4.2 Discharge Properties by Bipolar Distorted Square Voltages 30
4.2.3 Snapshots of Key Discharge Properties
To gain more insight into the discharge physics and chemistry, two sequential snapshots of the several key discharge properties in each period (I, II and II) are presented in Figure 4-6 and described in detail in the following.
Period I
Figures 4-6a and 4-6b show two typical snapshots of important discharge
properties in the earlier and later stages of Period I, respectively. They show that the peak plasma density (~8×1010 cm-3) was close to the anode (inner) at r≈0.84 cm, and
that it stayed nearly stationary in space, but with a very low density as compared to that of Period II, as will be shown later. However, the figures also clearly demonstrate that the electrons were attracted to the anode (inner), with the gap voltage increasing from 0.4 (Figure 4-6a) to 2 kV (Figure 4-6b). In the region around r≈1 cm, the rapid
growth of atomic ions, excited species (Xe*(met)) and excimer species (Xe (*2 Ο ,u+) Xe (* 12 Σ and u+) Xe (* 32 Σ ) could be seen due to a series of collisions by u+)
energetic electrons (~4 eV) moving towards the anode side (inner). On the other hand, the amount of Xe*(res) decreased through the reactions of conversion to metastable (No. 10 in Table 3-1) and conversion to dimers (No. 12 in Table 3-1). The main collision processes of generating excited and metastable species occurred through the excitation collision channels, such as Nos. 3 and 5 in Table 3-1. These in turn promoted the growth of excimers through the reaction channels, such as No. 13 in Table 3-1, with zero threshold energy. Interestingly, the atomic ions and electrons
moved towards the cathode side (outer), which will be more clearly shown in the details of Period II. A peak value of ~2×109 cm-3 of atomic ions (Figure 4-6b) occurred at r≈1.08 cm through the contribution of collision channels, such as Nos. 1, 6
and 16 in Table 3-1. Of these, the most productive channel was the electron impact
ionization (No. 1 in Table 3-1) due to the rapid increase in voltage. As the density of the metastable species grew to a certain level, the other two channels began to contribute more in generating atomic ions.
Period II
Figures 4-6c and 4-6d present two typical snapshots of important discharge
properties at earlier and later times in Period II-1, respectively. They show that the potential field was highly distorted near the cathode (outer) due to the shielding of the narrow quasi-neutral region (between r≈1.1-1.2 cm) close to the cathode side; this in
turn accelerated the few electrons near the cathode side (outer) and reached a very high electron temperature (~5-6 eV) (Figures 4-6c and 4-6d) at the edge of sudden change of the electric field (r=1.16 cm in Figure 4-6c and r=1.18 cm in Figure 4-6d).
These energetic electrons thus ionized and excited the ground-state xenon according to the reaction channels, such as Nos. 2-5 in Table 3-1, which could be seen clearly from the peaks of charged and excited species around r≈1.16 cm and r≈1.18 cm in
Figures 4-6c and 4-6d, respectively. At the same time, the molecular xenon ions
increasingly formed through the three-body ion conversion reaction channel (No. 18 in Table 3-1) which reduced the atomic ions behind the right-moving head, but still maintained strict quasi-neutrality. In general, the densities of Xe*(met) and Xe*(res) correlated very well with the density of electrons in Period II-1, which meant that they
were generated through direct electron impact reactions. An interesting phenomenon, the so-called “cathode-directed streamer-like” ionization wave, moving to the cathode was observed, in which the peak of atomic ions was ahead of that of the electrons with a speed of ~7,000 m/s, which was far less than that of a real streamer [Raizer,
1991].
Figures 4-6e and 4-6f present two typical snapshots of important discharge
properties at earlier and later times, respectively, of Period II-2. In this period, the applied voltage almost reached its peak and the gap decreased slightly, but the stream-like ionization wave moved to a location very close to the cathode dielectric surface (outer) and stayed almost stationary in Period II-2. The peak value of electrons greatly increased to a level of ~2.7×1012 cm-3 at the position of r=1.22 cm, while the dominating ion species became Xe2+ instead of Xe through the +
increasingly important three-body ion conversion channel (No. 18 in Table 3-1).
Accordingly, this rapidly consumed Xe . In addition, the amount of Xe+ *(met) and Xe*(ex) were greatly reduced from values of 4×1012 cm-3 and 2.7×1012 cm-3, respectively, down to 1.5×1012 cm-3 and 5×1011 cm-3, respectively, due to the less
energetic electrons; this was caused by the reduced electric field due to the shielding by the accumulated ions at the cathode dielectrics (outer); this led to the slight reduction of Xe (* 32 Σ from 2.5×10u+) 12 cm-3 to 2×1012 cm-3, which was the most
important species for VUV (172 nm) emission, across the gap. After Period II-2, the discharge became more diminished, as described next.
Period III
Figures 4-6g and 4-6h present two typical snapshots of important discharge
properties at earlier and later times of Period III, respectively. In this period, the quasi-neutral region expanded slowly from the cathode side (outer) towards the anode side (inner) with greatly decreasing plasma density in the peak (from 8×1011 cm-3 to 1.1×1011 cm-3) close to the cathode (outer); this was attributed to the decreasing
electron temperature caused by the reduced electric field in the sheath on both sides.
Especially, the electron temperature in Figure 4-6h was reduced to nearly zero because of the very small electric field in the sheaths. The major species in Period III were electrons and Xe2+, while the other species almost disappeared (<109 cm-3) and
came into a post-breakdown period (extinguished). After Period III, the polarity of the applied voltage changed and the above described pre-breakdown (Period I), breakdown (Period II) and post-breakdown (Period III) repeated temporally with opposite direction and location because of the higher plasma density and more abundant excited species due to the stronger electric field near the inner electrode caused by the small radius of curvature.
4.2.1 Temporal Variation of Discharge Properties
To further elucidate the discharge physics described above, we have presented the temporal variation of other discharge properties together in Figure 4-7, which include: a) the applied voltage (Va), the dielectric voltage (Vd) and the gap voltage (Vg); and b) the discharge current density at the inner side (r=0.8 cm) and the accumulated charges (Qa) at both dielectric surfaces (r=0.8 and 1.25 cm). Note that the dielectric voltage is defined as the sum of voltages across both quartz tubes.
Several important characteristics were drawn from Figure 4-7, as follows. “Memory effects” were clearly seen throughout the cycle. For example, in Period I, the gap voltage led the applied voltage (see Figure 4-7a) because of the shielding caused by the positive accumulated charges at the anode dielectric surface (inner) remnant from the previous cycle (see Figure 4-7b). During the breakdown period (Period II), the electrons rapidly accumulated on the inner anode dielectric surface (see Figure 4-7b), which resulted in a much smaller gap voltage (see Figure 4-7a) by shielding out the applied voltage. Throughout Period III, the gap voltage was almost zero (see Figure 4-7a) as the surface charge density remained roughly the same on both dielectric
surfaces (see Figure 4-7b), although the applied voltage was almost as high as 2 kV.
In addition, the magnitude of the accumulated surface charge density and current density at the inner dielectric surface was always greater than that at the outer dielectric surface because of the smaller inner area.
Figure 4-8 provides a general view of the discharge across the gap and the
exposure view of several important spatial-averaged discharge properties in the first 2 μs, in which the discharge occurred. During the discharge process (Period II), from 0.4 to 1.14 μs, the molecular xenon ions initially outnumbered the atomic xenon ions.
The trend did not change until 0.46 μs and lasted through 0.6 μs, in which the
discharge occurred. It was also clear that the molecular xenon ions were the dominant ion species at all times, except in the very initial period of the breakdown process, as mentioned above (0.46-0.6 μs). As for the trend of spatial-averaged electron
temperature, it was raised to a value of ~4 eV prior to when the discharge occurred, and decreased to less than 1 eV right after the discharge process because of the loss of most of the energy via ionizations and excitations. In addition, the amount of Xe*(met) and Xe (* 32 Σ both peaked in the early part of the breakdown period (Period II-1), u+) although the latter lagged behind the former by ~1 μs.