變壓器耦合環形電漿源數值模擬計算分析

Numerical Simulation Study of Transformer-Coupled Toroidal Plasma Source

周子傑(Tzu-Chieh Chou)

指導教授 ： 柳克強

國立清華大學/原子科學院/工程與系統科學系/碩士(2020年)

摘要

本研究探討鐵磁增強電感耦合電漿源 (ferromagnetic enhanced inductively coupled plasma, FMICP)的電漿放電機制，提出了能以較低功率產生出高密度電漿新的結構──2D TCTD x-y model，其以較貼近現實方式來計算：考慮了熱傳、流場和鐵芯的材料特性。並在2D RPS r-z (V) model探討了不同功率源下的放電差異。並分析比較氬氣電漿與氫氣電漿的不同特性。本研究以數值模擬計算分析進行探討，以流體模型分析電漿隨空間分佈與動態變化，同時考慮熱傳的影響，在頻域下以麥克斯韋方程求解電磁場與功率沉積，並且以effective BH curve近似鐵磁材料的非線性行為。
在0.1 cm DC break的二維平面模型中，探討了在較短的DC break下，電漿依然具有從低功率到高功率會從電容性轉換為電感性的特性。在2D TCTD x-y model中，鋁金屬與石英交界處具有較強的電場，使電漿在初始階段以電容耦合方式啟動，不需要以額外的高脈衝電壓來點燃電漿，在線圈電流200 A/m下，穩態平均電子密度大約1019 m-3，吸收功率5344.4 W/m。之後考慮了流場，並發現電漿有較高的均勻度。在2D RPS r-z (V) model中，考慮了兩種不同功率源，由電壓源來驅動的電漿因為起始電子密度低，看進去的阻抗較大，初始線圈電流低，感應電場低，相較於電流源，電子密度上升速度較慢；電流源因為維持在高電流，所以初始感應電場就很大，電子密度上升快速，但因為電子密度剛開始較低，所以大部分能量損耗在鐵芯中。
在氫氣電漿方面分別探討了兩種不同模型──2D RPS r-z (H2) model及2D TCTD x-y (H2) model，共考慮了8種粒子與34條反應式。在2D RPS r-z (H2) model中，在氣壓2 Torr、線圈電流100 A下穩態時，電漿密度約為1018 m-3，與相同條件下的氬氣電漿相比，氫氣電漿的密度較低，且主電漿區範圍較小，由於氫離子的質量較低，更容易受到鞘層裡的電場往腔壁加速，而主電漿區滿足準電中性條件，故電子密度也較低，因此氫氣電漿的感應電場較高，而電漿的吸收功率為Q_rh=1/2 R_e (E∙j_e)，所以氫氣電漿的吸收功率較氬氣電漿高，其值為12235 W。在氣壓2 Torr、線圈電流200 A/m下，2D TCTD x-y (H2) model 中H+及H3+為主要離子，生成與H原子相關。氫氣電漿相較於氬氣電漿，電子密度較低，且沒有出現環狀分布，主要集中在石英管中，穩態平均電子密度大約61017 m-3，吸收功率為89415 W/m，平均氣體溫度約332 K。

關鍵字

鐵磁增強電感耦合電漿 ； 遠距電漿源 ； 變壓器耦合環形電漿源 ； 氫氣電漿 ； 流體模型

並列摘要

The discharge mechanism of ferromagnetic enhanced inductively coupled plasma (FMICP) source is explored in this study, and proposes a new structure that can ignite high-density plasma with lower power, 2D TCTD x-y model, which is more realistic to simulate: considering heat transfer, flow field and the material properties of ferrite core. In the 2D RPS r-z (V) model, we discusses the discharge differences under different power sources. We also analyzed the different characteristics of argon plasma and hydrogen plasma. The numerical simulation is based on fluid model to describe the space distribution of plasma and plasma dynamic, and we also consider the effect of heat transfer. Maxwell equations are solved to determine the electromagnetic fields and electron power deposition in frequency domain. The effective BH curve is used to approximate the nonlinear behavior of the ferromagnetic materials.
The effect of shorter DC break is discussed in the case of 2D RPS x-y (0.1) model. Under a short DC break, the plasma still has the characteristic of changing from capacitive to inductive from low power to high power. In the 2D TCTD x-y model, there is strong electric field near the junction of aluminum and quartz, which enables the plasma to start in the capacitive coupling mode at the initial stage, so there is no need to ignite the plasma with an additional high pulse voltage. The steady-state average electron density is about 1019 m-3, and the absorbed power is 5344.4 W/m when the coil current is operated at 200 A/m. The plasma distribution is more uniform after the gas flow was considered. In 2D RPS r-z (V) model, two different power sources are considered. The plasma driven by the voltage source has a low electron density at the beginning, so the high resistance leads to the low coil current which result in a low induced electric field. Compared with the current source, the electron density rises slowly. Due to the high operating current in current source, the induced electric field is strong at the beginning which leads to the electron density rises rapidly, but the electron density is low at the beginning, and most of the energy is lost in the core.
In terms of hydrogen plasma, two different models have been discussed, 2D RPS r-z (H2) model and 2D TCTD x-y (H2) model. The simulation model using hydrogen plasma takes into account 8 gaseous species and 34 reactions. In the 2D RPS r-z (H2) model, when the pressure is 2 Torr and the coil current is 100 A, the electron density is about 1018 m-3. Compared with the argon plasma under the same conditions, the density of hydrogen plasma is low, and the range of the bulk plasma region is smaller. Due to the low mass of hydrogen ions, it is more likely to be accelerated by the electric field in the sheath region to the chamber wall, and the main plasma region meets the condition of quasi-neutrality, so the electron density is also smaller. Due to the low electron density, the induced electric field of hydrogen plasma is relatively high. The absorption power of plasma is Q_rh=1/2 R_e (E∙j_e), so the absorption power of hydrogen plasma is higher than argon plasma, and its value is 12235 W. At a pressure of 2 Torr and a coil current of 200 A/m, H+ and H3+ are the main ions in the 2D TCTD x-y (H2) model, and the production is related to H atoms. Compared to argon plasma, hydrogen plasma has a lower electron density and there is no loop shape distribution. The electron density is mainly concentrated in the quartz tube. The steady-state average electron density is about 61017 m-3, the absorbed power is 89415 W/m, and the average gas temperature is about 332 K.

並列關鍵字

Ferromagnetic Enhanced Inductively Coupled Plasma ； remote plasma system ； Transformer-Coupled Toroidal Plasma Source ； Hydrogen plasma ； fluid model

參考文獻

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