1. MODELING OF MICRO-DIELECTRIC BARRIER DISCHARGES
Jun-Chieh Wanga), Napoleon Leonib), Henryk Bireckib),
Omer Gilab), Eric Hansonb) and Mark J. Kushnera)
a)University of Michigan, Ann Arbor, MI USA
b)Hewlett Packard Research Labs, Palo Alto, CA USA
37th IEEE International Conference on Plasma Science
Norfolk, Virginia
June 20 – 24, 2010
Good afternoon, I am Jun-Chieh Wang. Welcome to my presentation today.
During my talk, I am going to present some interesting findings from our study titled
“Modeling of micro-dielectric barrier discharges”
This work is supported by Hewlett Packard research Lab.

2. University of Michigan Institute for Plasma Science & Engr.
AGENDA
Introduction to micro-Dielectric Barrier Discharges (mDBD)
Extraction of charge
Description of model
mDBD Scaling
mDBD sustained in N2 (1 atm)
Electron current extraction vs rf frequencies
Charge per pulse and FWHM vs frequency
Concluding Remarks
I will first begin with an introduction to micro-dielectric barrier discharges
and extraction of charge,
followed by a description of the model we use,
and the simulation result of mDBD sustained in Nitrogen
at atmosphe’ric pressure.
We also compare the current extraction, charge and width versus
different driving frequencies
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Institute for Plasma Science & Engr.
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3. DIELECTRIC BARRIER DISCHARGES
The plasma in DBDs is sustained between parallel electrodes of which one (or both) is covered by a dielectric.
When the plasma is initiated, the underlying dielectric is electrically charged, removing voltage from the gap.
The plasma is terminated when the gap voltage falls below the self-sustaining value and so preventing arcing.
On the following half cycle, a more intense electron avalanche occurs due to the higher voltage across the gap from previously charged dielectric.
The plasma in DBD is sustained between parallel electrodes where
one or both of the electrodes are covered by dielectrics
which separate the electrodes from the gas.
When the plasma is generated and impinges on the dielectrics,
the dielectrics charge and reduce the voltage across the gap.
When the voltage falls below the self-sustaining value, the plasma is quenched,
thereby preventing the formation of an arc.
“When the polarity changes, a more intense electron avalanche occurs”
due to the higher voltage drop across the gap
from the previously charged dielectric,
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4. University of Michigan Institute for Plasma Science & Engr.
MICRO-DBDs
Microplasmas (10s to 100s m) are interesting for planar current sources due to the ability of fabricating large arrays.
Non-arcing, micro-DBDs (mDBDs) using rf voltages are attractive for these arrays due to inexpensive mass production or area-selective modification.
“Microplasma stamps” based on mDBDs are applied to area-selective surface modification at atmospheric pressure.
These tens to hundreds “of” microns of micro-plasma are interesting
for planar current sources due to its ability to
fabricate large arrays.
So the non-arcing micro-DBDs using rf voltages are attractive
for these arrays due to inexpensive mass production.
Here is an application.
Based on the principle of mDBDs, this micro-plasma stamp
is applied to area-selective surface modification at
atmosphe’ric pressure. The plasma is formed
in the cavities which are generated
between the micro-plasma stamp and
the substrate to be treated by compression.
Ref: J. Phys. D: Appl. Phys. 41, (2008)
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5. University of Michigan Institute for Plasma Science & Engr.
SCALING OF MICRO-DBDs
At atmospheric pressure, plasma formation and decay times can be a few ns whereas the rf period is 10s to 100s ns – the mDBD may need to be re-ignited with each cycle.
Electron extraction from the mDBD may require a third electrode and so the structure, electron emitting properties and dynamics are important to the operation.
We have computationally investigated the extraction of electron current from mDBDs:
Geometry
Frequency
Gas mixture
However, at atmospheric pressure, the plasma formation and decay times
can be “only” few ns whereas the rf period is 10s to 100s “of” ns;
which means the mDBDs need to be re-ignited with each cycle.
Furthermore, electron extraction from the mDBDs may require a third electrode,
so the structure, electron “emission” and plasma dynamics
are important to the operation.
In our study, we have computationally investigated the extraction of electron currents
from the mDBDs by varying frequencies, gas mixture, and geometry
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6. MODELING PLATFORM: nonPDPSIM
Poisson’s equation:
Transport of charged species:
Surface Charge:
Electron Temperature
Radiation transport and photoionization:
The model we “are using” in the investigation, nonPDPSIM, is shown here.
The fundamental equations for charged species are
poisson’s equation for electric potential,
“the” continuity equation for the transport of charged species
and “the” surface charge balance equation.
The electron temperature is obtained” by solving the
electron energy equation”
after the charge density and potential” have been updated”,
Radiation transport is addressed using a Green’s function approach.
S(Te) is “the” energy source J ot E, and L(Te) is “the” energy loss
due to inelastic collision.
Xxx in div.() is the flux density of electron energy,
kappa is “the” electron thermal conductivity
The equations are integrated using Newton-Raphson method.
“The” Scharfetter-Gummel(銷非特兒 辜摸) form is used for electron and ion flux.
The electron transport coefficient and rate coefficient for bulk electrons as a function of
electron temperature are obtained by solving Boltzmann equation
for the electron energy distribution. Although the electron energy
distribution is not a Maxwellian, we still refer Te=2/3 * average electron energy.
G is the probability of survival of the emitted photon and divergence of its flux between
emission and ionization.
A is the Einstein coefficient.
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7. University of Michigan Institute for Plasma Science & Engr.
mDBD GEOMETRY
The mDBD is a “sandwich” cylindrical geometry.
rf electrode buried in printed-circuit-board
Grounded electrode separated from rf by dielectric sheet – 35 m hole.
Biased extraction electrode across a gap of 500 m
rf: 1.4 kV at MHz.
Extraction: 1-2 kV, ballasted (Rb= 100 kΩ) to prevent arcing or run away current
The model geometry is shown here.
The mDBD is a sandwich structure and “has” cylindrical symmetry.
The rf electrode is buried in “the” printed circuit board.
A grounded electrode “is” separated from “the” rf electrode by a dielectric sheet,
with “an” opening of 35 microns in the center.
A biased extraction electrode is separated by a gap of 500 microns.
The voltage applied to “the” rf electrode is 1.4 kilo-volt at 10 to 25 MHz.
A one or 2 kilo-volt voltage and 100 kilo-ohm ballast resistor connected to
“the” bias electrode are to extract current and
“to” prevent arcing or run-away current.
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8. mDBD N2 (1 atm): SURFACE CHARGE, [e]
 (-2x1016~2x1016 cm-3)
 [e] (5x1015 cm-3, 3 dec)
 [e] (1016 cm-3, 6 dec)
Vrf= 1.4 kV, 25 MHz, 1 kV bias
Vrf=+1.4 kV: Avalanche in mDBD cavity. Electrons charge dielectric negatively.
Vrf= 0: Biased electrode extracts electrons from cavity.
Vrf=-1.4 kV: Positively charged dielectric reduces voltage drop.
Vrf= 0: E-plume extinguishes. e-flux neutralizes positively charged dielectric.
(case_97;icops2010_pdpsim_total_nezoom_ne;timeframe=560(280ns)~640(320ns)
=last cycle I have;size=1353x673);Left: linear scale,middle: log sclae, right: log scale,
Here is the simulation results of atmospheric nitrogen plasma.
The animation on the left is the total charge density, and the middle and right
are electron density.
The rf votage of 1.4 kilo-volt at 25 MHz is shown in the bottom of the animation.
On the top is “a” 1 kilo-volt bias voltage.
At the “positive” peak of the rf vooltage, the grounded electrode acts as a cathode
to enable the avalanche to occur in the mDBD cavity.
Electrons charge to the dielectric negatively.
As the rf voltage decreases to zero, no net potential “is applied”
other than that produced by the negative charge on the dielectric.
electrons are extracted from the cavity,
Even before” the negative peak of rf voltage
the electron plume “has already reached” its greatest extent,
sufficient ions have been collected on the dielectric
“which” reduces the net voltage drop
“The” electron plume begins to diminish.
As the rf voltage returns to zero, net voltage across the gap is sufficiently small
due to the positive charges the dielectric,
electron plume is attracted to the dielectric and extinguished.
This electron flux neutralize the positive charged dielectric.
MIN MAX
University of Michigan
Institute for Plasma Science & Engr.
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Animation Slide-GIF

9. mDBD N2 (1 atm): E/N, Te, BULK IONIZATION
E/N (40~4000 Td)
 Te (0.1~15 eV)
 [Se] (1024 cm-3 s-1, 12dec)
(case_97;icops2010_pdpsim_EN_TE_SEIMPACT;timeframe=560(280ns)~640(320ns);
size=1352x670)
We can see the plasma “is” nearly extinguished every cycle “from the previous slide”,
hence it requires re-initiation “each time”.
The animations here are E/N on the left, electron temperature “in” the middle
and electron sources due to electron impact ionizations in bulk plasma
on the right.
When the electrons are extracted or recombined, larger E/N occurs at “the” zero crossing
of rf voltage due to the previously charged dielectric,
higher E/N increases the electron temperature and
electron impact ionization.
When the electrons are attracted to the cavity, the conductive plasma
shields out the electric field and lower the E/N and reduce the
ionization in the cavity.
Ionization reaction, threshold energy for ionizaiton:
E + N2 > N2^ + E + E; threshold energy=15.5 ev
E + N2V > N2^ + E + E; ev
E + N2* > N2^ + E + E ; ev
When electrons recombine or are extracted, larger E/N occurs at zero-crossing of Vrf due to previously charging of dielectric. Te and Se follow E/N.
Conductive plasma shields out electric field and lowers E/N which reduces ionization in the cavity.
MIN MAX
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_June2010_p8
Animation Slide-GIF

10. mDBD N2 (1 atm): Te, Ssec, N2**
 Te (0.1~15 eV)
Ssec (1025 cm-3s-1, 4dec)
 N2** (1016 cm-3, 5dec)
(case_97;icops2010_pdpsim_TE_SEMCS_NStarStar;timeframe=560(280ns)~640(320ns);
size=1352x671)
In addition to electron impact ionization in the bulk plasma, ionization from secondary
electrons is in the middle, and Nitrogen excited state density is on the right,
and the electron temperature is repeated on the left.
We find that ionization from secondary electrons is commensurate with bulk ionization
which is up to 10 to the 24.
The secondary electrons alternately come from “the” electrode
or “the” dielectric.
Also, the long lived(/I/) excited states of nitrogen facilitate re-ignition
by production of UV photons that seed the secondary electrons at surface
until “the potential is favorable” to generate plasma.
Excited state N2** reaction:
E + N2 > N2** + E; ev
E + N2** > N2 + E; ev
N2** > N : 1.00D+08 [ 0.0 ] 0.00E+00 ! 2 $0& 0. # 0. % => decay time=10 ns (1/(1.00D+08))
N2** > N2* : 1.00D+08 [ 0.0 ] 0.00E+00 ! 2 $0& 0. # 0. % => decay time=10 ns
Ionizations from secondary “beam” electrons are commensurate with bulk ionization. Secondary electrons alternately come from electrode or dielectric.
Long lived excited states of N2 facilitate re-ignition by production of UV photons that seed the secondary electrons at surfaces.
MIN MAX
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_June2010_p9
Animation Slide-GIF

11. mDBD N2 (1 atm): IONIZATION SOURCE, [e]
[Se] (1025 cm-3s-1, 7 dec)
 [e] (1016 cm-3, 7 dec)
Re-ignition is by avalanche by small residual electrons remaining in the plasma – and photo-electrons from surfaces.
+1 kV extraction does not produce sufficient net electron impact ionization across gap. Plasma is ignited in the mDBD cavity and extracted.
(case_97;icops2010_pdpsim_ne_&_Seimpact;timeframe=560(280ns)~640(320ns);
size=902x673)
We have seen the ionization in the cavity, “but” do we also have similar ionization
sources in the gap?
The electron sources due to electron impact ionization and electron density
are shown on the left and right
For 1KV on “the” top electrode, it is not enough to produce sufficient net electron impact
ionization across the gap.
So the plasma is ignited in the mDBD cavity and extracted.
MIN MAX
University of Michigan
Institute for Plasma Science & Engr.
Animation Slide-GIF
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12. ELECTRON CURRENT EXTRACTION vs FREQUENCY
25MHz
20MHz
Top Electrode Voltage
Top Electrode Current
Vrf = 1.4 kV, MHz, 2 kV bias and ballast resistor 100 kΩ
Peak currents collected at top electrode tend to increase with increasing frequency.
The higher the frequency, the narrower the current pulse.
rf Voltage
15MHz
10MHz
(Case_146(25MHZ)~149(10MHz); icops2010_pdpsim_cir_con, size=600x?;
last 2 cycles; icops2010_pdpsim_cir_con_case146_case_147_case_148_case_149.tif)
I-V characteristics were investigated for rf frequencies of MHz
in atmospheric nitrogen plasma.
A 1.4 kV rf voltage, and “a” 2kV bias potential and 100 kohm ballast resistor are applied
to “the” top electrode.
Traces are shown for the rf voltage, and voltage and current on the top electrode.
The peak current collected on the top electrode is between 1.5 to 2 mA per pulse
with a trend of higher currents at higher frequencies.
Also, we find that the higher the frequency, the narrower the current pulse.
Although the top electrode is applied with a 2KV dc voltage, the ballast resistor
produces small dips in the applied voltage across the gap.
There is a transient in current peaking on the first pulse
which is due to the initial conditions and consequences of
suddenly applying voltage, followed by the pulse-to-pulse increase
“in” current until it reaches a quasi-steady state.
There are pulse-to-pulse variations that is due to the “statistical” nature of MCS
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13. University of Michigan Institute for Plasma Science & Engr.
CHARGE PER PULSE
Case_149\presentation\icops2010_146_147_148_149_coulomb_per_pulse.TIF
Here is the charge per pulse versus pulse number.
Due to the positive ions “accumulating” in the gap over time,
the extraction field is enhanced.
“This is” the reason for charge per pulse to increase over time.
However, charge collected on “the” top electrode gradually reaches a steady state
when the field enhancement by the increasing positive ions balance
the decay due to recombination per pulse.
The first pulse is not shown here, that’s because the charge is
affected by the initial condition.
25MHz x10^-11
20MHz x10^-11
15MHz x10^-11
10MHz x10^11
Positive ion accumulation in gap over time increase extraction field.
Charge collected on top electrode gradually reaches a steady state when the field enhancement by the increasing positive ions balance the decay due to recombination per pulse.
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14. AVERAGED CHARGE PER CULSE vs FREQUENCY
icops2010_146_147_148_149_average_coulomb_per_pulse_vs_frequency.TIF
icops2010_146_147_148_14_FWHM.TIF (last pulse)
The figures shows here on the left and right are
average charge per pulse and width.
By averaging the last 3 charges per pulse, we found that
the averaged charge per pulse collected on the top electrode increases
at higher frequency due to “a/the” larger dV/dt.
However, the width is shorter at higher frequency
due to the more rapid charging of dielectric.
The trend is likely attributed to the “overshoot” of quasi-steady state conditions
that are enabled by the larger dV/dt of the high frequency
wave form. (?? Current or just pre-current?)
The current width is about half of the period
(measured from the beginning of the current).
(base to base)
Averaged charge per pulse collected on top electrode increases at higher frequency due to larger dV/dt.
Shorter pulse width at higher frequency due to more rapid charging of dielectric
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15. University of Michigan Institute for Plasma Science & Engr.
CONCLUDING REMARKS
Two modes of operation:
Low extraction voltage: Little ionization in gap and charge is extracted from cavity.
High extraction voltage: Charge from cavity seeds avalanche in gap.
Long lived excited states facilitate re-ignition by production of UV photons which continuously seed the secondary electrons at surface.
Peak currents collected at top electrode (10-25MHz) tend to increase with frequency with narrower pulses.
Average charge per pulse collected on top electrode increases with rf frequency (10-25 MHz)
In summary:
2 modes of operation are investigated:
for the low extraction voltage, little ionization is in “the” gap and
charge is extracted from the cavity.
for the high extraction voltage, charges from the cavity seed the avalanche
in gap.
Also, the long lived excited states facilitate re-ignition by production of UV photons
which continuously seed the secondary electrons at “the” surface
until the potential is favorable to generate plasma.
Furthermore, Peak currents collected at “the” top electrode at 10 to 25 MHz
tend to increase with frequency with narrower pulses.
Finally, the average charge per pulse collected on top electrode increases
with rf frequency at 10 to 25 MHz
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