7.1 Conclusion
7.1.3 Effect of Gas Heating on VUV Emission from a Coaxial Xenon
Voltages
In this study, the gas heating effect in a homogeneous coaxial xenon excimer UV discharge (EUV) driven by 50 kHz distorted bipolar square voltages has been investigated numerically. A self-consistent radial one-dimensional fluid model, taking into consideration non-local electron energy balance, was employed to simulate the condition with and without gas heating effect. The results show that by including gas heating in the fluid modeling one can explain reasonably well the experimentally observed VUV emission at various background pressures, especially the extinguishment of the discharge as pressure exceeds some threshold value.
The major mechanisms of the above phenomena are described as follows: 1) Increasing pressure leads to higher gas heating because of increasing electron energy loss through the elastic collision with xenon atoms in the bulk region; and 2) The above leads to higher gas density at outer region of the gap (r≈ 1.1~1.16 cm), because
of heat conduction and uniform pressure distribution, as compared to the case without gas heating which promotes the three-body Xe+-to-Xe2+ ion conversion and e-Xe2+
recombination that greatly reduces the plasma density as pressure exceeds some threshold.
7.2 Recommendation of Future Work
To further understand the plasma physics and chemistry inside a practical xenon
excimer lamp, recommendations of possible future work are summarized as follows:
1. The study of gas heating due to ion bombardment on the inner dielectric layer, in addition to the electron energy loss due to elastic collision in the bulk region and ionic ohmic heating in the inner sheath region.
2. It has been observed that by mixing some small amount of helium with xenon one can obtain 20-30% of increase of VUV emission without proper understanding [Lu, 2008]. Thus, the research along this direction using the fluid modeling is strongly encouraged.
3. More extensive parametric study such as: 1) power source (e.g., rate of voltage increase, voltage amplitude and duty cycle); 2) geometry (e.g., gap size, dielectric thickness) and material properties (e.g., conductivity and dielectric permittivity 4. Multidimensional fluid modeling (e.g., 2D and 3D)
Table 3-1 Reaction channels of the xenon discharge
Radiation to lower level (visible and infrared)
23 Xe ex*( )→Xe res*( )+hν′ 0.0 2.7×107 s-1 [28]
Table 4-1 Power transfer efficiency between sinusoidal and bipolar square voltages.
Pp (W) P172 (W) P172/ Pp (%)
Sinusoidal voltages 1909.9 49.2 2.6
Distorted bipolar square voltages 1860.5 124.8 6.7
Table 5-1 Test conditions for the parametric study.
* Permittivity of dielectric material: 4 (F/m)
Figure 1-1 Common planar and cylindrical dielectric-barrier discharge configurations.
[Kogelschatz et al, 1999].
Figure 1-2 Evolution of electron avalanche in discharge gap, showing avalanche development, avalanche-to-streamer transition, and streamer propagation. [Chirokov et al, 2005].
Figure 3-1 Reaction processes in a Xe discharge.
Figure 3-2 The comparison of simulated result with Beleznai et al. and ours.
(a)
(b)
Figure 3-3(a) a sketch of the coaxial xenon excimer lamp and (b) the configuration of the coaxial xenon excimer lamp.
Figure 3-4 The comparison with simulated result and experimental data.
Figure 4-1 Spatiotemporal diagram of number densities of charged species: electron (upper), atomic xenon ion (middle) and molecular xenon ion (bottom).
I
II-1 III
IV V-2
VI I
II-2
V-1
Figure 4-2 Spatiotemporal diagram of number densities of excited species: Xe*(met) (upper), Xe (* 32 Σu+) (middle) and electron temperature (bottom).
Figure 4-3 The temporal variations of (a) applied voltage (Va), dielectric voltage (Vd), gap voltage (Vg), discharge current density at inner side (r=0.8 cm) and accumulated charge (Qa) and (b) the number density of electron, the ion species Xe+ andXe2+, the
main excited species Xe*(met), the main excimer species Xe (* 32 Σ and Te utilizing u+) sinusoidal waveform over a cycle.
I II III IV V VI I
Figure 4-4 Spatiotemporal diagram of number densities of charged species: electron (upper), atomic xenon ion (middle) and molecular xenon ion (bottom).
Figure 4-5 Spatiotemporal diagram of number densities of excited species: Xe*(met) (upper), Xe (* 32 Σu+) (middle) and electron temperature (bottom).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 4-6 Two snapshots of total species of (a) and (b) in the period I, (c) and (d) in the period II-1, (e) and (f) in the period II-2, (g) and (h) in the period III.
Figure 4-7 The temporal variations of (a) applied voltage (Va), dielectric voltage (Vd) and gap voltage (Vg) in upper figure (b) discharge current density at inner side (r=0.8 cm) and accumulated charge (Qa) in bottom figure utilizing distorted square voltages over a cycle.
Figure 4-8 The temporal variations of number density of electron, the ion species Xe+ andXe2+, the main excited species Xe*(met), the main excimer species Xe (* 32 Σ and u+) Te during the period t=0 ~ 2 (μs).
Figure 4-9 The power emission in the upper figure and power deposition utilizing distorted square voltages over a cycle.
(a)
(b)
Figure 4-10(a) The efficiency and P172 under different power source. (b) The deposition power and power partition under different power source.
Figure 4-11 The comparison of light power emission (P172) between sinusoidal voltages (the upper figure) and distorted square voltages (the bottom figure).
Figure 4-12 The comparison of power deposition between sinusoidal voltages (the upper figure) and distorted square voltages (the bottom figure).
Figure 4-13 A snapshot of distributions of electron energy consumption components using distorted square voltages.
Figure 5-1 Spatial distribution of cycle averaged discharge properties: a) VUV light emissions across the gap b) power depositions of charged species across the gap.
Figure 5-2 Spatiotemporal diagram of: a) 172 nm line UVU light emission and b) electron power deposition.
Figure 5-3 Spatiotemporal diagram of power depositions: a) atomic xenon ion and b) molecular xenon ion.
(a)
(b)
(c)
Figure 5-4 Effect of frequency on: a)η172, Ptot and P172, b) power deposition of various charged species, and c) fraction of power deposition for different charged species at 400 torr of gas pressure, 4.5 mm of gap distance and 2 dielectric layers.
(a)
(b)
(c)
Figure 5-5 Effect of gas pressure on: a) η172, Ptot and P172, b) power deposition of various charged species, and c) fraction of power deposition for different charged species at 50 kHz of power source, 4.5 mm of gap distance and 2 dielectric layers.
(a)
(b)
(c)
Figure 5-6 Spatial distribution of cycle-averaged power densities of various charged species at different gas pressus: a) electron, b) atomic xenon ion and c) molecular xenon ion.
(a)
(b)
(c)
Figure 5-7 Effect of gap distance on: a) η172, Ptot and P172, b) power deposition of various charged species, and c) fraction of power deposition for different charged species at 50 kHz of power source, 400 torr of gas pressure and 2 dielectric layers.
(a)
(b)
Figure 5-8 Spatial distribution of cycle-averaged power densities at different gap distances: a) VUC emission and b) ions and electron.
(a)
(b)
(c)
Figure 5-9 Effect of number of dielectric materials on: a) η172, Ptot and P172, b) power deposition of various charged species, and c) fraction of power deposition for different charged species at 50 kHz of power source, 400 torr of gas pressure and 4.5 mm of gap distance.
(a)
(b)
Figure 5-10 Spatial distribution of cycle averaged properties for one and two dielectric cases: a) electric field and b) power densities of charged species at 50 kHz of power source, 400 torr of gas pressure and 4.5 mm of gap distance.
Figure 6-1 Comparison of the experimental and simulated data with and without gas heating.
Figure 6-2 The spatial variations of background gas temperature (Tg) at different pressures across the discharge gap.
Figure 6-3 The spatial variation of ionic ohmic heating and electron energy loss due to elastic collision with xenon at different pressures with gas heating.
Figure 6-4 The spatial variations of background gas temperature (Tg) w/ k = const at different pressures across the discharge gap.
Figure 6-5 The variation of thermal conductivity in the region of Tg = 400 – 700.
Figure 6-6 The distribution of Tg at r =1 cm in the region of 100 – 513 torr.
Figure 6-7 The spatial distribution of background gas temperature (Tg) and number density (Ng) at 510 torr across the discharge gap.
Figure 6-8 The comparison of temporal variations of charge species and Te at 510 torr between with gas heating and without gas heating.
Figure 6-9 The comparison of spatial variations of Xe+-to-Xe2+ ion conversion and e-Xe2+ recombination at 510 torr between with and without gas heating.
Figure 6-10 The temporal variations of a) applied voltage (Va) and electron number density (Ne) b) electron temperature (Te) in the range of p=100-510 torr over a cycle.
Figure 6-11 Temporal distribution of electron power densities in period 0-2 (μs) at different gas pressures.
Figure 6-12 Temporal distributions of electron elastic collision loss power densities in period 0-2 (μs) at different gas pressures.
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