2.4 Impedance Matching and Output Power
3.1.2 Optical Emission Spectroscopy
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Time (µs)
Probe voltage (V)
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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.
of the Ar II 434.8 nm emission line (measured by adjusting the monochromator wavelength away from the line center until the measured signal level was half of the peak value) was
∼0.8 nm, so only lines separated by ∆λ 1 nm could reliably be distinguished from one another. Wavelength calibration of the monochromator was carried out by observing a set of known atomic emission lines from hydrogen, oxygen, and argon spectral lamps [72].
During initial optimization of the RF plasma source, the plasma properties were moni- tored as the experiment setup was varied by observing neutral argon (Ar I) emission lines at 696.5 nm (electron transition: 4p→4s; upper level energy≡Ek = 13.36 eV ; transition rate ≡Aki = 6.4×106s−1) and 703.0 nm (6s→4p ;Ek= 14.88 eV ;Aki = 2.7×106s−1) and a singly ionized argon (Ar II) emission line at 434.8 nm (4p → 4s ; Ek = 19.55 eV ; Aki = 1.2×108 s−1)2. Quantitative interpretation of the spectroscopic data, which would have required a detailed numerical calculation (usually known as a “collisional-radiative”
model) since the plasma density was expected to fall in between the low-density coronal and high-density local thermodynamic equilibrium (LTE) regimes [74], was not attempted.
However, it was still possible to draw useful qualitative conclusions from the relative line intensities.
The intensity of an emission line is proportional to the population density of the upper level of the corresponding atomic transition times the rate for spontaneous transitions from the upper level to the lower level, i.e.,Iki ∝n(k)Aki, whereAkiis a property of the atom or ion that can be calculated from quantum mechanics alone. In a low density plasma, the level kis populated primarily by collisional excitation from the ground state, and the equilibrium value of n(k) is determined by balancing this excitation rate with the rate of depopulation to all other levels through spontaneous emission (this is the coronal equilibrium regime). At higher densities, collisional de-excitation and collisional excitation out of levels other than the ground state become important. Furthermore, recombination of ions and electrons can lead to enhanced population densities in the upper atomic energy levels, as electrons recombine into high energy levels and then cascade to the ground state through a series of spontaneous transitions.
Fujimoto [75] showed that for any plasma, the population density of an energy level k in ionization stage j may be expressed as the sum of a term proportional to the ground
2Atomic data cited here and elsewhere in this thesis are from the National Institute of Standards and Technology (NIST) [73].
state population density of the ionj and a term proportional to the ion density in the next ionization stagej+ 1, i.e.,
nj(k) =Zj(k)r0(k)nj+1ne+ [Zj(k)/Zj(1)]r1(k)nj(1), (3.1) wherer0(k) andr1(k) are temperature- and density-dependent coefficients that encapsulate the detailed atomic physics. Zj(k) is the Saha-Boltzmann coefficient:
Zj(k) = g(k) 2gj
h2 2πmkBTe
3/2
exp
−χ(k) kBTe
, (3.2)
where g(k) and gj are the statistical weights for the levelk and the ion j, and χ(k) is the energy of the levelkrelative to the ionization energy (soχ(k)<0). A plasma in which the term involving r1 dominates is labeled an “ionizing” plasma, while a plasma in which the term containingr0 dominates is labeled a “recombining” plasma. These terms refer solely to the dominant mechanism populating the atomic energy levels and do not necessarily imply that the ionization balance of the plasma is changing in time. For example, many laboratory plasmas are in the “ionizing” regime because recombination is negligible in comparison to charged particle losses to the walls, and it is these diffusive losses that are balanced by ionization in the steady state (see Sec. 3.3). This was the case in our pre-ionization source when power was being supplied to sustain the plasma.
For an ionizing phase plasma, neglecting the detailed dependence of r1(k) on Te andne, we see that the population density of level kroughly scales as
nj(k)∼[Zj(k)/Zj(1)]nj(1) = g(k) g(1)exp
E(1)−E(k) kBTe
nj(1), (3.3) whereE(k) is now defined relative to the ground state energy (i.e., it is equal toχ(k) +χj, where χj is the ionization potential) for consistency with the upper level energies given above for specific argon lines. The ratio of the population of a levelkto a different level m of the same ionization stage scales roughly as
nj(k)
nj(m) ∼ g(k) g(m)exp
E(m)−E(k) kBTe
. (3.4)
IfE(k)> E(m), then at low electron temperatures, the population of levelkwill be negligi-
400 450 500 550 600 650 700 Wavelength (nm)
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Line Intensity (a.u.)
I I I I I V
Figure 3.6: Theoretical argon optical emission spectrum [73], with Ar I lines shown in black and Ar II lines shown in red. The spectrum was calculated under the local thermody- namic equilibrium (LTE) approximation, assuming Te = 1 eV and ne = 1021 m−3. These parameters are not relevant to our RF plasma, but were chosen so that the Ar I and Ar II line intensities would be comparable in order to demonstrate the clustering of ion lines at blue/violet wavelengths and neutral lines at yellow/red wavelengths. The visible Ar I emission is dominated by the 696.5 nm line, and there are a number of additional strong lines in the infrared (not shown).
ble compared to the population of levelm. For higher temperatures, the rationj(k)/nj(m) will tend to increase, along with the ratio of the intensity of any emission line with upper level k to the intensity of any other line with upper level m. This principle was applied to use the measured [Ar I 703.0 nm] / [Ar I 696.5 nm] ratio as a qualitative temperature diagnostic (to use the ratio as a quantitative diagnostic, the detailed form of r1(ne, Te) for each line’s upper level would have to be known). Since the upper level energy of the 703.0 nm line is higher than that of the 696.5 nm line by 1.52 eV, the line ratio is sensitive to temperature in the Te= 1–5 eV regime relevant to RF discharge plasmas.
The [Ar II 434.8 nm] / [Ar I 696.5 nm] line ratio was used to qualitatively track the ionization fraction in the pre-ionization plasma3. It is clear intuitively, and from the factor nj(1) in Eq. 3.3, that the population density of a level k is proportional to the overall population density nj of the ionization stage. However, the exponential factor in Eq. 3.4
3Both line intensity ratios studied were corrected for the wavelength-dependent quantum efficiency of the PMT, but this constant correction factor was of little consequence since only variations in the line ratios were of interest.
Figure 3.7: Photos of the RF plasma during preliminary experiments on the test chamber using the Nagoya type III (NIII) antenna. The solenoid was removed for these photos. Left:
Discharge with mostly neutral argon (Ar I) emission. Right: Discharge with a higher level of ionized argon (Ar II) emission.
leads to a strong temperature dependence in the [Ar II 434.8 nm] / [Ar I 696.5 nm] ratio (independent of the temperature dependence of the ionization balance itself) because the upper level energy for the 434.8 nm line is 6.19 eV higher than that of the 696.5 nm line.
Thus having an independent Te measurement from the [Ar I 703.0 nm] / [Ar I 696.5 nm]
ratio was important for decoupling the two effects.
The measured line ratios may have been modified by re-absoprtion of 696.5 nm emission.
Based on the population density of the 4s metastable state calculated by the global discharge model described in Sec. 3.3 (see Fig. 3.11), the mean free path for 696.5 nm photons was
∼2–4 cm (see Eq. E.7). This is longer than the discharge tube radius but shorter than the axial length of the antenna, so spectroscopic measurements made with a line of sight along the axis were possibly affected. Although the quantitative values of the line ratios may have been moderately altered by this effect, the basic qualitative conclusions presented in Sec.
3.4.2 should not have been affected.
An interesting feature of argon plasmas is that the strongest ion emission lines are con- centrated toward the blue end of the visible spectrum, while the strongest neutral lines are in the red and near infrared (see Fig. 3.6). Thus one can make a quick visual determination of how much Ar II is present simply by looking at the color of the plasma. Examples are shown in Fig. 3.7.