氏名　TRAN NGOC DAM
学位の種類　博士（工学）
学位記番号　博甲第603号
学位授与の日付　平成23年8月31日
学位論文題目　Optimization of Annealing Conditions for Metallic Wire using Dielectric Barrier Discharge at Atmospheric Pressure　（大気圧下の誘電体バリア放電を用いた金属細線アニーリング条件の最適化）
論文審査委員
　主査　教授　原田　信弘
　副査　教授　江　偉華
　副査　教授　末松　久幸
　副査　准教授　伊東　淳一
　副査　准教授　菊池　崇志

• 論文目次
• 論文要旨
• 論文審査の結果の要旨

［平成23（2011）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

CONTENTS
Chapter 1　INTRODUCTION　p.1
　1.　Background　p.3
　1.1.　Hardworking-drawing　p.4
　1.2.　Annealing　p.4
　1.3.　Plasma annealing　p.5
　1.3.1.　Electron bombarding　p.7
　1.3.2.　Ion bombarding　p.7
　1.4.　Adaptive annealing factor　p.7
　1.5.　Optimal methods　p.8
　2.　State of art of thin wire annealing　p.9
　3.　Research objectives　p.11
　4.　Scope and limitation　p.11
　5.　Organization　p.11
　6.　Reference　p.13
Chapter 2　OPTIMIZATION OF ANNEALIMG CONDITIONS　p.15
　1.　Introduction　p.15
　2.　Mathematical optimal analyses　p.19
　3.　Model plasma annealing system　p.23
　3.1.　Discharge characteristic　p.23
　3.1.1.　Discharge mechanism　p.23
　3.1.2.　Discharge ware from characteristics　p.25
　3.2.　Equivalent circuit model　p.31
　3.2.1.　At dielectric　p.33
　3.2.2.　At ion sheath　p.33
　3.2.3.　At plasma bulk　p.36
　3.3.　Plasma parameters　p.38
　3.3.1.　From equivalent circuit model　p.38
　3.3.2.　From experiment　p.39
　3.3.3.　Plasma parameters　p.40
　3.4.　Results and discussion　p.41
　3.5.　Summary　p.47
　4.　Power balance for annealing　p.48
　4.1.　Heating power　p.48
　4.1.1.　Electron bombardment heating power　p.48
　4.1.2.　Ion bombardment heating power　p.49
　4.2.　Annealing power　p.50
　4.3.　Conducting power　p.51
　4.4.　Power balance of annearing　p.51
　4.5.　Summary　p.56
　5.　Breakdown discharge conditions　p.56
　6.　Stable elongation rate condition　p.57
　6.1.　Adaptive annealing factor　p.57
　6.2.　Results and discussion　p.58
　6.3.　Summary　p.64
　7.　Conclusion　p.65
　8.　Reference　p.66
Chapter 3　OPTIMAL RESULT AND DISCUSSION　p.67
　1.　Introduction　p.67
　2.　Mathematical equation for optimization　p.67
　3.　Optimal result　p.71
　3.1.　Comparison of the result parameters from optimal calculation with those from measurement　p.71
　3.2　Result　p.74
　3.3.　Dependence of optimal results on design parameters　p.77
　3.3.1.　Dependence of optimal parameters on frequency　p.77
　3.3.2.　Dependence of optimal parameters on dielectric thickness　p.78
　3.3.3.　Dependence of optimal parameters on discharge gap　p.80
　3.3.4.　Dependence of optimal parameters on applied voltage　p.82
　3.3.5.　Dependence of optimal parameters on annealing speed　p.84
　3.3.6.　Comparison the dependence of annealing efficiency on the design parameters　p.86
　2.　Conclusion　p.87
　3.　Reference　p.88
Chapter 4　SUMMARY AND CONCLUSIONS　p.89
　1.　Mathematical optimal analyses　p.89
　2.　Model plasma annealing system　p.90
　2.1.　Discharge characteristic　p.90
　2.1.1.　Discharge mechanism　p.90
　2.1.2.　Discharge ware from characteristics　p.90
　2.2.　Equivalent circuit model　p.90
　2.3.　Plasma parameters　p.91
　3.　Power balance for annealing　p.91
　3.1.　Heating power　p.91
　3.2.　Annealing power　p.92
　3.3.　Conducting power　p.92
　3.4.　Power balance of annearing　p.92
　4.　Stable elongation rate condition　p.92
　5.　Optimal result　p.92
　6.　Recommendation for further work　p.93

　The thin metallic wire annealing system in which the annealing and cleaning processes are simultaneously operated in Atmospheric Pressure Dielectric-Barrier Discharge （APDBD） is the potential solution for the problem of energy and environment of the conventional manufacturing process. However the annealing efficiency in APDBD remains low about 3% and this annealing process uses expensive gas such as helium or argon. The main objective of the present study is to find the way to optimize annealing conditions in order to find the minimum applied power i.e. improve annealing efficiency under sufficient annealing effect.
Equations for optimization were established for determining the minimum applied power in case of definite discharge gas. They are functions which minimize the total power loss using design parameters within a region specified by constraints and upper and lower limits of practical applications. The design parameters are the electrical efficiencies （applied voltage, and frequency）, the size of reactor （radius of thin wire, outside discharge gap, outside dielectric and discharge length） and the annealing speed. The equality constraints are the balance of heating power of annealing and stable elongation rate. The inequality constrain is breakdown discharge condition.
Based on the analysis of discharge characteristics and the physical structure of the plasma reactor, thin metallic wire annealing system in cylindrical APDBD was modeled by the equivalent electrical circuit. The applied power was defined from the circuit. The plasma parameters were also estimated by the comparison of the resistance, reactance and active power from annealing system with those from the model. The bombardment of ions heats the thin metallic wire surface and part of this heat is used for annealing and the rest is lost to environment. The balance of heating power for annealing was estimated by the analysis of heating power, annealing power and power dissipation. A function for stable elongation rate of 23% was set by using Arrhenius equation in that the different temperature and duration of annealing were measured from experiments. The inequality breakdown discharge constrains was also estimated by using the Paschen curves.
The plasma parameters, temperature of thin metallic wire and the design parameters for minimum applied power were determined from equivalent electrical model, the balance of heating power and equations for optimization, respectively. It is shown that the results from optimal analysis are the same as that from experiment when annealing parameters are set to be equal experimental conditions. The bombardment of ions is dominant for thin wire heating. The thin wire temperature is proportional to applied voltage. The elongation rate depends on both temperature and duration of annealing. For adapting the stable elongation rate condition, the temperature annealing is inversely proportional to the duration of annealing. The annealing efficiency strongly depends on the design parameters. The annealing efficiency with optimized design parameters is higher about two times than those before the optimization, and the elongation rate is still guaranteed. The annealing efficiency of helium, argon and nitrogen were compared. The results show that the nitrogen is a potential gas for annealing metallic wire in APBDB because of high annealing efficiency and low cost. For the comparison of the dependence of annealing efficiency on the design parameters, it was found that the discharge gap, the frequency and dielectric thickness have strong effect, being the discharge gap the most predominant. However the applied voltage, the length of reactor and the annealing speed have slight effect on annealing efficiency. As the discharge gap is increased two times, the annealing efficiency is also increased two times even though another parameter has been recalculated for optimal solution. In order to increase annealing speed, increasing applied voltage and increasing the length of reactor are necessary. The comparison of annealing efficiency in two cases of them, the annealing efficiency is higher in case of increasing reactor length.
In conclusion, the optimization of annealing conditions for metallic wire using APDBD is very useful for saving energy. For optimal annealing conditions, the discharge gap, dielectric thickness, frequency were the first three parameters need to be considered, the applied voltage, length of reactor, and annealing speed were three relationship parameters which could be changed but did not affect annealing efficiency much. Wide discharge gap, thin dielectric thickness and high frequency were good for saving energy. Discharge gap is the crucial parameter that decides the annealing efficiency; the higher discharge gap gave the higher annealing efficiency. In order to increase annealing speed, the length of reactor needs to be increased firstly to improve annealing efficiency for saving energy. For the industrial application, nitrogen was a potential gas.

　本論文は，「Optimization of Annealing Conditions for Metallic Wire using Dielectric Barrier Discharge at Atmospheric Pressure」（大気圧下の誘電体バリア放電を用いた金属細線アニーリング条件の最適化）と題し，4章より構成されている．
　第1章「Introduction」では，金属細線の製造プロセスになかでの，アニーリングの必要性と従来型と比べた，大気圧下の誘電体バリア放電を用いたアニーリングの特徴を述べ，これまでの研究の総括からアニーリング用リアクタの設計条件や実際のアニーリング条件の最適化の必要性を指摘し，本研究の目的を述べている．さらに本研究展望と範囲を述べている．
　第2章「OPTIMIZATION OF ANNEALING CONDITIONS」では，アニーリングシステムのモデル化をしている．誘電体バリア放電の電流-電圧特性から，プラズマを電気的等価回路として表現し，プラズマへ投入される電力を実験結果と比較し，提案した等価回路モデルでプラズマへの投入電力を表すことができることを明らかにしている．また，金属細線のエネルギーバランスを解析し，金属細線の加熱は荷電粒子の衝突によるエネルギー付与と周辺ガスへの熱伝導による損失とのバランスで決まることを明らかにし，実験結果と良く一致したことを示している．これらから，数学的に金属細線温度の評価が可能となり，種々の設計条件や運転条件でのアニーリング効果を正確に評価できることが可能となっている．
　第3章「OPTIMAL RESULT AND DISCUSSION」では，種々の設計条件やアニーリング条件に対して最適化を行うための数学モデルを提案し，実際に投入電力を最小にする最適化を行って，放電ギャップ，誘電体厚さ，電源周波数がアニーリング効率に対する影響が大きいこと，放電ギャップは長いほど荷電粒子の加速エネルギーが大きくなるために効果的なアニーリングができ，アニーリング効率が上昇することを明らかにしている．さらに実際のアニーリング工程に適用するため，金属細線の搬送速度の増加に対応するためには，印加電圧を増加するかリアクタ長を長くする必要があること，リアクタ長さを長くする方が投入電力を小さくでき，省エネルギー化が可能なことを提示している．
　第4章「SUMMARY AND CONCLUSIONS」では，各章の主要な結論をまとめ，本研究の総括をしている．
　以上のように，本論文は大気圧下の誘電体バリア放電を用いた金属細線のアニーリングに関して，等価回路による入力電力の評価，荷電粒子の衝突を主たる機構として，金属細線の温度の評価を行い，これらを基礎として，ガス種の違いやリアクタの形状等の設計条件，さらに印加電圧や電源周波数など運転条件の最適化によって，投入エネルギーを最小にする最適化手順の提案を行い，実際に実験条件に合わせた最適化を実施して，実験結果と比較から本最適化手法の妥当性を明らかにしている．よって、本論文は工学上及び工業上貢献するところが大きく、博士（工学）の学位論文として十分な価値を有するものと認める。