube radius was too narrow. Chen [87] carried out extensive studies on helicon sources with 1 cm and 2 cm tube radii and found that discharges in the smaller tube did not follow standard helicon scalings; the plasma densities achieved withR = 1 cm were no higher than those achieved withR= 2 cm with the same RF input power, and the density did not rise significantly as the magnetic field strength was increased (similar to our results shown in Fig. 3.18). The discharge became turbulent for
B &100–200 G. Chen concluded that electrostatic charging of the tube walls was playing an important role in the discharge behavior, and also found that the boundary conditions at the end of the tube were important. Other helicon experiments with R <2 cm include the work of Toki et al. [94], Kerdtongmee et al. [95], Kuwahara et al. [96], Shinohara et al. [97], and Batishchev [98]. Although all of these authors called their plasma a helicon source, the presence of propagating helicon waves was not directly verified in any of the experiments. Kerdtongmee et al. and Toki et al. did not observe a jump to helicon mode operation in plots of ne vs.PRF. Kuwahara et al. did measure such a mode jump, but the density below the jump was low enough (∼1017m−3) that the transition could have been from a CCP to an ICP mode. Batishchev observed a dramatic increase in Ar II optical emission when a strong magnetic field was applied but did not directly measure ne. Only Shinohara et al. [97] identified two separate mode transitions from a CCP mode to an ICP mode and then to helicon mode. Kuwahara et al. found that higher RF power was needed to achieve ne ≈ 1019 m−3 with R = 0.5 cm than with R = 1 cm, and with R = 1 cm a higher density inside the antenna was achieved withB = 0 than with finiteB.
Based on the trend of non-ideal helicon performance in experiments with small discharge tubes, we suspect that the narrow tube radius was to blame for the lack of helicon mode operation in our source. However, this conclusion has not been verified experimentally and remains speculative. Most small helicon experiments, including ours, were designed with a specific application in mind such as pre-ionization or electric propulsion [94, 97] and thus were not optimized for studying fundamental helicon physics. Since there are a number of practical uses for small RF plasma sources [95, 96, 98], there is a clear need for well-designed, dedicated experiments to explore the scaling of helicon source operation with tube radius, building on the work of Shinohara’s group [97]. Diagnostic accessibility is intrinsically challenging in small radius discharges, but measurements of ne, Te, and wave magnetic fields in a larger chamber downstream of the source tube can provide useful insights. Since perturbation of the plasma by probes is difficult to avoid in small radius discharges, the use of non-invasive measurement techniques such as interferometry, spectroscopy, and laser- induced fluorescence can be valuable.