It is well known that decaying plasmas emit intense visible and infrared (IR) radiation as they recombine [111]. The so-called emission “afterpeak” in argon pulsed inductively coupled plasmas and pulsed DC glow discharges has been studied in detail [106, 112, 113] due to the applications of these plasmas for sample analysis using mass spectrometry and optical emission spectroscopy [114] and also in semiconductor processing and other industries [83, 112]. However, there is still controversy regarding whether the high level of afterglow
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672 mTorr
16 mTorr
Figure 5.1: Optical and infrared emission measured by a photodiode viewing the rear side of the source tube during argon discharges with the RF power on from t = 0–200 µs.
The photocurrent was always negative, with its magnitude proportional to the incident brightness. The bias magnetic field was turned on for these experiments (Vbias = 80 V, Vsol. = 0 V), but similar results were also obtained with B = 0. Left: Photodiode signal during experiments with the fast gas valve used (the legend shows the gas bank voltage Vgas,RF). The gas bank was triggered attgas,RF =−6.0 ms for all experiments discussed in this section. Right: Photodiode signal during experiments with a uniform pressure in the discharge tube.
emission in experiments at pAr ∼0.2–2 Torr can be accounted for by plausible three-body recombination rates [112, 113] or whether electron-ion dissociative recombination involving positive molecular ions (Ar+2 + e−→Ar∗+ Ar, whereAr∗ denotes an excited argon atom) must play a critical role [106].
We measured the overall level of optical and IR emission in our RF discharge using the photodiode described in Sec. 3.1.3, which was mounted inside the re-entrant port between the UV flashlamp / gas feed assembly and the end of the solenoid bobbin (see Fig. 2.2), at z ≈ −29 cm. The line of sight was toward the rear end of the HTH antenna. The time-dependent emission during experiments with argon gas supplied by a fast gas valve (see Sec. 1.6.4) is shown for a range of gas bank voltages in the left panel of Fig. 5.1. The plasma brightness dropped rapidly after the RF power was turned off at t = 200 µs, but at higher gas bank voltages it rose again a few µs later, exhibiting a strong afterpeak.
For Vgas,RF & 550 V, the peak afterglow brightness exceeded the quasi-steady state main discharge brightness recorded at t≈100–200µs.
Similar emission patterns were produced during experiments with a uniform gas pressure
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460 V 128 mTorr
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575 V 672 mTorr
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575 V 480 mTorr
Figure 5.2: Examples of the close correspondence between photodiode signals obtained during experiments with the fast gas valve used and with a uniform pressure in the discharge tube. Left: The time-dependence and brightness of the emission with a gas bank voltage Vgas,RF = 460 V was closely reproduced with a uniform pressure of pAr = 128 mTorr.
Center and right: For Vgas,RF = 575 V, the best match to the emission during the RF on period (t <200 µs) was obtained with pAr = 672 mTorr, while the best match to the afterpeak brightness was obtained withpAr= 480 mTorr.
in the discharge tube (a leak valve was used to feed in argon gas at the midplane of the main vacuum chamber), shown in the right panel of Fig. 5.1. In fact, as illustrated in Fig. 5.2, an extremely close correspondence existed between the magnitude and time-dependence of the photodiode signal obtained at a given fast gas valve bank voltage and the signal recorded at some uniform gas pressure. The match between the measured emission patterns was so precise that the plasma conditions, and in particular the argon gas pressure, must have been nearly identical between the pairs of shots shown in Fig. 5.2. Therefore, we may interpret the time-dependent optical and IR emission as giving an indirect measurement of the pressure produced in the discharge tube by the fast gas valve. Knowledge of the neutral gas density was very important for determining the appropriate transport and collisional- radiative regimes for analyzing the RF discharge behaviors discussed in Chapter 4 and Sec.
5.2, so this was a valuable measurement1. The technique could be applied even though the detailed excited state population densities that produced the observed line emission were not known; in fact, the complexity of the emission processes was advantageous, as this made it very unlikely that a close match between the overall time-dependent emission patterns in two different discharges could have been obtained if the gas pressures were not equal. This
1Ideally, one would measure the time-dependent gas pressure produced by a fast gas valve puff directly using a fast ion gauge [43, Appendix B], but it would have been difficult to build one that could be inserted into the narrow discharge tube, and in any case such a gauge inserted into the tube would have significantly perturbed the gas flow.
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Corresponding Pressure (mTorr) Match during RF on time
Match during afterglow
Figure 5.3: Pressure in the discharge tube as a function of gas bank voltage, as determined from matching photodiode traces between experiments that used the fast gas valve and experiments that had uniform gas pressure. The two curves show the best fit pressure from emission comparisons during the RF on time (as in the center panel of Fig. 5.2) and in the afterglow (as in the right panel of Fig. 5.2).
method for inferring the gas pressure could also be useful in other experiments that employ a fast gas valve to feed gas to an RF plasma source, such as the helicon pre-ionization source at the University of Washington’s HIT-SI experiment [49].
As shown in the left panel of Fig. 5.2, at low gas bank voltages the correspondence between the emission produced during experiments with the fast gas valve and during uniform pressure experiments was nearly exact at all times, while at higher bank voltages a somewhat different uniform pressure was needed to match the emission during the main discharge period versus during the afterglow. A plausible explanation involves re-absorption of line emission, which was shown to be important in our discharge in Secs. 3.3, 4.4.2, and E. The 1D time-dependent discharge model in Sec. 4.4.2 showed that the Ar I 4s and 4p excited state population densities fell drastically after RF power turn-off (see Fig. 4.23), so re-absorption of visible and IR emission (which arose from electron transitions between excited states) was negligible in the afterglow but may have played a role while the power was on. Therefore, the emission detected by the photodiode during the afterglow may have come from a location deeper into the discharge tube, on average, than the emission
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Peak Afterglow Photocurrent Magnitude (mA)
Figure 5.4: Measured photocurrent magnitude at t= 210µs, around the time of the peak afterglow emission, from the data shown in the right panel of Fig. 5.1.
detected during the main discharge period. The gas pressure produced by the fast gas valve was probably higher near the gas inlet at the rear of the discharge tube (see Fig. 2.2), i.e., near the photodiode, than closer to the jet experiment electrodes, so the pressure inferred from the emission comparison was higher during the RF on time than during the afterglow.
Since the pressure toward the front of the discharge tube near the electrodes was of the most interest for interpreting the data in Chapter 4 and Sec. 5.2, the pressure measurement using the afterglow emission was preferred.
The inferred pressures produced by the fast gas valve as a function of bank voltage are shown in Fig. 5.3. The pressure increased rapidly with Vgas,RF between Vgas,RF = 450–500 V, but then nearly leveled out at higher gas bank voltages. This nonlinear behavior is in stark contrast to the results of total throughput measurements (see Fig. 1.9), which showed a roughly linear dependence of the time-integrated gas valve output on bank voltage.
Apparently the time dependence of the gas puff was quite different above and belowVgas= 500 V.
According to Fig. 5.3, the pressure in the pre-ionization source tube for the most com- monly used fast gas valve bank settings, Vgas,RF = 550 V and tgas,RF = −6.0 ms, was
pAr ≈ 460 mTorr. To estimate whether this is reasonable, note that when the fast gas valve plenum (V = 2.3×10−6 m3 [43, Appendix B]) was filled with argon at a pressure 60 psig above atmospheric pressure, the total number of gas particles in the plenum was
∼ 3×1020. However, from Fig. 1.9, only ∼ 5×1019 of these particles actually made it into the chamber when the fast gas valve was triggered at Vgas,RF = 550 V. If all of these particles were in the quartz tube at the same time, at room temperature2, then the pressure in the tube (V ≈1.4×10−4 m3) would have been ∼1 Torr. Thus the inferred pressure of 460 mTorr corresponds to roughly half of the particles from the gas puff being in the tube simultaneously, which is plausible based on the ∼ 1 ms gas travel time down the length of the tube (using the tube length L≈35 cm and the room temperature sound speed for argon,c≈320 m/s) and the results of fast ion gauge measurements in a similar experiment [43, Appendix B], which showed that the pressure rise time associated with a fast gas valve puff was a few ms.
The peak brightness of the afterglow emission in uniform gas pressure experiments is shown as a function of pAr in Fig. 5.4. The afterpeak brightness increased approximately linearly with argon pressure up to 384 mTorr, then jumped higher at 480 mTorr, perhaps indicating a transition to a different regime in which the dominant mechanism populating the argon excited states changed. Some insight into the underlying physics may be obtained from the 1D time-dependent discharge model developed in Sec. 4.4.2. A quantitative pre- diction of the time-dependent afterglow emission is beyond the scope of the model, since it does not track the population densities of argon excited states above the 4plevel, which are a major source of afterglow emission, as illustrated in Figs. 4.8 and 4.9. However, if three- body recombination was the primary source of excited argon atoms in the afterglow, then assuming that the spontaneous emission timescale was short compared to the timescales for changes in the electron density and temperature, the visible brightness of the afterglow should have approximately scaled with the recombination rate. The model prediction for
2The gas may have been colder than room temperature due to adiabatic cooling as it expanded out of the fast gas valve, in which case the true pressures were lower than those stated here. However, it was the gas particle density rather than the pressure that actually mattered for the RF discharge, so the uncertainty in the gas temperature prior to initiating the discharge is unimportant—pressure values at 300 K have simply been calculated in order to facilitate comparison (for example, in Fig. 5.3) between the number densities produced by the fast gas valve and those present with uniform gas fills.
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Figure 5.5: Left: 1D time-dependent discharge model calculations (see Sec. 4.4.2) of the total three-body recombination rateR
νrnedV. Right: Peak recombination rate from the model as a function of pressure, overlaid on the measured afterpeak brightnesses atpAr <400 mTorr.
The model calculations all assumedPRF = 1600 W,Ti= 0.05 eV, and an 8.5 cm-long power deposition region. The model is valid for unmagnetized plasmas, while the bias field was applied in the experiments shown, but similar photocurrents were measured in experiments with no magnetic field.
the total recombination rateνrne(whereνr(ne, Te) was calculated from Eq. 4.27) integrated over the discharge volume is shown for four different argon pressures in the left panel of Fig. 5.5. These curves are qualitatively similar to the measured afterpeaks visible in Fig.
5.1. In the right panel of Fig. 5.5, the peak recombination rate in the model as a function of pressure is overlaid on the measured peak afterglow brightnesses. The predicted recom- bination rate increases approximately linearly with pAr below 100 mTorr, but levels out at higher pressures, in contrast to the measured afterpeak brightness. This may indicate that some other process in addition to three-body recombination became important for producing enhanced excited state population densities at pAr & 200 mTorr3. However, it is difficult to draw firm conclusions without more detailed modeling specifically tailored to understanding the afterglow emission, such as has been carried out by Bogaerts [106] and Kang et al. [112].
Another interesting aspect of the photodiode data in Fig. 5.1 is that the quasi-steady state visible/IR brightness during the RF on time scaled inversely with pAr, even though
3Although it was shown in Sec. 4.4.2.2 that the model became less accurate at pAr ≥120 mTorr, this applied primarily during the RF on time—the simulations atpAr= 120–240 mTorr fit the measured rate of ion saturation current decline in the afterglow quite well, as shown in Figs. 4.20 and 4.21.
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Figure 5.6: Measured photodiode signals averaged from t = 100–200 µs (solid line), com- pared with the average visible and IR radiated power over the same interval predicted by the 1D discharge model using Eq. 5.1 (dashed line). The model calculations all assumed PRF = 1600 W, Ti = 0.05 eV, and an 8.5 cm-long power deposition region.
the plasma density was higher at higher pressures (see the ion saturation current data in Sec. 4.4.2.2). We can roughly estimate the level of visible and IR emission predicted by the 1D discharge model by assuming that it is proportional to the rate of Ar I 4p → 4s transitions, corrected for re-absorption, i.e.,
Pvis./IR≈np(Apm,ef f.+Apr,ef f.)EpsπR2L (5.1)
(see Sec. 3.3 for definitions of the quantities on the right hand side). This formula accounts for most of the emission that would be detected by the photodiode because transitions between the 4sresonant level and the ground state produced UV photons (λ≈106 nm), and emission lines produced by transitions originating from levels above 4pwere relatively weak compared to the strongest lines produced by 4p→4stransitions while the RF power was on (see Figs. 4.8 and 4.9). Fig. 5.6 shows the quasi-steady state photodiode signal as a function of pressure, along with the total visible/IR radiated power predicted by Eq. 5.1. The model reproduces the basic result that the level of emission decreases with increasing pressure
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Figure 5.7: Langmuir probe ion saturation current measured at z = 6.7 cm for discharges with the RF amplifier turned off at four different times. The fast gas valve was used with Vgas,RF = 550 V, and the bias field coil and solenoid were turned on.
forpAr &50 mTorr, although the predicted pressure dependence is gentler than what was
observed. Although one might have expected the excited state population densities, and consequently the radiated power, to be higher in discharges with high pAr and ne, this was not the case in the simulation—the electron temperature was lower at higher pressures, partially negating the effect of higherne on the collisional excitation rates, and the balance of collisional and radiative populating and depopulating processes (see Eqs. 4.32, 4.33, and 4.34) ultimately causednm,nr, andnp to be nearly independent of pressure in the 30–300 mTorr range.