J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Optimization Input Power to Obtain the Stable Annealing Conditions of a
Plasma Annealing System at Atmospheric Pressure
N. Dam TRAN, Toru SASAKI, Takashi KIKUCHI, Nob. HARADA
Plasma Laboratory, Department of Electrical Engineering, Nagaoka University of Technology
1603-1 Kamitomioka Nagaoka, Niigata, 940-2188, Japan(Received: 30 October 2009 / Accepted: 2 June 2010)

We investigated one-step, rapidly cleaning, and annealing thin wire copper using plasma generated byDielectric-Barrier Discharge (DBD) at atmospheric pressure in a coaxial cylindrical reactor. The thin copper wire
cleaning and annealing processes strongly depend on the input power, the dimensions of the reactor, and theannealing duration. The minimum input power was calculated under stable annealing conditions. When obtaining
the conditions, an equivalent RLC circuit model was obtained by analyzing the sheath dynamics and power loss tothe ions, electrons, and heating dielectrics during high frequency, high voltage in helium. In addition, the plasma
parameters and the power balance in this system were considered. To demonstrate the optimal absorbed power forthe plasma annealing system for the analysis model, comparisons of absorbed power, surface temperature of copper
wire, and RMS current and voltage between the analysis model and experiments were investigated. For optimal
problems, minimal absorbed power is an objective function. The design parameters were electrical efficiencies(voltage, current, frequency, and a power factor), the dimensions of reactor (the diameter of the thin wire, thedischarge gap, and the discharge length), and the duration of the annealing. The inequality constraint was thebreakdown discharge conditions. The equality constraints were a stable temperature for the annealing and rapid
annealing conditions. The optimization results at the smallest absorbed power showed that the 0.2 mm diametercopper wire was annealed at a 20% elongation rate in the plasma reactor at an annealing velocity of 0.714 m/s.
Keywords: Annealing index, Dielectric-Barrier Discharge (DBD), optimal problem, equivalent circuit, sheath
dynamic.
Section 4.1. To meet the annealing conditions, the source
heating from the plasma discharge must be equal to thesink heating due to conduction to the copper wire and theoutside environment. This equal constraint is shown in
Section 4.2. The annealing index represents the rapid
annealing condition, one of the important conditions ofthin wire annealing. It is a constant, represented for each
property material, which performs at different temperatures
and times but achieves the same elongation. Section 4.3
shows how to choose the temperature and time ofannealing, with Section 4.4 showing the breakdown
discharge condition, and that the magnitude of the input
voltage is greater than the breakdown discharge voltage
during annealing. Comparison with experiments confirms
the results of the optimal calculations and this is shown in
Sections 3.2 and 6.

1. Introduction
The atmospheric-pressure plasma generated byDielectric-Barrier Discharge (DBD) is widely applied in
manufacturing such as ozone production, cleaning, surface
modification, deposition and sterilization [1-5]. In ourprevious study, the cylindrical DBD plasma in helium gas
was applied for rapidly cleaning and annealing thin copper
wire [6, 7]. As it functions, a bombardment of ions on thewire surface, collisions between electrons and neutral
particles, and sheath dynamics rapidly heat, clean, pickle,
deoxidize, and polish the wire surface. The cleaning andannealing processes strongly depend on the input power
and the dimensions of both the reactor and the dielectric. In
this paper, we found the minimum input power of thisannealing system to satisfy a rapid annealing condition.
The plasma discharges in a cylindrical DBD withlength l, inner radius r1, outer radius r2, a discharge
effective cross sectional area Aeff, and an effective
diameter deff of plasma bulk are
A   πr  r   πlr  r ,d 



A

.

2. Experiment setup
Reactor(1)
Impac IGAR12-LO(2)

ElectrodeTo analyze the power loss to the ions and electrons in
the reactor, we must calculate the minimal input power byusing the minimal conditions at each element, shown inControl Panel 1Ga
Tan

Control Panel 2

Power Supply

Fig. 1 Experimental setup for plasma wire annealing.

Author’s e-mail: tndam@stn.nagaokaut.ac.jp503©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

N.D. Tran et al., Optimization Input Power to Obtain the Stable Annealing Conditions of a Plasma Annealing System at Atmospheric Pressure

We propose an experiment where the annealing andcleaning processes can be simultaneously operated byusing discharge plasma with a coaxial cylindrical DBD
reactor in atmospheric pressure. Fig. 1 shows a schematicof the annealing system. The system was composed of agas tank, a carrier with control panel 1, a power supply
with control panel 2, a plasma reactor, and Impac
IGAR12-LO equipment for measuring the surface
temperature of the copper wire in the reactor. The gas tankis used to supply helium with reconstituted air (purity >99.9%). The gas is fed into reactor under a controlled ﬂow
rate. The air was purged before plasma treatment. Control
panel 2 controlled the voltage and the frequency. The
reactor is constructed by a cylindrical dielectric inside athin cylindrical aluminum electrode as shown in Fig. 2.
The outer electrode, connected to a high power, is wrappedaround the dielectric. The inner electrode, connected to theground, is a copper wire, carried in the centre of reactor bya carrier.

physical discharge configuration: (1) dielectric wall, (2)dynamic sheaths and (3) plasma bulk.
When the sheath fully expands on one side andshrinks on the other side, the current at the expanded sideis the displacement current and the current at the shrankside is the conduction current. Here we assume that the
thickness of each sheath is the Child-Langmuir sheathmodel [8, 9]. In sheath dynamics, the power dissipationof the oscillation sheath heating is connected tooscillation resistances, Rsoa,b (a and b are the indices forthe positions near the copper wire and dielectric,
respectively). The sheath layers are connected to thesheath capacitances, Csa,b. The ion current in sheath, Ii isparallel to the electron current, Ie. At the dielectric, theadmittance of the dielectric is connected to the parallel ofthe dielectric capacitance, Cd and the dielectric heating
resistivity, Rd. At the bulk plasma, the admittance of thebulk plasma is connected to the parallel combination of
the series, Lp and Rp, with cylindrical space capacitance,
Cp. The diodes, Da and Db, are used to specify the sign ofthe input voltage. The gas capacitance of the reactor
before discharging is also connected to the parallel Cg.
The expressions for equivalent electrical elements areshown as follows.
For long time scale and high plasma density, thedynamic sheath radius, rs and ion current, Ii flowing
between two electrodes are obtained [10] by

Fig. 2 The cylindrical DBD reactor.



3. Model analysis
3.1. Equivalent circuit model

I 



   ε  M    ,





(3)

 

  ε  M  





,

(4)

where V(t) is the applied voltage, ne is the electron
number density, ε0 is the free-space permittivity, M is theion mass, rs and rt are the sheath and electrode radius,
respectively, and β is the tabulated function oftime-varying ratio, rs/rt expressed by the infinite series
 













 ,

(5)

where      .
Assuming that all the ions in the sheath are implanted
to the cathode surface and that the cathode is heated tothe annealing temperature, the ion heating power is thenFig. 3 Equivalent circuit model.
The circuit model reflects the physical structure of thecylindrical DBD reactor. The combination between series
and parallel circuit models is equivalent to the total
reactor impedance. During the first half cycle of theapplied high voltage, the thin copper wire is the cathode,the electrons are driven away, and the ions areaccelerated into the cathode. Electrons move faster thanions, leaving the ions behind to form an ion sheath layer
near the copper wire. The sheath edge is extended to thecentre by extracting new ions from the plasma. The same
situation occurs in the second half cycle, where the ion
sheath layer is formed near the dielectric. The plasma
bulk is formed between the sheaths. A RLC electricalcircuit models the plasma bulk, sheaths, and dielectric.
Fig. 3 shows three main parts of the correspondingP  tI .

(6)

From the dynamic sheath thickness, S = rs - rt we canassume that the sheath capacitance in atmosphericpressure isC  .ε     .




(7)

Under high frequency voltage, the sheath stretches
and shrinks near an electrode with a high frequency. The
oscillating sheath randomly heats the electron withstochastic power, Pso [11]. The equivalent oscillating
sheath resistance is504

N.D. Tran et al., Optimization Input Power to Obtain the Stable Annealing Conditions of a Plasma Annealing System at Atmospheric Pressure

R   S  A,

R    A ,

L 




 C

P



,(19)

P   V I  


 



  Vt dt


(11)

1/2





  It dt


.

(20)

results  

,

(12)






  

,




(13)

  

,





















a. Irms(A) from experimenta. Irms(A) from modelb. Pabs(kW) from experimentb. Pabs(kW) from modelc. 1000xTw from experimentc. 1000xTw from modelFig. 4 Comparisons of absorbed power, surface temperature ofcopper wire, RMS current and RMS voltage between theanalysis model and the experiment.

where A is the dielectric area, d is the dielectric thickness,tanδ is the loss tangent, and εr is the relative permittivityof the dielectric material.
The capacitance of the coaxial reactor, Cg before
discharge is simplified to the capacitance of a cylindricalgeometry




 





(14)

C   k    ,









 



where ra and rb are the inner and outer radius of thedielectric, respectively, and kd is the dielectric material
constant.
Power lost due to dielectric heating, Pd [12] isconnected to the equivalent dielectric heating, Rd. This
resistance is in parallel with the dielectric capacitance
A

(18)



cosθ   P

where wpe= (e ne/ε0m) is the electron plasma frequency.
The capacitance of the cylindrical geometry dielectric,
Cd isR  

P   VtItdt,
3.2. Comparison of numerical with experimental,C   k (17)where V(t) and I(t) are the voltage and current waveforms
obtained from an oscilloscope. The V-I phase differencecos(θ) and the apparent power in the plasma are(10)C  C  2V

where vm is the electron-neutral collision frequency.
The admittance of bulk plasma leads to an equivalent
RLC. This admittance is the parallel combination of theseries, Lp and Rp, with the cylindrical space capacitance,
Cp [11],R    L ,   I  sinθ,


(9)



(16)

I

where ve = (8eTe/πm)1/2 is the mean electron speed, m isthe electron mass, and Te is the electron temperature.
When plasma is generated, the characteristics of theplasma bulk are same as a resistor with plasma resistivity.
The ohmic heating power, Pohm [11] leading to theequivalent ohmic heating resistivity is 

VR    cosθ,(8)The plasma annealing reactor shown in Fig. 2 ismodeled as an equivalent circuit shown in Fig. 3. For
comparison of numerical calculations with experimentresults, the geometry of the reactor is constructed byusing a cylindrical dielectric inside a thin cylindricalaluminum electrode. The outer electrode (15 mm
in-diameter, 0.25 mm thick, and 60 mm long wrappedaround the dielectric) is connected to the high power(20[kV p-p], 2[A p-p] and 45[kHz]). The dielectricbarrier discharge is a quartz tube (10 mm in-diameter, 2.5mm thickness, and 300 mm long). The inner electrode isthin copper wire of diameter 0.2 mm, connected to theground, and moved into the centre of reactor by carrier.
The used gas is helium. The ﬂow rate of gases was ﬁxed
to 5 l/min. The voltage and current (V(t), I(t)) aremeasured in real time by an oscilloscope. Impac
IGAR12-LO equipment is used to measure the surface(15)

where kg is the dielectric gas constant, and r1 and r2 are
the inner and outer radius of the reactor, respectively.
From the equivalent circuit shown in Fig. 3, thecomplex impedance of the discharge is Z = R + jX. The, and the plasma
absorbed power is   
parameters (vm, Te and ne) are obtained from the following
three equations505

N.D. Tran et al., Optimization Input Power to Obtain the Stable Annealing Conditions of a Plasma Annealing System at Atmospheric Pressure

time ∆t, annealing volume, ∆V, and increasing temperature,∆Tw in the wire is described bytemperature of the copper wire in the reactor. We use theinput RMS voltage, Vrms as a parameter to compare theabsorbed power, Pabs, the RMS current, Irms and the wire
surface temperature, Tw between the analysis model andthe experiments. The wire surface temperature is calculatedby the balance power in the reactor as shown in Eq. 26.
Figure 4 shows the results of power loss, surface
temperature of copper wire, and RMS current and voltage
between the analysis model and the experiments. The
results indicate that the absorbed power and surface
temperature of the copper wire from the experiments andthe analysis model are similar. We can conclude that theanalysis model is acceptable for the optimal problem.



   ABε   A  A








 I ,  
 



  

.

(25)

P  P  P .

(26)

4.3. Rapid annealing condition
The purpose of annealing is to use temperature to
overcome the activation energy, Q of the thin wire after
cold working. The annealing process, which was
performed at different temperatures and durations but
achieved the same result, is called the annealing index I[14], and is calculated by
I



.

 QRT dt,

ln  e(27)

where Q is the activation energy for recrystallization, R is
the universal gas constant, t is annealing duration and Tw is
the annealing temperature. Depending on material
recrystallization or physical properties, the annealing index
can be related. Associated with the specific degree of cold
working, the activation energy for recystallization can be
related to(21)

I  l t 

The source and sink heating are the balance of theannealing temperature of the copper wire and must be
equal. The source heating is generated by ions bombarding
the surface. The sink heating conducts to both the copper
wire and the environment. In one cycle input voltage, theions bombard the surface of copper wire in only half thecycle. In this half cycle, the plasma discharge only happens
when the input voltage is greater than the breakdown
voltage, Vb. Assume that all ions in the sheath implanted
into the copper surface create the ion source heating,described byT T

The balance power in the reactor is

4.2. Power balance for annealing



(24)

P 

where uB = (eTe/M)1/2 is the Bohm velocity of ions, ω =2πf is the angular frequency, f is frequency of the applied
voltage, and Ain and Aout are the cross sectional areas ofthe sheaths.

P   VtI   Vt  ε  M

P   2Πvr  ∆T ,where v is velocity of copper wire.
The power dissipated by conduction to air at an
ambient temperature is calculated by measuring thetemperature difference between the copper wire and theoutside electrode Tout[13]The losses due to internal power loss, Bremsstrahlung,and atomic line radiation are negligible because of thevery small power comparisons with the absorbed power.
The time-averaged absorbed power, Pabs, by both electrons
and ions must be equal to the average dissipated power.
The power dissipation to the ions is Psi. The total power
dissipation to the electrons is a nonlinear sheath oscillating
power at the inner and outer electrodes (Psoa, Psob), ohmic
heating power (Pohm), and dielectric heating power (Pd). In
this paper, the dielectric heating power was ignored
because proper choosing of a dielectric material canminimize it [12]. The absorbed power, Pabs is calculatedusing the following equation [11],  A

(23)

where Cv is the specific heat capacity, ρ is the density, andTw is the temperature of wire surface. The power loss tothe copper wire is rewritten as

4. Optimal analyses
4.1. Minimum input power analysis

P  n P ∆t   ∆V∆T ,2.6

Q.RT

.

(28)

elongation rate 15%

2.5ln(1/t)

2.4
2.3
2.2
2.1
2

, (22)

1.9
1.08

when    .
The power loss to the copper wire during annealing

1.1

1.12

1.14
1.16
1/Tw

1.18

Fig. 5 A plot of 1/Tw versus ln(1/t)

506

1.2
-3

x 10

N.D. Tran et al., Optimization Input Power to Obtain the Stable Annealing Conditions of a Plasma Annealing System at Atmospheric Pressure

From experiments, the activation energy (Q =5.17x104 kcal/mol) of material recrystallization associatedwith the cold working condition of the copper wire can beobtained by plotting data as 1/Tw versus ln(1/t) for an
elongation rate of 15% in helium. The copper wire is
carried through the plasma reactor with velocities of 25
m/min and 50 m/min and temperatures of 923 K and 827 K,
respectively. Fig. 5 shows the slope of a linear regression
through the above data. The index annealing of the copper
wire annealing at temperature 600°C and duration 0.144 s
is I = -4. From equation (28), two parameters (t,  ) areconsidered, and I and Q are constant.

  

where




,


A    








  A

 x  6,          ,
  ,  



A 

(29)

(31)

(32)



 P P P

 



(30)

   (29)

 x5, (33)

,

Q



(34)

and the upper and lower boundary condition of X are,where A and B are determined by experiment [14]. For
helium, A = 3[1/cmTorr], B = 34[V/cmTorr], and γ = 0.3.

Xlb = [0.0001;0.0005;0.01;0.007;5000;0.01;9000;0.2;0.2], (35)4.5. Mathematical optimal equation         ,       Experiments verified the breakdown voltage of thereactor (Vb) and this voltage is called the Paschen curves.
This voltage depends on the pressure, the discharge gap,
the dimensions of reactor, the gas type and the secondary
electron emission coefficient, γ. The discharge condition isthat the input voltage must be greater than the breakdown
voltage     A

with constraints

4.4. Breakdown discharge conditionsx5     BA
Min P  Min  
 A

Xub = [0.0001; 0.1; 4; 0.2; 12000;5; 50000; 3; 0.9].



Table 1.

(36)

The design parameters of the cylindrical
DBD reactor plasma for the wire annealing.















  





Fig. 6 Cylindrical DBD reactor with design parameters

Parametersx(1)[m]x(2)[m]x(3)[m]x(4)[m]x(5)[V]x(6)[A]x(7)[Hz]x(8)[m/s]x(9)The objective function of the mathematical optimal
equations (Eq. 29) is the minimum absorbed power of theplasma reactor, shown in Fig. 6, where the design
parameter, X(i), i = 1-9, is shown in Table 1. The nonlinear
inequality constraint is the breakdown discharge condition,and the nonlinear equality constraints are the rapid
annealing condition and the heating balance annealing. The
boundary inequality constraints are the discharge gap anddielectric thickness. The mathematical optimal equations
areX

Description
Inside radius of reactor
Outside radius of reactor
Length of reactor
Outside radius of dielectric
RMS Input voltage
RMS Input current
Input frequency
Velocity of carrier
Power factor

5. Optimal results and discussion
The reactor is supplied by helium with a thermal
conduction of 0.142 W/mK and constructed by acylindrical quartz dielectric inside a thin cylindricalaluminum electrode. The secondary electron emission
coefficient is chosen as γ = 0.3. Based on experiment, theannealing index of the activation energy 5.17x104 kcal/mol,
is -4, the universal gas constant is 8.314, and the annealing
temperature, Tw = 600°C. The result of the design507

N.D. Tran et al., Optimization Input Power to Obtain the Stable Annealing Conditions of a Plasma Annealing System at Atmospheric Pressure

cylindrical DBD. The annealing temperature generated by
the ion heating power in the analysis model is similar tothe one measured from the experiments, which
demonstrates that the analysis model represents anannealing reactor. From the optimal calculations, thedimensions of the coaxial cylindrical DBD plasma wererecalculated to meet the discharge conditions. The
velocity of the copper wire in reactor was also calculated
to satisfy the rapid annealing condition. The mostimportant finding of this study is that with minimum
input power, the annealing conditions of the present
plasma annealing system at atmospheric pressure can still
be guaranteed.

parameters from optimal calculation are
X = [0.0001; 0.005; 0.0833; 0.0075; 4,540; 0.2915; 45000;
0.714; 0.6844].
and the absorbed power, Pabs = 905 W. This result showsthat to anneal a 0.2 mm diameter copper wire with a 0.417
m/s carrier speed and an elongation rate greater than 20%,
we have to setup the dimensions of the reactor as follows:
outside radius 5 mm; length 83 mm; outside radiusdielectric 7.5 mm; RMS input voltage power supply 4,540
V; RMS input current 0.291 A; and 45,000 Hz frequency.
For a plasma annealing system in reality, an impedancemismatch must prevent the reﬂected power from theplasma reactor back to the power supply. The power
factor of the system is the data to design a parallelmatching network with a plasma reactor. The carrier
velocity and the length of the reactor are proportional andare parameters of the constant index annealing function.
If we want to increase outcome product, we have toincrease the length of reactor.

8. References
Ulrich Kogelschatz, Plasma Chem. Plasma Process. 23, 1(2003).
[2] Yu.V. Filippov and Yu.M. Emelýanov, Russ. J. Phys.
Chem. , 32-12, 2817 (1958).
[3] J.Y. Jeong, S.E. Babayan, V.J. Tu, J. Park, I. Henins, R.F.
Hicks and G.S. Selwyn, Plasma Sources Sci. Technol. 7,282 (1998).
[4] S.E. Babayan, J.Y. Jeong, V.J. Tu, J. Park, G.S. Selwyn
and R.F. Hicks, Plasma Sources Sci. Technol. 7, 286(1998).
[5] M. Koide, T. Horiuchi, T. Inushima, B.J. Lee, M.
Tobayama and H. Koinuma, Thin Solid Films. 316, 65(1998).
[6] T. Nakamura, Ch. Buttapeng, S. Furuya, N. Harada: 2ndIEEE international conference on power and energy(PECon 08) December 1-3, 2008, Johor Baharu, Malaysia.
[7] T. Nakamura, Ch. Buttapeng, S. Furuya, N. Harada:
VASSCAA-4. 256-4, 1096 (2009).
[8] C. D. Child, Phys. Rev.. 32-5, 492 (1911).
[9] I. Langmuir, Phys. Rev.. 33-6, 954 (1929).
[10] Scheuer, J. T., Shamim, M., and Conrad, J. R., J. Appl.
Phys., 67-3: 1241 (1990).
[11] M. A. Liberman and A. J. Lichtenberg, Principles of
Plasma Discharges and Materials Processing. New York:
Wiley, 1994.
[12] J. Reece Roth and Xin Dai, AIAA , 1203, 6 (2006).
[13] H. Sadat, N.Dubus et al., Applied Thermal Engineering, 29,
1259 (2009).
[14] F.F.Kraft, R.N. Wright, and M.K. Jensen, JMEPEG, 5, 213(1996).
[1]

6. Comparable results and discussions
Table 2 shows the comparison between the results ofthe experiments and the optimal calculation at the same
initial conditions, with experiment parameters: gas type He,
dielectric material BN, gas flow rate 5 l/min, dielectric
thickness 2.5 mm, gap length 5 mm, reactor length 60 mm
and frequency 45 kHz. At the same initial conditions, we
obtained the same design parameters: electricalefficiencies (voltage, current, and frequency), dimensionof both reactor and dielectric, annealing duration, andpower loss. Again, we can conclude that the analysis
model is useful for the optimal analysis.
Table 2. The result of design parameters from optimal
calculation and from experiment.
ParametersXGasx(1)[m]x(2)[m]x(3)[m]x(4)[m]x(5)[V]x(6)[A]x(7)[Hz]x(8)[m/s]
x(9)Pabs[Watt]

ExperimentHe
0.0001
0.005
0.06
0.0075
5540
0.278
45000
0.416
0.679
1006

Optimalcalculation
He
0.0001
0.005
0.05
0.0075
5540
0.26
45000
0.416
0.679
1000

7. Conclusions
In summary, the characteristics of annealing bycylindrical DBD were investigated by analyzing thesheath dynamics and the power loss to ions and electrons
during high frequency and high voltage in helium. A RLC
equivalent circuit modeled the physical structure of the508