2.4 Impedance Matching and Output Power
3.1.1 Langmuir Probes
Electrostatic probes were perhaps the original plasma diagnostic, invented by Irving Lang- muir and colleagues in the 1920s [68, 69], and they were the workhorse tool for studying our RF plasma. The technique involves inserting a small biased electrode into the plasma and measuring the current collected (the biasing and measurement circuit used is shown in Fig.
3.1). By scanning the probe potential over a range of voltages, the “I-V characteristic” is determined, and plasma parameters such as the density, electron temperature, and plasma potential (Vplasma) may be extracted. There are three main segments of the I-V curve (see the sample probe data in Fig. 3.2):
1. ForVprobeVplasma, electrons are repelled from the probe and only ions are collected.
The current collected in this regime is known as the ion saturation current, and its magnitude is roughlyIsat.≈0.6niecsA, where cs=p
kBTe/mi is the ion acoustic or
Probe tip
Vps
Vprobe Rprobe
Figure 3.1: Circuit used to bias the Langmuir probes and measure the current collected.
The measurement resistor was placed between the probe tip and the power supply, and two oscilloscope probes were used to simultaneously measureVprobeand Vps, with the probe current given by Iprobe = (Vprobe−Vps)/Rprobe. Although it would have been convenient to place the resistor on the ground side of a floating power supply and measure VR with a single oscilloscope probe, it was found that the measurement had poor time resolution in this configuration because of the power supply’s internal capacitance to ground (hundreds of nF), which was effectively in parallel withRprobe.
Bohm velocity andA is the exposed surface area of the probe [70].
2. ForVprobe< Vplasma, the electron current grows exponentially asVprobeis increased (if the electron velocity distribution is Maxwellian), because only electrons with kinetic energy sufficient to overcome the potential barrier are collected. The slope of a plot of ln|Ie|vs.Vprobe is e/kBTe.
3. ForVprobe> Vplasma, the electron current stops growing exponentially, and negligible ion current is collected. The current collected in this regime, the electron saturation current, is much larger in magnitude than the ion saturation current sincevT ecs. Details of the analysis procedure that was used to determine Te, Vplasma and ni from the Langmuir probe I-V curves are given in Appendix D. Accurate electron temperature measurements were only possible after the RF power was turned off, because the probes used did not have RF compensation (see Appendix D). Furthermore, for measurements inside the glass discharge tube, the plasma may not have been in good contact with a ground potential reference, meaning that the probe tip itself could modify the plasma potential1,
1To see that this is possible, suppose that the capacitance to ground of the plasma is 10 pF. If the probe draws 10 mA of current from the plasma, then the rate of change of the plasma potential would be
Vplasma
Figure 3.2: Sample Langmuir probe I-V curve for a cold afterglow plasma. Ion saturation current is collected forVprobe.−2 V, the electron current grows exponentially for−2 V. Vprobe.0.5 V, and electron saturation current is collected for Vprobe> Vplasma ≈0.5 V.
invalidating the temperature measurement [71]. Fortunately, the plasma density was the main property of interest. For most measurements presented in this chapter and in Chapter 4, only the ion saturation current was measured, andne≈ni was calculated from Eq. D.9 by plugging in the Te predicted by the global discharge model described in Sec. 3.3. Only for measurements taken out in the main vacuum chamber during the afterglow (described in Chapter 5) was the full I-V curve was analyzed.
Three Langmuir probes were constructed by threading lengths of .085” OD semi-rigid coaxial cable (purchased from Cross RF) through cylindrical stainless steel (SS) probe shafts. Vacuum epoxy (Torr Seal Low Vapor Pressure Resin) was used to make a vacuum tight attachment between the semi-rigid cable and the SS tube (the interfaces between the conductors and insulation of a semi-rigid cable are generally vacuum tight, enabling this simple probe-construction strategy). The shield and dielectric were stripped off the end of the cable to expose a probe tip withL≈3 mm andR≈0.25 mm.
The first Langmuir probe, shown in Fig. 3.3, was used for the initial optimization of the RF plasma source carried out on a small test vacuum chamber. The semi-rigid cable extended all the way through the short SS probe shaft and was terminated with a BNC
dVp/dt= (dQ/dt)/C=−1 V/ns, if there is no other net current flowing to/from the plasma.
Probe tip
Semi-rigid cable coated
with boron nitride Torr Seal ¼” SS tube
Figure 3.3: Photo of a Langmuir probe constructed using semi-rigid coaxial cable. In this photo, taken after the probe was pulled out of the discharge tube through the 1/4”
quick-disconnect, some of the boron nitride insulating coating had rubbed off, exposing the stainless steel probe shaft.
connector, and the grounded cable shield and SS tube were coated with boron nitride aerosol spray (from ZYP Coatings) to insulate them from the plasma and avoid drawing large amounts of current, which would have perturbed the plasma excessively. The probe was inserted into the plasma through a 1/4” quick-disconnect welded to a 2 3/4” CF flange (MDC part number 412003) attached to the end of the quartz discharge tube, so that the axial position of the probe tip was adjustable. A similar Langmuir probe with a longer shaft was subsequently used once the source was installed on the main vacuum chamber.
The probe was inserted through a 1/4” quick-disconnect on one of the chamber’s 2 3/4”
side ports, allowing it to slide radially at a distance z= 3.8 cm in front of the electrodes.
Finally, in order to make measurements inside the quartz discharge tube in the final experiment configuration, a third probe was constructed by bending semi-rigid cable into a U-shape using a tubing bender (see Figs. 2.2 and 3.4). The 3/8” OD SS probe shaft was inserted through a 3/8” quick-disconnect welded onto a 2 3/4” CF flange (MDC part number 412005) mounted on one of the chamber’s end dome ports. The probe could slide axially and make measurements betweenz≈30 cm andz≈ −9 cm (i.e., 9 cm into the RF source tube).
It was found that the boron nitride coating on the straight probe was being eroded when the jet experiment was run (even though the probe was not used for measurements during jet experiment shots and was pulled as far out of the chamber as possible), so the U-shaped probe was designed differently, with the outer conductor of the semi-rigid cable isolated
Figure 3.4: Left panel: Photo of the U-shaped Langmuir probe installed in the chamber.
The straight Langmuir probe coated with white boron nitride is also visible at the bottom of the photo (when in use, it would be slid upwards so that the probe tip was at or near the chamber’s central axis). Right panel: Guide structure used to prevent the U-shaped probe from rotating when it was being moved axially. The vertical bars were clamped onto the probe shaft with set screws and fit tightly into the groove at the bottom of the structure.
from the grounded probe shaft. This was accomplished by cutting off the semi-rigid cable near the Torr Seal vacuum interface and using a normal wire with an insulating jacket to carry the signal the rest of the way out of the probe shaft; the short length of semi-rigid cable inside the probe shaft was covered with heat shrink. This design ensured that the probe tip was the only conductor drawing current from the RF plasma; the downside was that the semi-rigid cable’s outer conductor did not provide shielding.
In order to reduce the RF signal picked up from the nearby RF amplifier, the exposed portion of the wire near the power supply and oscilloscope was wrapped in aluminum foil, and the foil was clamped to the end of the probe shaft to form a continuous conducting shield. RF currents on the foil were diverted to ground using the procedure developed by Perkins and Bellan [67]: the wire with its foil shield was passed through a ferrite choke near the point of connection to the probe resistor and power supply, and the foil was explicitly grounded just upstream of the ferrite by taping it firmly to the cart carrying the RF amplifier and other experimental apparatus. This procedure reduced the RF signal picked up by the long wire enough that the signal picked up by the probe within the plasma dominated, allowing temporal and spatial variations in RF fluctuations in Vprobe to be measured (see Fig. 3.5).
0 100 200 300 400 500 600 700 800 900 1000
−20
−15
−10
−5
Time (µs)
Probe voltage (V)
0 100 200 300 400 500 600 700 800 900 1000
−20
−15
−10
−5
Time (µs)
Probe voltage (V)
Figure 3.5: Left: Langmuir probe voltage measured with a 1x oscilloscope probe with no shielding on the Langmuir probe’s signal wire (probe tip at z =−4.2 cm, Rprobe = 270 Ω, measuring ion saturation current). The RF oscillations are mostly pickup from the high voltage RF amplifier output coupled into the signal line outside the vacuum chamber. Right:
Probe voltage under the same conditions measured with aluminum foil shielding on the probe wire and the scheme from [67] used to prevent RF ground currents from coupling to the signal line. With this setup, the RF oscillations are mostly picked up by the section of the probe within the plasma. Dramatic temporal variations in the amplitude of the RF oscillations are seen that do not correspond to any changes in the RF amplifier’s output voltage or current; these must reflect changing plasma properties, but the mechanism is not yet fully understood.