**4.1. Discharge mechanism**

The moving of electron and ion in the reactor leads to the discharge current behaviors. Figure 15 shows the reflection of discharge current on the applied voltage 9 kV of Al2O3 dielectric. At the beginning of the discharge, when increasing the increment of the applied voltage, dV/dt > 0, the discharge current crossing the discharge gap increases. The electrons and ions run instantaneously toward anode and cathode and deposit on them to form two space charges. The internal electric field generated by separation of electron and ion space charge. This electric field increases with the increment of applied voltage and is reversely proportional to external electric field. When the incremental applied voltage reaches the peak, dV/dt = 0, the discharge current (displacement current) crossing the discharge gap is zero and the internal electric field reaches maximum, the reverse current is formed. When dV/dt < 0, the reverse current exists until the applied voltage reaches the local bottom value (dV/dt = 0). The process starts again with the same situation when the instant voltage increases again. From experiment, the currents profile of discharge gases is an invariant sine profile and the total current becomes very broad due to the dominant of displacement current. The behavior of voltage-current in the cylindrical APDBD discharge is the same as that of a series RLC circuit.

The discharge characteristics of the annealing system are represented by the total discharge current, which includes the total of displacement current and the conduction current. From Figure 15, the negative current cycle has higher and shaper peak current than that positive one, that leads to the conclusion that the conduction current at negative cycle is higher than that at positive cycle. It is also shown that the phase different between total current waveform and voltage waveform is almost 90°, which indicate that the displacement current takes up large scale value in the total current. The small conduction current in APDBD is because of high resistivity of dielectric. Figure 15 also shows the changing of displacement current (sine shaped profile) and conduction current (narrow peaks) when increasing applied voltage. As shown from the current waveform, in every haft cycle, the waveform has multi peaks and every peak has a sine shape profile during discharge. This characteristic is different from micro-discharge model (contain many very small, short-lived (nanoseconds), many current filaments). In our experiment, the currents profile of all three discharge gases is an invariant sine profile and total current becomes very broad due to the dominant of displacement current. Therefore, the cylindrical APDBD discharge with helium, argon or nitrogen can be modeled by an equivalent series RLC circuit.

**Figure 15.** Voltage and discharge current waveform of argon at 8.5 kV

#### **4.2. Equivalent circuit model**

192 Dielectric Material

**4. Equivalent circuit model** 

compare with that from experiment.

**4.1. Discharge mechanism** 

that of a series RLC circuit.

In this part, an equivalent circuit model is used to analyze the dependence of the thin copper wire annealing temperature on the dielectric in APDBD. From analysis model, the main factor that determines annealing temperature is the ion bombardment on the wire surface. The average temperature of the thin copper wire in APDBD reactor is calculated as a function of dielectric diameter, dielectric material, applied voltage, ion mass, and gas thermal conductivity. The effect of dielectric on annealing from analysis model is used to

The moving of electron and ion in the reactor leads to the discharge current behaviors. Figure 15 shows the reflection of discharge current on the applied voltage 9 kV of Al2O3 dielectric. At the beginning of the discharge, when increasing the increment of the applied voltage, dV/dt > 0, the discharge current crossing the discharge gap increases. The electrons and ions run instantaneously toward anode and cathode and deposit on them to form two space charges. The internal electric field generated by separation of electron and ion space charge. This electric field increases with the increment of applied voltage and is reversely proportional to external electric field. When the incremental applied voltage reaches the peak, dV/dt = 0, the discharge current (displacement current) crossing the discharge gap is zero and the internal electric field reaches maximum, the reverse current is formed. When dV/dt < 0, the reverse current exists until the applied voltage reaches the local bottom value (dV/dt = 0). The process starts again with the same situation when the instant voltage increases again. From experiment, the currents profile of discharge gases is an invariant sine profile and the total current becomes very broad due to the dominant of displacement current. The behavior of voltage-current in the cylindrical APDBD discharge is the same as

The discharge characteristics of the annealing system are represented by the total discharge current, which includes the total of displacement current and the conduction current. From Figure 15, the negative current cycle has higher and shaper peak current than that positive one, that leads to the conclusion that the conduction current at negative cycle is higher than that at positive cycle. It is also shown that the phase different between total current waveform and voltage waveform is almost 90°, which indicate that the displacement current takes up large scale value in the total current. The small conduction current in APDBD is because of high resistivity of dielectric. Figure 15 also shows the changing of displacement current (sine shaped profile) and conduction current (narrow peaks) when increasing applied voltage. As shown from the current waveform, in every haft cycle, the waveform has multi peaks and every peak has a sine shape profile during discharge. This characteristic is different from micro-discharge model (contain many very small, short-lived (nanoseconds), many current filaments). In our experiment, the currents profile of all three discharge gases is an invariant sine profile and total current becomes very broad due to the dominant of displacement current. Therefore, the cylindrical APDBD discharge with

helium, argon or nitrogen can be modeled by an equivalent series RLC circuit.

Combination between the discharge characteristics of plasma annealing and the reflected physical structure of the plasma reactor, the equivalent circuit model is formed as a RLC circuit in which the total impedance is the combination between series and parallel circuit model. The corresponding main physical part of discharge mechanism shows that plasma reactor can be divided into three parts: (1) dielectric wall, (2) dynamic sheathes and (3) plasma bulk as shown in Figure 16(a). The impedances of dielectric, ionization (Zp), and non ionization gas capacitance Cg are shown in Figure 16(b). The equivalent circuit model with impedances of dielectric, sheath and plasma bulk is shown in Figure 16(c). In that the impedance of the dielectric is the parallel combination of dielectric capacitance and dielectric heating resistance [32], the impedance of the sheath is the parallel combination of sheath capacitance and ion heating resistance which is presented by ion current in sheath, and the impedance of the plasma is the parallel combination of the Rp (only the ohm heating by streamer is considered) with the cylindrical space capacitance Cp [33]. The diodes, Da and Db, are used to specify the sign of the input voltage. The gas capacitance of the reactor before discharging is also connected to the parallel Cg.

Effect of Dielectric in a Plasma Annealing System at Atmospheric Pressure 195

(5)

(6)

(7)

where Vin(t) is the applied voltage, Iin(t) is the total discharge current, q is the charge of the ion, M is the ion mass, l is the length of the reactor, and ra, rb, rc and rs are thin wire radius, the dielectric inner and outer radii and sheath radius, β is a tabulated function of the timevarying ratio ra/rs, λ is the discharge gas thermal conductivity, f is the applied voltage frequency, v is the copper wire velocity, T0 is the copper wire temperature before coming into the plasma reactor, Cv is the specific heat capacity, ρ is the density, Aa and Ab is the cross-section of thin wire and dielectric, respectivity and Tw is the wire surface temperature. Zdie is the dielectric admittance and is a parallel combination of the admittance of the

. *d d*

*c b*

*r r*

*d d R Z*

<sup>0</sup> tan , <sup>2</sup> *d*

*fA* 

where Ad is the dielectric area, d is the dielectric thickness, tanδ is the loss tangent, and f is

For a typical experimental test, the numerical result is calculated with the same input parameters as in the experiment. Equation (4) is used to calculate the copper wire average temperature in the DBD reactor as a function of the dielectric material parameters. The data in Figure 16 is used as the input current parameter to analyze the effect of the dielectric

The plasma annealing system shown in Figure 8 is modeled by an equivalent circuit, as shown in Figure 16 with carrier speed 20m/min, dielectric Al2O3. Following Child's law for a collision-less sheath in atmospheric pressure plasma annealing with a high plasma density, the area ratio scaling exponent I = 3. The wire temperature outside of the plasma reactor is

Figure 17 shows the weakly positive relation between the annealing temperature and the input frequency. When the frequency is increasing from 25 kHz to 40 kHz, the annealing

*d*

*R Z*

0 <sup>1</sup> 2 , ln

where kd is the dielectric permittivity. The dielectric heating Rd is obtained from the power

*dk*

*d d*

*C K*

 

*d*

*R*

*die*

*Z*

dielectric capacitance Zd and the dielectric heating Rd,

The cylindrical geometry dielectric capacitance Cd is

loss in dielectric heating Pd [35],

the applied voltage frequency.

**4.4. Modeling results and discussions** 

material and the frequency on the wire temperature.

assumed to be equal to room temperature (T0 = 20 °C).

*4.4.1. Dependence of annealing temperature on frequency* 

**Figure 16.** Equivalent circuit model

#### **4.3. The dependence of annealing result on dielectric material**

Based on the assumption of the ion heating power, the thin wire temperature from model is [34]

$$T\_w = \frac{8r\_o l \varepsilon\_0 \sqrt{\frac{2q}{\mathcal{M}}} \int\_0^{\frac{\pi}{2}} \left( \frac{0.84 \left( V\_{in} \left( t \right) - Z\_{dic} I\_{in} \left( t \right) \right) \left( A\_{\mu} \right)^{\frac{1}{2}}}{1 + \left( \frac{A\_{\mu}}{A\_a} \right)^i} \right)^{\frac{5}{2}} dt}{9r\_s \rho^2 \left( \rho C\_v v r\_a^2 + \frac{4 \pi \lambda}{\ln \left( \frac{r\_c}{r\_b} \right)} \right)} + T\_0 \tag{4}$$

where Vin(t) is the applied voltage, Iin(t) is the total discharge current, q is the charge of the ion, M is the ion mass, l is the length of the reactor, and ra, rb, rc and rs are thin wire radius, the dielectric inner and outer radii and sheath radius, β is a tabulated function of the timevarying ratio ra/rs, λ is the discharge gas thermal conductivity, f is the applied voltage frequency, v is the copper wire velocity, T0 is the copper wire temperature before coming into the plasma reactor, Cv is the specific heat capacity, ρ is the density, Aa and Ab is the cross-section of thin wire and dielectric, respectivity and Tw is the wire surface temperature. Zdie is the dielectric admittance and is a parallel combination of the admittance of the dielectric capacitance Zd and the dielectric heating Rd,

$$Z\_{dic} = \frac{\mathcal{R}\_d Z\_d}{\mathcal{R}\_d + Z\_d}.\tag{5}$$

The cylindrical geometry dielectric capacitance Cd is

194 Dielectric Material

**Figure 16.** Equivalent circuit model

**4.3. The dependence of annealing result on dielectric material** 

2

2 0.84

0

0

8

*w*

Based on the assumption of the ion heating power, the thin wire temperature from model is [34]

(c)

(a)

Equivalent circuit model

Copper Sheath a

Dielectric

Plasma bulk Sheath b

Electrode

(b)

2 2

*s va*

*r C vr*

 

<sup>4</sup> <sup>9</sup>

1

*in die in <sup>b</sup> <sup>a</sup> <sup>i</sup> <sup>a</sup> <sup>b</sup>*

 

*<sup>q</sup> V t ZI t <sup>A</sup> rl f dt M A A A T T*

*a*

 

ln

 

*c b*

*r r*

5 2

*i*

0

(4)

$$C\_d = 2\pi\varepsilon\_0 K\_d \frac{1}{\ln\left(\frac{r\_c}{r\_b}\right)}\,\tag{6}$$

where kd is the dielectric permittivity. The dielectric heating Rd is obtained from the power loss in dielectric heating Pd [35],

$$R\_d = \frac{dk\_d \varepsilon\_0 \tan \delta}{2\pi f A\_d},\tag{7}$$

where Ad is the dielectric area, d is the dielectric thickness, tanδ is the loss tangent, and f is the applied voltage frequency.

#### **4.4. Modeling results and discussions**

For a typical experimental test, the numerical result is calculated with the same input parameters as in the experiment. Equation (4) is used to calculate the copper wire average temperature in the DBD reactor as a function of the dielectric material parameters. The data in Figure 16 is used as the input current parameter to analyze the effect of the dielectric material and the frequency on the wire temperature.

The plasma annealing system shown in Figure 8 is modeled by an equivalent circuit, as shown in Figure 16 with carrier speed 20m/min, dielectric Al2O3. Following Child's law for a collision-less sheath in atmospheric pressure plasma annealing with a high plasma density, the area ratio scaling exponent I = 3. The wire temperature outside of the plasma reactor is assumed to be equal to room temperature (T0 = 20 °C).

#### *4.4.1. Dependence of annealing temperature on frequency*

Figure 17 shows the weakly positive relation between the annealing temperature and the input frequency. When the frequency is increasing from 25 kHz to 40 kHz, the annealing temperature incrementally increases only 10°C. The comparison this result with experiment result we can see that there are the same. Thus, we estimate that frequency has no effect on the annealing temperature.

Effect of Dielectric in a Plasma Annealing System at Atmospheric Pressure 197

In this chapter, the authors succeeded in setting up the experiment and examining the potential application of dielectric in atmospheric pressure dielectric barrier discharge (APDBD) for annealing and cleaning thin copper wire. The new model of annealing thin copper wire in APDBD also was modeled to RLC equivalent circuit. In conclusion, the dielectric material and dielectric thickness are two parameters which strongly affect to annealing and cleaning thin metallic wire. For optimal annealing conditions, the dielectric with the thinner thickness and the higher dielectric constants is more effective to reach the elongation rate and cleaning surface. Moreover, the dependence of dielectric on frequency of applied power also were considered. The results show that the frequency is slightly effect to

*Energy and Environment Lab., Department of Mechanical Engineering, University of Technical* 

*Plasmadynamics Lab., Department of Electrical Engineering, Nagaoka University of Technology,* 

First and foremost, I would like to thank Professor Nobbuhoro HARADA for introducing me to the world of plasmasdynamics. I also would like to thank Associate Professor Takashi Kikuchi and Assistant Professor Toru Sasaki for their generous guidance with worthy advices carrying out this work. I sincerely thank Maeda, Kubo, Kawaii and other colleagues from Plasmadaynamics Lab. for assisting me in experiments and helping me improve my

[1] K. Maeda, S. Furuya, T. Kikuchi, and N. Harada: 47th AIAA Aerospace Sciences

[6] T. Nakamura, C. Buttapeng, S. Furuya, N. Harada: presented at IEEE Int. Conf. Power

[7] M. M. Santillan, A. Vincent, E. Santirso, and J. Amouroux: journal of Cleaner

[5] S. Ono, S. Teii, Y. Suzuki, and T. Suganuma: Thin solid films, 518 (2009) 981.

*Education Hochiminh City, Thu Duc District, Hochiminh City, Vietnam* 

**5. Conclusions** 

dielectric and annealing result.

T. Kikuchi, N. Harada and T. Sasaki

*Kamitomioka, Nagaoka, Niigata, Japan* 

work with their invaluable suggestions.

Meeting, Orlando, Florida, (2009), p. 1538. [2] V. D. Sype: U.S. Patent 6270597B1 (2001). [3] J. V. O'Gradi: U.S. Patent 2589283 (1951). [4] Consonen: U.S. Patent 3717745 (1973).

**Acknowledgement** 

**6. References** 

and Energy, 2008.

Production, 16 (2008) 198.

**Author details** 

N.D. Tran

### *4.4.2. Dependence of annealing temperature on dielectric material*

Figure 18 shows the dependence of annealing temperature on dielectrics material, glass and aluminum oxide. Simulation result shows that the aluminum oxide dielectric is more effective at reaching the annealing temperature than the glass dielectric. This result also is the same as that from experiment. We can conclude that the dielectrics material affects to annealing and cleaning result. The dielectric material that has higher dielectric constants is more effective to reach the annealing temperature.

**Figure 17.** Temperature of copper wire as a function of frequency

**Figure 18.** Temperature of copper wire depending on the dielectric material
