Comparison of VUV Emission Efficiency between Sinusoidal

Figure 4-10 shows: a) P172 and corresponding efficiency of 172 nm VUV as

defined earlier in Eq. (2.19); and b) the power deposition and corresponding fraction in different charged species for the two types of power source (sinusoidal and distorted bipolar square) under the same test conditions (p=400 torr; f=50 kHz; d=4.5 mm). Note that P172 is defined as the total VUV emission power as referred in Eq.(2.18). Figure 4-10a shows that the emitted power density for 172 nm using

distorted bipolar square voltages increased 2.5 times (from 49.2 to 124.8 W) more than when using idealistic sinusoidal voltages, while the corresponding efficiency increased from 13.4% to 28.9%. Figure 4-10b clearly shows that the fraction of power deposition through the electrons using distorted bipolar square voltages was nearly 2 times greater (22.7% to 43.5%) than when using idealistic sinusoidal voltages. In other words, the fraction of total power deposition through the two types of ions decreased from 76.9% (sinusoidal case) to 56.5% (distorted bipolar square case). Note that this dramatic increase of power deposition through the electrons was responsible for the large increase of the 172 nm VUV emission, as found in Figure 4-10a, in which the energetic electrons efficiently excited the ground-state xenon and generated much more abundant excimers to emit 172 nm VUV photons.

To further understand the reason for the increase in VUV emission using distorted bipolar square voltages as compared to idealistic sinusoidal voltages, phase diagrams of 172 nm VUV emission power distribution for both cases are shown in

Figure 4-11. The results show that VUV emission occurred much earlier, with greater

intensity and more uniformity across the whole gap during the discharge process in the former case. This was attributed to the rapidly rising voltage of the distorted bipolar square voltages and thus, higher energy absorption efficiency by the electrons,

which then generated abundant Xe^*(met) and, thus Xe (^{* 3}2 Σ for the 172 nm VUV _u⁺) photon emission.

Figure 4-12 shows the temporal variation of power deposition through the

charged species along with the gap voltage of the sinusoidal case. It was found, for example, that in the first half cycle (Period II-1), the electron power deposition of distorted bipolar square voltages was much higher than that of the sinusoidal ones (see bottom of Figure 4-9) (45 Wcm^-3 vs. 13 Wcm^-3) because of the much larger

g /

dV dt (~3.8 times) in the pre-breakdown period. The larger value of dV dt _g /

represented the shorter period prior to the breakdown gap voltage (~2.4 kV), during which only the electrons could respond instantly (almost without inertia) and gain energy from the field efficiently without much elastic collision loss. This is shown in Figure 4-13, in which the electrons gain energy through ohmic heating and lose

energy mostly through inelastic collisions, especially the excitations of ground-state xenon (No. 4 and 5 in Table 3-1). In the case of distorted bipolar square voltages, the electron temperature in Period I increased up to ~4 eV (see Figure 4-8), while it only

reached 2-3 eV in the case of sinusoidal voltages (not shown here). This also explained why the atomic xenon ions absorbed the energy with some phase lag, as compared to the electrons, because of the inertia effects in both cases. As for the power deposition through Xe₂⁺, it was still quite appreciable and extended for a

relatively long period, even in the post-breakdown period for the sinusoidal case; this was caused by non-vanishing gap voltages in this period which were beneficial for the power absorption of Xe₂⁺, unlike the nearly vanishing gap voltage in the same period

for the case of distorted bipolar square voltages.

In addition, Table 4-1 shows the amount of power output from the sinusoidal voltages (Pp,sin.) and the distorted bipolar square voltages from power supply ( Pp,dis.) is 1909.9 (W) and 1860.473 (W) respectively. From Table 4-1, the power conversion efficiency (P172/Pp) of the distorted bipolar square voltages (6.7%) is much better than the sinusoidal voltages (2.57%).

4.4 Brief Summary of This Chapter

Major findings of this chapter are summarized briefly as follows:

1. The insight of plasma physics and chemistry of a homogeneous coaxial xenon excimer ultraviolet lamp driven by sinusoidal and distorted bipolar square voltages have been described. According to the temporal variation of electron number density, the cycle can be divided into six periods. The periods I and IV

are pre-breakdown regions, the periods II and V are breakdown regions and the periods III and VI are post-breakdown regions. In period II and V, it can be further divided into two sub-periods (II-1 and II-2; V-1 and V-2). We have described the phenomenon in each period in this chapter.

2. Comparison of VUV emission efficiency between sinusoidal and distorted sinusoidal voltages has been made in detail. The results show that the efficiency of VUV emission using distorted bipolar square voltages is much higher than that using sinusoidal voltages (28.9% vs. 13.4%). This is attributed to the two following mechanisms. The first is the greater rate of voltage increase in bipolar square voltages as compared to that of sinusoidal voltages, which allows only the electrons to efficiently absorb the power in a short period of time without much elastic collision loss. The second is the comparably smaller amount of

“wasted” power deposition by Xe₂⁺ in the post-breakdown period.

Chapter 5

Parametric Study of VUV Emission from a Homogeneous Coaxial Xenon Excimer Ultraviolet Lamp Driven by Distorted Bipolar Square Voltages

In this chapter, an extensive parametric study of VUV emission from a homogeneous coaxial xenon excimer ultraviolet lamp driven by distorted bipolar square voltages is described. First, we summarize a typical characteristic of power deposition and VUV emission based earlier results presented in Chapter 4. Second, a set of simulation conditions are described. Third, results by varying power frequency, background gas pressure, gap distance are number of dielectric layers are described one by one. Finally, major findings of the parametric study are summarized briefly at the end of this chapter.

5.1 Typical Characteristics of Power Deposition and VUV Emission

Figure 5-1 shows the cycle averaged data of VUV emission (upper figure) and power deposition of charged species (bottom figure) across the discharge gap over a cycle. It can be found that 172 nm line of VUV is the major source of VUV emission

as compared to the other two lines (147 and 152 nm). It can also be noted that the strength of VUV power emission in the inner side is larger than that in the outer side because the electric field in the inner side is stronger than in the outer side. In the bottom figure, it can be found that electron power deposition occurs mainly across the discharge gap and ion power deposition occurs mainly in the sheath region. In addition, the amount of ion power deposition density in the inner side is nearly 1.67 times higher than in the outer side. The reason is the same as the variation of VUV power emission because of larger electric field in the inner side with the characteristic due to smaller radius of curvature. The trend of 172 nm line of VUV power emission (top) is similar to that of electron power emission (bottom) because, through the collision of energetic electrons, more species Xe^*(met) and Xe (^{* 3}₂ Σ are generated, _u⁺)

leading to 172 nm radiation.

Figure 5-2 shows the phase diagrams of VUV power emission (λ=172nm)

(upper figure) and electron power deposition (bottom figure) over a cycle, while

Figure 5-3 shows the phase diagrams of ion power deposition (Xe in the upper and ⁺

Xe2⁺ in the bottom figure). Again, we only describe the variations of power deposition and VUV radiation in the first half cycle (I, II and III) in detail. Besides, the slightly difference of the amount of the above properties results from the different areas of the inner and outer electrodes.

Period I

In the earlier part of Period I (negative applied voltage, 19.57-20 μs in both

Figures 5-2 and 5-3), it can be found that electrons responded to the variations of

electric field immediately, which leads to increasing electron power deposition in the region of r=0.95-1.05 cm. Accordingly, the concentrations of metastable and excimer species start to increase in the region of r=0.95-1.05 cm (see top and middle of Figure 4-5) due to electron impact collisions. Thus, power emission of 172 nm line also

increases with the increasing of concentrations of metastable and excimer species.

Generally, power deposition of Xe is less than the order of 10^{+ -2} (Wcm^-3) although

number density of Xe increases up to 10^{+ 5} (cm^-3) (see Figure 4-4). At the same time, power deposition of Xe₂⁺ mainly occurs in the outer sheath region.

In the later part of Period I (positive applied voltage, 0-0.25 μs in both Figures

5-2 and 5-3), energetic electrons, moving from the outer sheath into the bulk

(r≈0.95-1.05 cm), generates many excited species such as Xe^*(met) and Xe (^{* 3}₂ Σ in _u⁺)

the bulk (see Figure 4-5). VUV emission thus rises to the order of 1 (Wcm^-3). The

concentration of Xe increases up to ~ 10^{+ 6} (cm^-3), as a result of direct impact ionization, as shown in the middle of Figure 4-4. However, the power deposition of

Xe is still less than the order of 10+ ^-2 (Wcm^-3) because the number density of Xe ⁺ is too small in this period (see middle of Figure 4-4). In contrast, the power deposition

of Xe₂⁺ is much higher than the order of 1 (Wcm^-3) because very large amount of

Xe2⁺ exists in this region and large electric field in the outer sheath. Near the outer dielectric tube (cathode side), although the electric field is very high due to the rising voltage at the inner electrode, both VUV power emission and electron power deposition are weak because of very few Xe^*(met), Xe (^{* 3}₂ Σ and electrons (see _u⁺)

Figures 4-4 and 4-5) in this region. Thus, it can be observed that the major power

deposition of Xe₂⁺ is in the region of r≈0.83-0.94 cm in the sheath where a large

potential drop exists.

Period II

In Period II-1, electron power deposition increases dramatically and the peak moves towards outer quartz tube in a speed of ~7,000 m/s (from anode towards cathode, see bottom of Figure 5) due to the huge growth of electron number density by direct electron impact ionization (see top of Figure 4-4). The amount of electron power deposition rapidly increases to the maximal value (>1x10³ Wcm^-3) within

~0.388 μs at r≈1.06 cm and then decreases gradually afterwards (see bottom of Figure

5-2). The moving direction of Xe power deposition is the same as the electrons, ⁺ with the maximal value of 7x10² (Wcm^-3) located at r≈1.22 cm, which is smaller than

that of the electrons due to its heavier mass. Afterwards, the power deposition Xe ⁺ decreases gradually in Period II-2 (see top of Figure 5-3). At the same time, number

of Xe₂⁺ increases through the three-body ion conversion channel (No. 18 in Table 3-1), and thus Xe₂⁺ power deposition increases towards the cathode (see bottom of Figure 5-3). However, the power deposition of Xe₂⁺ is smaller than that of Xe ⁺

because the former is about two times heavier than the latter. In addition, both Xe^*(met) and Xe (^{* 3}₂ Σ are both highly abundant across the gap (see Figure 4-5) _u⁺)

because of the excitation of ground-state xenon (No. 3 and 5 in Table 3-1) by the collision of energetic electrons. During this period, the 172 nm VUV power emission (see top of Figure 5-2) originates from the process that both the excimer species

* 1

Xe (2 Σ (less dominating) and _u⁺) Xe (^{* 3}₂ Σ (most dominating) fall to the ground _u⁺) state (No. 19 and 20 in Table 3-1).

In Period II-2, both Xe^*(met) and Xe (^{* 3}₂ Σ begin to disappear because of less _u⁺) energetic electrons existing in the bulk region (r≈1.1-1.2 cm; see bottom of Figure

4-4), which in turn reduces the VUV emission (P172) dramatically (see top of Figure 5-2). In the cathode sheath region, highly depleted electrons (see top of Figure 4-4)

can not absorb enough energy from the electric field which leads to much less power

deposition of electrons (bottom of Figure 5-2). At the same time, Xe is rapidly ⁺ consumed by Xe₂⁺ through the three-body collision as described earlier. Thus, the power deposition of Xe₂⁺ is much larger than that of Xe as can be clearly seen in ⁺ the cathode sheath (Figure 5-3). Noticeably, the maximal value of Xe₂⁺ power

deposition can reach a value of 4x10² (Wcm^-3) in the cathode sheath region.

Period III

In this post-breakdown period, the VUV emission decays with time in the bulk region, which strongly correlates with the variation of number densities of both Xe^*(met) and Xe (^{* 3}₂ Σ , as shown in Figure 4-5 and top of Figure 5-2. In addition, _u⁺) power deposition to charged particles mainly goes through the Xe₂⁺ remaining in the

cathode sheath throughout Period III (see bottom of Figure 5-3). Note the power deposition in the bulk region with much more Xe₂⁺ is much smaller as compared to

that in the cathode sheath mainly because of much smaller electric field in this region.

5.2 Simulation Conditions

Four parameters, which include driving frequency of the power source, background gas pressure, gap distance between electrodes and number of dielectric layers, are varied systematically to study their effects on the efficiency of 172 nm line (η₁₇₂), the total power deposition (Ptot) and the VUV emission from 172 line (P172).

The test conditions are summarized in Table 5-1.