本研究使用PIC (Particle in cell)方法模擬在低壓、高氣體密度和低電離率下，氬氣的電漿行為。粒子碰撞行為－包括電子與中性粒子間彈性、非彈性及電離碰撞，離子與中性原子間彈性及電荷交換碰撞，還有電子與離子間的庫倫碰撞。設定的模型條件為：(1) 在兩個極板之間給一穩定電壓值；(2)考慮磁場所帶來的效應，求解泊松方程式(Poisson’s Equation)和馬克斯威爾方程式(Maxwell’s Equation)；(3) 不考慮二次電子散射(secondary electron emission)；(4) 中性粒子為均勻分布，並滿足麥斯威爾(Maxwellian)速度分布，不個別追蹤中性粒子的位置及速度；(5) 不考慮電子與離子的複合碰撞。本研究採用數值模擬的方法觀察鞘層(Sheath)的生長情形。結果將顯示粒子碰撞對於整個電漿行為以及鞘層的影響。理論之比較將進一步了解電漿在鞘層的運動與熱傳遞現象。

This study uses the PIC (Particle-in-cell) method to simulate unsteady three-dimensional dynamics of particles in argon plasma under low pressure, high density, and weak ionization between two planar electrodes subject to a sudden biased voltage. Plasma has been widely used in materials processing, film manufacturing, nuclear fusion, lamps, etc. Properties of plasmas are also becoming important area for research. This work includes elastic collisions between electrons and neutrals, ions and neutrals, and inelastic collisions resulting in ionization from impacting neutrals by electrons, and charge exchange between ions and neutrals, and Coulomb collisions between electrons and ions. The model ignores secondary electron emission, recombination between ions and electrons, and assumes uniform distribution of the neutrals having velocity of Maxwellian distribution. The computed results show the effects of elastic and inelastic collisions on the characteristics of plasma and sheath (space charge region) in front of the workpiece surface. Unsteady mass, momentum and energy transport from the bulk plasma through sheath to the workpiece is confirmatively and exploratorily studied after successful comparison between PIC prediction and experimental data has been made.

摘要............................................................. I
英文摘要......................................................II
謝誌.............................................................III
目錄............................................................ IV
圖目錄......................................................... VI
符號說明..................................................... VII
第一章 緒論..................................................1
1.1 研究背景與目的....................................1
1.2 粒子網格(PIC)方法簡介......................3
1.3 本論文研究內容簡介............................8
1.4 本論文大綱............................................9
第二章 理論分析與方法.............................10
2.1 物理模型與基本假設............................10
2.2 碰撞理論簡介........................................11
2.2.1 蒙地卡羅法處理碰撞的問題.............12
2.2.2 庫倫碰撞.............................................21
2.3 外加電場................................................26
2.3.1 泊松方程式邊界條件.........................26
2.3.2 泊松方程式.........................................27
2.3.3 電場.....................................................30
2.4 粒子自洽電磁場.....................................31
2.4.1 電磁場的時域有限差分法..................32
2.4.2 電磁場的邊界條件..............................37
2.4.3 Courant 穩定準則...............................41
2.5 粒子受力運動情況..................................42
第三章 研究結果與討論................................44
第四章 結論與未來方向.................................51
附錄A 模擬系統參數.......................................52
參考文獻..........................................................54

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