隨著目前半導體製程中基板尺寸逐漸加大，對於大面積電漿製程的均勻性的議題將越來越重要，電漿模擬約可分為三大項: (1)氣流場與溫度場的模擬 (2)電場與磁場的模擬 (3)化學反應的模擬。電漿是由帶電荷粒子所組成的多粒子系統，彼此之間會有庫倫力的存在，故交互作用的影響是連續且長程的，電漿製程同時存在化學反應、熱流場與電磁場三者並互相影響，這些特性大幅增加電漿系統分析的困難。本文分析電容式耦合電漿電漿源設備蝕刻均勻性模擬，以克努森數 (Knudsen number)為評估依據選擇適當的氣體分子均勻性數值模擬方式，採用氣流場與電場的混合模擬方法，結合粒子模型的粒子網格法 (PIC)與直接模擬蒙地卡羅 (DSMC)方法混合方法 (PIC-DSMC)方法，並透過數值模擬軟體pdFOAM進行模擬分析氣體分子均勻性，粒子碰撞過程中亦考慮到DSMC和PIC方法的網格計算尺度的差異，並避免過度稀疏或過度密集區域導致的計算失衡。並將電子密度數值模擬分布結果與FR4表面改質後的水滴角量測結果進行比對，於均勻性分布趨勢高度一致，證實pdFOAM可作為介電質材料表面改質之可靠預測工具，並使用田口方法得到電子密度均勻性的控制因子影響程度排序為:射頻功率 > 腔體壓力 > 進氣流量的結論，最後本研究得到的最佳參數條件與最初的參數條件相較，模擬電子密度均勻性指標變異係數由18.55 %再降至11.15 %。

With the fact that the substrate size is gradually increasing in the current semiconductor process, the uniformity for large area plasma process is therefore critical. And the plasma simulation for uniformity is divided into three main categories: (1) the simulation of air flow field and temperature field (2) the simulation of electrical field and magnetic field (3) the simulation of chemical reactions. Plasma is composed of charged particles of the multi-particle system, and there exists Coulomb force between each other. Thus, the interaction of the impact is continuous and long range. Also, chemical reaction, thermal gradients and electromagnetic fields are tightly coupled in the plasma process. This interaction greatly affects the difficulties of plasma system analysis.
This study analyzes the simulation of etching uniformity of Capacitively Coupled Plasma-Reactive Ion Etching (CCP-RIE) system. By Knudsen number, the appropriate numerical simulation of gas molecular uniformity is evaluated. With the adoption of the hybrid simulation method of gas flow field and electrical field, and the combination the hybrid method of particle-in-cell/direct-simulation-Monte-Carlo (PIC-DSMC) method, the gas molecular uniformity is analyzed by the numerical simulation software, pdFOAM. In addition, the difference in the mesh computational scales between the DSMC and PIC methods is considered in the particle collision process. In this way, the computational imbalance caused by the overly sparse or overly dense regions will be avoided.
In this study, the simulated electron-density distributions are validated by comparing them with water-contact-angle measurements taken on FR-4 substrates after surface modification. The uniformity distribution trend is highly consistent. This indicates that pdFOAM is a reliable predictive tool for dielectric-surface modification. Last but not least, Taguchi analysis is applied to conclude the sensitivity ranks of control factors affecting electron-density uniformity. RF power is higher than the chamber pressure, which in turn is higher than the inlet flow rate. Under the identified optimum settings, the coefficient of variation of the simulated electron-density uniformity can be decreased from 18.55 % to 11.15 %, an improvement of approximately 7.4%.

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