1. Plasma Bubble
(+) Bias Electrode
Ambient Plasma
Breakdown Conditions of Local Sheath Discharge in front of Positively Biased Electrode immersed in Inductively Coupled Plasma
2007 IEEE Pulsed Power and Plasma Science Conference
June 18th, 2007, Albuquerque, New Mexico, USA
Yeong-Shin Park, K.J. Chung, and Y.S. Hwang
NUPLEX, Dept. of Nuclear, Seoul National University San 56-1, Shillim-dong, Gwanak-gu, Seoul , Korea

2. Abstract
In researching the double layer, additional dense plasma near the small anode in bulk plasma, so called fireball, have been known and widely used as the simplest method to form the double layer. However, breakdown condition and discharge mechanism of the fireball itself have been not elucidated sufficiently.
In this study, discharge mechanism for the fireball have been introduced compared to DC glow discharge. The fireball is named “local sheath discharge”, since the plasma occurs in anode sheath between electrode and bulk plasma. Breakdown conditions for the local sheath discharges have been investigated experimentally by varying the discharge conditions such as gas pressure, power for generating background plasma, and geometry of the electrode. An electrode screened by dielectric material except small circular area, is immersed in inductively coupled plasma (ICP) and biased with positive voltage with respect to the space potential of the plasma.
A bright plasma bubble is observed locally just above the exposed part of the biased electrode with abrupt increase of current to the electrode when the bias voltage exceeds a certain threshold, breakdown voltage. The breakdown voltage decreases as the gas pressure is raised. Radio frequency power for generating ICP as well as the electrode geometry influences on the breakdown voltage too. These experimental results indicate that ambient plasma properties such as density, temperature, and space potential play an important role in generating local sheath discharges.

3. Previous Work
▶ Anodic Double Layer ( Fireball, Plasma-Contactor, Anode-Spot, Complex Space Charge Structure)
Many researchers including M. Sandulovciu, B. Song, R. Schrittwieser, D.G. Dimitriu, and L. Conde have studied anodic double layer.
Small electrode immersed in plasma and biased positively generates dense plasma, so called fireball, as well as anodic double layer between fireball and ambient plasma inherently.
Fireball has been used as a simplest method to generate double layer in which the researchers are interested.
Spatial plasma potential distribution, electron density, diameter of the fireball, current spike / oscillation, stratification, and so on have been investigated. Recently, L. Conde has reported a paper for transition from an ionizing electron collecting plasma into and anodic double layer. [3]
◈ Fireball, anodic double layer [1]
◈ Potential distribution [2]
◈ Scheme of the transition from an electron collecting sheath to a double layer [3]
Fireball
After breakdown
Double layer
Before breakdown
[1] M. Sanduloviciu, C. Borcia, and G Leu, “Self-organization phenomena in current carrying plasmas related to the non-linearity of the current versus voltage characteristic”, Phys. Lett. A 208, 136 (1995)
[2] B. Song, N. D’Angelo, and R.L. Merlino, “On anode spots, double layers and plasma contactors”, J. Phys. D: Appl. Phys. 24, 1789 (1991)
[3] L. Conde, C.F. Fontan, and J. Lambas, “The transition from an ionizing electron collecting plasma sheath into an anodic double layer as a bifurcation”, Phys. Plasmas 13, (2006)

4. Motivation of the Research
for
Breakdown
Condition
Fireball,
Anodic
Double Layer
Contributions
of the
Research
Introduction of discharging model of the local sheath discharge.
Investigation of breakdown voltage dependence on operating conditions experimentally.
Find out the factors of determination of the breakdown.
Expectation of breakdown voltage under a practical operating condition.
Optimum condition for local sheath discharge.
Research has focused only on anodic double layer, not on the fireball itself.
Breakdown condition and discharge mechanism of the local sheath plasma have not been elucidated sufficiently.

5. Breakdown Mechanism of DC Glow Discharge
◈ Schematic diagram of DC glow discharge
1. Electron-avalanche from cascading ionization collisions between accelerated electrons and neutrals is the key of discharge.
2. Electrons are supplied from cathode.
3. Discharge gap is determined by distance between two powered electrodes.
4. Potential difference is fixed with voltage at power supply.
5. Ions impinging on cathode enhance the electron flux.
▶ Breakdown Voltage of the DC Glow Discharge
▶ Characteristics of DC Glow Discharge : Paschen’s Curve
◈ Paschen’s curve from numerical result ( γse=0.01)
Breakdown voltages are characterized by the product of pressure and distance between the two electrodes.
- In the left side of Paschen’s curve, breakdown voltages are reduced as raising the product of pressure and distance.
- breakdown voltages increase with growth of the product pressure and distance in the right side.

6. Breakdown Mechanism of Local Sheath Discharge
▶ Local Sheath Discharge compared to DC Glow Discharge
◈ Schematic diagram of local sheath discharge
1. Electron-avalanche from cascading ionization collisions between accelerated electrons and neutrals is the key of discharge.
2. Electrons are supplied from plasma.
3. Discharge gap is determined by length of sheath between anode and plasma.
4. Potential Difference is fixed with sheath voltage.
5. Ions accelerated into plasma enhance the electron flux.
6. Electrons entering into the sheath have thermal velocity and are accelerated by
▶ Characteristics of Local Sheath Discharge
Breakdown voltages are characterized by pressure, properties of bulk plasma, and length of the sheath.
Sheath size is decided by properties of plasma.
Plasma == Cathode
Length of Sheath == Distance btw. electrodes

7. Experimental Apparatus
▶ Inductively Coupled Plasma
▶ Bias Module
Single-turn RF antenna, L-type matching network
Gas : Argon, Pressure : 1 ~ 25 mTorr, RF Power : 100 ~ 500 W
Using diffused plasma
Electrode Material : S/S, Al, Cu, Mo
Hole Diameter : 1 ~ 5 mm
Hole Depth : 1 ~ 6 mm
Sweeping Voltage : -100 ~ 300 V
Measuring Resistance : 5 ohm
◈ Overview of the experimental system
◈ Bias module (bias electrode)

8. Confirmation of Local Sheath Plasma
▶ Macroscopic Observation
▶ Plot of Bias Current & Voltage
Direct evidence of local sheath plasma (plasma bubble)
Comparison of local discharge effect in FIB to plasma ball in anodic double layer phenomenally
Can not catch up the exact breakdown point but give the most reliable proof of breakdown.
When the additional plasma occurs,
- Sudden current jump. - Voltage drop.
Hysteresis is shown in graph.
→ Existence of self-consistent plasma
◈ Figure of local sheath plasma (right, dashed circle, captured at movie clip) and its schematic cross-section (left)
◈ Bias voltage and corresponding current of local sheath discharge
Plasma Bubble
(+) Bias Electrode
Ambient Plasma

9. Determination of Breakdown Point
▶ Voltage Sweep Method
Sweeping frequency : several Hz, sweeping voltage : -100 ~ 300 V
Two knees from characteristic curve of bias current and voltage
- first knee : properties of ambient plasma
- second knee : occurrence of local sheath plasma, current jump, voltage drop, hysteresis
Breakdown voltage (VB) : voltage just before current jump or maximum voltage before voltage drop
◈ Characteristic I-V curve of local sheath discharge
◈ Raw data of bias voltage and current
Plasma
Properties
Breakdown
Conditions
knee
Current jump Voltage drop

10. Experimental Result 1 : VB - Pressure and Power
▶ Pressure Effect on Breakdown
▶ RF Power Effect on Breakdown
As raising the operating pressure, the breakdown voltage decreases. The result shows linear dependence of the pressure increment on reduction of breakdown voltage.
It is shown that the neutral particles contribute to discharge local sheath plasma. Therefore, the operating regime would be correlated to the left side of Paschen’s curve.
In the state of E-mode heating in ambient plasma, breakdown voltages decrease steeply as the RF power increases. On the other hands, breakdown voltages are raised with the increase of RF power in H-mode ICP,
It is shown that the properties of ambient plasma such as electron density, electron temperature, and plasma potential affect on breakdown condition.
◈ Breakdown voltage according to RF power variation
◈ Plot of breakdown voltage as a function of mass flow

11. Experimental Result 2 : VB - Plasma Properties
▶ Effect of Ambient Plasma Properties
◈ Breakdown conditions and plasma properties as varying the RF power
- Gas : Argon, Hole Thickness : 1 mm, Hole Diameter : 3 mm
Strictly, the breakdown potentials are acquired by subtracting plasma potential from bias voltage.
Plasma potential does not affect on breakdown voltage directly but acts as a reference potential for the bias voltage.
Electron temperature effect can be negligible since the electron temperature is very small compared to the bias voltage.
Over 200 W, breakdown voltage increases corresponding to the increment of electron density.
Breakdown currents are proportional to electron density.
Below 200 W, breakdown voltage decreases steeply with increment of power, since plasma could less contact with bias electrode than above 200 W and thus higher voltage would be needed to attract sufficient electron to discharge.
Electron sheath, discharging gap of local sheath discharge, expands as the electron density is reduced.
Expanded electron sheath helps that the electrons are accelerated enough to ionize neutral particles.

12. Electron Sheath and its Evolution
▶ Equation for Electron Sheath Size
▶ Electron Sheath as a Discharge Gap
Hypotheses
1. Collisionless sheath having relatively high potential drop
2. Electron impinging to the sheath has the thermal velocity.
3. Ion distribution in the sheath, follows Boltmann’s relation.
Governing Equations
1. electron energy conservation equation
2. electron flux conservation equation
3. electron flux at the sheath edge
Sheath Size ∝ V03/4, ne-1/2, Te-1/4
Decreasing tendency of breakdown voltage as rising pressure indicates that more collisions are needed to generate local sheath plasma. Therefore, long discharge gap (electron sheath in local sheath discharge) is more favorable than short one for easy breakdown.
As aforementioned, breakdown occurs more easily at low density plasma. It is because the electron sheath, which is inversely proportional to a second of electron density, becomes longer. The result has a correlation with left side of the Paschen’s curve in DC discharge.
◈ Electron sheath thickness with variation of sheath voltage
- electron density : 1.0x1010 cm3, electron temperature : 3 eV

13. Experimental Result 3 : VB - Geometric Effect
▶ Hole Depth (Thickness) Effect
▶ Hole Size (Diameter) effect
Thinner screening dielectric is favor in reducing breakdown voltage and expands the pressure limit for discharge.
Thickness effect on breakdown voltage in low pressure regime is appreciable, however, in high pressure regime, the effect is almost negligible.
Discharge gap is determined not by dielectric thickness but by electron sheath.
Smaller electrode area is favor in reducing breakdown voltage in low pressure regime.
Larger electrode area reduces breakdown voltage a little in high pressure region.
Area effect on decreasing breakdown voltage is significant only in low pressure.
◈ Dependence of Breakdown Voltage upon Hole Diameter
- Gas : Argon, Input Power : 400W, Hole Thickness : 1 mm
◈ Dependence of breakdown voltage on dielectric thickness
Low Pressure
/ Low Density
High Pressure
/ High Density

14. Experimental Result 4 : Another Considerations
▶ Fluctuation in Ambient Plasma
▶ Anode Material Dependence
Local sheath plasma disturbs ambient plasma. As the electron density in ambient plasma is lower, magnitude of the perturbation is bigger.
High density plasma is recommended in order to prevent the fluctuation.
Material of bias electrode does not play a role in discharging sheath plasma since ambient plasma contributes to supply electron for discharging local sheath plasma.
Therefore, only sputtering yields and thermal conductivity are considered in choice of bias electrode.
◈ Fluctuation of Floating Potential in Ambient Plasma as a function of Time with varying RF power
- Gas : Argon, Operating Pressure : 10 mTorr, Hole Thickness : 1 mm, Hole Diameter : 4 mm
◈ Breakdown voltages with variation of bias electrode material
S/S Al Cu Mo

15. Conclusion
Discharging mechanism of local sheath plasma has an analogy with the DC glow discharge.
Breakdown point can be decided by analyzing electron-voltage curve of the bias electrode.
Breakdown voltage is reduced as the operating pressure increases.
As power for ambient plasma is raised, breakdown voltage increases in high power region. - Plasma potential does not affect on breakdown voltage but plays a role of reference potential. - Effect of electron temperature can be negligible compared to bias voltage. - Variations of breakdown voltages are mainly affected by electron density of ambient plasma.
Length of electron sheath is inversely proportional to square root of the electron density. Therefore, increasing electron density lead to reduction of electron sheath; discharging gap.
As the electron sheath is reduced, higher voltage is need for breakdown.
Breakdown voltage of Local sheath plasma shows analog tendency with the left side of Paschen’s curve in DC glow discharge.
Bias electrode having small exposed area and thin dielectric cap is recommended for reducing breakdown voltage.