Global models of microdischarges

Laboratoire de Physique des Plasmas

Pascal CHABERT and Claudia LAZZARONI
Laboratoire de Physique des Plasmas, Ecole Polytechnique, Palaiseau FRANCE

Michael A. LIEBERMAN and Allan J. LICHTENBERG
Departement of Electrical Engineering, UC Berkeley, USAAcknowledgments• Micro-Hollow Cathode Discharges (MHCD’s):- Antoine Rousseau- Nader Sadeghi• RF capacitive microdischarges at atmospheric pressure- Jochen Waskoenig- Timo Gans

Microdischarges• History of microplasmas : plasma displays (since 60s..)– Microhollow cathode type (Schoenbach 1996)
DC source

100µm– Microarray (Eden 2001)
AC source– Microneedle (Stoffels 2002)
rf source– Micro APPJ (Schulz-von der Gathen 2008)
rf source• Applications in various fields:
Surface treatment/ Light sources (excimer)/ Biomedicine

Agenda• In this talk global models will be used to model
microdischarges at high (up to atmospheric) pressure• A global model of Micro-Hollow Cathode Discharges(MHCD’s) in argon• A global model of RF capacitive microdischarges atatmospheric pressure in He/O2

Global models• Volume-averaged (0D) model: densities and temperatures
are uniform in space• Particle balance:• Electron power balance:

Particle balance: low pressure• Particle losses at the walls. The term P contains volumeand wall losses. For the electron particle balance at low
pressure, wall losses dominate and in one dimension:• A plasma transport theory is required to relate thespace-averaged electron density to the flux at the wallParticle balance: issues in µdischarges• In microdischarges, ionization is often non uniform.
Classical low-pressure transport theory do not apply• Fortunately in someinstances volume losses
dominate (recombination)• However, evaluation ofwall losses is a criticalpoint for high-pressure
discharges modelingOther issues• Properly evaluate the reaction rates:― Electron energy distribution function is unknown― In microdischarges, Te is often strongly non uniform
in space, and may vary in time…

• Properly evaluate the electron power absorption:― Distinguish between electron and ion power (andother power losses in the system)― Equivalent circuit analysis is often useful. I-V
characteristic of a device is a good starting point

So why one would use global models?
• They are easily solved, sometimes analytically. Therefore
they provide scaling laws and general understanding of
the physics• They can be coupled to electrical engineering models togive a full description of a specific design• They allow very complex chemistries to be studied
extensively. Numerical solutions of global models withcomplex chemistries only take seconds

Micro Hollow cathode Discharges(MHCD’s)Laboratoire de Physique des Plasmas• Gas : ArgonDC• Pressure : 30-200 Torr

• Excitation : DCI-V Characteristics: mode jumps
450
400

0,6 Torr.cm

Voltage (V)0,84 Torr.cm

confined inside
the micro-hole

350
1 Torr.cm

300

1,2 Torr.cm

250
200
150
0,00,4self-pulsing

0,8

1,2

1,62,02,4

current (mA)

Aubert et al., PSST 16 (2007) 23–32

normal: cathode expansion

Equivalent electrical circuit
Hsu and Graves, J. Phys.D 36 (2003) 2898
Aubert et al., PSST 16 (2007) 23

P. Chabert, C. Lazzaroni and A. Rousseau,J. Appl. Phys. 108 (2010) 113307
C. Lazzaroni and P. Chabert, Plasma
Sources Sci. Technol. (2011) 20 055004

Non-linear plasma resistance
500150 Torr

Rp (k )

400
300

Rp = switch

200
1000abnormal:
confined in the hole

A3=00

1

Current (mA)2normal:cathode expansion

Rp controls the physics of the transition between the two stable regimes

Stable and unstable regimes
320

13

2

Voltage (V)dV/dt=0
equilibrium

240

dId/dt=0160

01equilibrium

2

Current (mA)

13

Abnormal regime
Stable regimes
Normal regime

2

Self-pulsing regime

Electrical signals/ Phase-space diagramElectrical model of the MHCD• Total absorbed power simply:• What is the physical origin of Rp? What fractionof the total power goes into electrons?

Decomposition in two main regions

Makasheva et al, 28th ICPIG(2007) 10

The resistance of the positive column is small

Structure in the cathodic region
1000

Intensity (arb. u.)

200Torr
800
600

Ar line400200+

Ar lineDistance from cathode (µm)

0-0.2

-0.1

0.0

0.1

0.2r (mm)120100+Ar line maximum

80
60
40
20050

100

150

P (Torr)

200250Calculation of sheath thickness (d)sheathdR• One-dimensional cylindrical geometry:r0bulk• Ions/electrons fluxes:ii(R d )i(R d )

i(R ) Cathode( R)e(R d )
Sheathee(R )( R) . ei( R)(r) eSheath thickness vs pressure

Distance from cathode (µm)

120-decrease of the sheath size with theincrease of pressure100
Ar line maximum-maxima of both emission lines
located after the sheath edge

80
60-same trends for the evolution of dthan that of the maxima of the+Ar line maximum emission line

dionizing

40
20
050

100150200

250300-the sheath edge coincide with themaxima of the ionic line

P (Torr)
C. Lazzaroni, P. Chabert, A. Rousseau and N. Sadeghi, J. Phys. D: Appl. Phys. 43 (2010) 124008

Abnormal and self-pulsing regime
Voltage (V)

350

300

250

200

150

1200

050

100t (µs)

800

Allowed region forthe cathodic expansiond>RVoltage (V)

1000

600
400

P and V high enough200
0Too low voltage

040

80

120P (Torr)

160

200

150200Power absorbed in the cathode sheath• Electrons:• Same for ions with:Power absorbed by electrons• Fraction of power absorbed byelectrons:• Power absorbed in the volume
under consideration:Power balance

Power loss at the wall is negligibleParticle balance

Results in the self-pulsing regime

Global modelExperiments

Results in the self-pulsing regime

This has been observed experimentally:
Aubert et al., Proceedings of ESCAMPIG, Lecce, Ed. M. Cacciatore, S. D. Benedictis,
P. F. Ambrico, M. Rutigliano, ISBN 2-914771-38-X, Vol. 30G (2006).

RF capacitive discharges at
atmospheric pressure
Laboratoire de Physique des Plasmas~ElectrodeHe/O21 mm

Plasma bulk
Electrode• RF frequency : 13.56 MHz• electrode gap :1 mm• Helium with small admixture of O2• Comparison to a fluid model
developed by Waskoenig et al
J. Waskoenig, Thesis, Queen’s University Belfast (2010)
J. Waskoenig et al. PSST 19 (2010) 045018

Homogeneous discharge model
nsm
electrode0nibulks(t)neelectrodelx• Three regions: - a quasi-neutral plasma (ni=ne=n0=const)- two sheaths (ni=n0 and ne=0)• Ions do not respond to the RF field• Analytical expressions of JC(t), s(t), E(t) and PC(t)Potential across the electrodes

5Electric field (10 V/m)

432-linear increase of
E in the sheaths

10-E(bulk) almost aslarge as E(sheath)-1-2-3-4-500-250

electrode

0x (µm)250

500
electrodeΦ1=37.6°; Φ2=125°; Φ3=213°; Φ4=304°

Global model
Particle balance/

Global e- power balance

numericallyanalytically3) Mean rate coefficient

1) Pc(t)  homogeneous discharge
2) Te(t)  analytical integration

Discharge equilibriumElectron temperature
Electron energy balance:

Hypothesis: -Te(t) uniform in the bulk
-ne uniform and independant of time
integration

Electron temperature

Te (eV)

1,61,20,80,40,00100200300

Time (ns)
Unlike at low pressure, Te oscillates during the rf cycle. This point isextremely important for the global modeling.

Effective rate coefficients• Electron-activated processes strongly affected by Te(t)• Maxwellian rate coefficients:• Averaging over the oscillating Te enhanced rate coefficient:Enhanced ion losses- A large part of the gap istransiently explored by thesheaths5Electric field (10 V/m)

4Time-averaged
plasma bulk

32-Therefore, the time-averaged
electric field is large in theseregions

10-1-2-3-4-500

electrode-2500x (µm)

250500electrode- Ions born in these regions
are lost faster than those bornin the bulk plasma- this needs to be taken into
account

Particle balance: chemistry• Particle balance for each species:• System numerically integrated

Electronegative plasma
He-O2 mixture++• 16 species: He, He , He2 , He*,
• 0.5 % of O2
He2*, O2, O, O3,• 16 species++O , O2 , O , O2 ,• 127 reactions
O3 , O*, O2* and e• Tg=345 k

1E22

O

1E21

O3

1E20

O2-3

Density (m )Reactive Oxygen Species (ROS)

*

1E19

O

1E18
1E17

1

2

3
2P (W/cm )

*

4

1E22

O

1E21

O3

1E20

O2-3

Density (m )ROS: comparison global/fluid models

*

1E19

O

1E18
1E17

12

3

Global model  lines
Fluid model  dash lines*

42P (W/cm )- Good qualitative agreement- Global model predictions lower than that of fluid model(factor of 2 for O and O3 and factor of 3 for O* and O2*)

Charged particles (CP)-3Electron density (10 m )30--3Density (m )

16O3
20

10e-

1E17-O2O

0

1232P (W/cm )41-

2

32P (W/cm )4

CP: comparison global/fluid models
Global model  symbols + lines
Fluid model  open symbols + dash lines-3

Electron density (10 m )30--3Density (m )

16O3
20

10e-

1E17-O2O

0

12

32P (W/cm )

41-23

4

2P (W/cm )- Good qualitative agreement- ne (global model) ≈ 3*ne (fluid model)- Negative ion densities (global model) ≈ 3/2*Negative ion densities (fluid model)

Conclusions (1)• Global models are very useful to understand the generalbehavior of plasma discharges• They provide analytic solutions and scaling laws andallow fast numerical solutions of complex chemistry• However, they rely on many assumptions and therefore
need to be benchmarked by experiments or moresophisticated numerical simulations

Conclusions (2)• The need for many simplifications and assumptions forces
one to propose physical explanations, sometimes at theexpense of being “rigorous”• Global models do not explain the detailed and microscopic
phenomena taking place in plasma discharges. they offer
a representation of reality that becomes more accurate
when more realistic fundamental assumptions are madeDownload this talk:www.lpp.fr/?Pascal-Chabert,128

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