Precise control of capacitively coupled radiofrequency (CCRF) plasma reactors is required to achieve desired outcomes in surface functionalisation and material synthesis processes. This necessitates detailed mapping of the large process parameter space and a thorough understanding of spatial and temporal variations of the plasma throughout the reactor. These goals can only feasibly be achieved with accurate numerical modelling. Previous numerical studies of CCRF discharges have implemented a range of simplifying assumptions to improve numerical tractability, such as small electrode spacing, radial uniformity, fewer active species and simplified boundary conditions, while neglecting self-bias formation. Although this approach is useful in developing the methodology for continuum plasma modelling, it poses challenges for direct comparison with experimental data and for understanding the behaviour of plasma processes employed in the surface treatment of large, complex objects, or the synthesis of nanoparticles. Here we report the development of a two-dimensional axisymmetric continuum model for a CCRF reactor with a pure argon 13.56-MHz discharge using the finite element method. The large electrode spacing and reactor design result in two distinct discharge regions and the formation of a strong DC self-bias on the powered electrode. The plasma discharge is studied as the pressure is varied from 0.1 to 0.3 Torr, over the radiofrequency input power range of 25–100 W, which leads to consistent enhancements of the electron density and self-bias. The impact of the electron energy distribution function (EEDF) on the discharge is assessed, with the assumption of a Druyvesteyn EEDF resulting in a bulk electron density and temperature of 3.4 × 10¹⁵ m⁻³ and 3.3 eV, respectively, compared with 8.1 × 10¹⁵ m⁻³ and 1.9 eV in the Maxwellian case. The asymmetric power distribution throughout the reactor is quantified to build a reduced domain model with a lower computational cost. The effect of an electrically floating parallel plate electrode is assessed, resulting in a 42% higher bulk plasma potential as compared with the grounded case. The inclusion of resonant and 2p excited states of argon is shown to have a major impact on the discharge dynamics, leading to an order of magnitude reduction in bulk electron density. This study proposes a robust numerical model of a CCRF argon plasma discharge to facilitate future simulations of more complex discharges with important implications in plasma surface engineering and synthesis of materials.

中文翻译：

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非对称 CCRF 氩等离子体反应器的连续模型：更高激发态的影响和对模型参数的敏感性

需要精确控制电容耦合射频 (CCRF) 等离子体反应器才能在表面功能化和材料合成过程中实现预期结果。这需要对大型工艺参数空间进行详细映射，并彻底了解整个反应器中等离子体的空间和时间变化。只有通过精确的数值建模才能切实实现这些目标。先前对 CCRF 放电的数值研究已经实施了一系列简化假设以提高数值易处理性，例如小电极间距、径向均匀性、较少的活性物质和简化的边界条件，同时忽略了自偏置的形成。尽管这种方法在开发连续等离子体建模方法方面很有用，它对与实验数据的直接比较以及理解用于大型复杂物体的表面处理或纳米粒子合成的等离子体工艺的行为提出了挑战。在这里，我们报告了使用有限元方法开发具有纯氩 13.56 MHz 放电的 CCRF 反应器的二维轴对称连续介质模型。大电极间距和反应器设计导致两个不同的放电区域，并在通电电极上形成强直流自偏压。当压力在 0.1 到 0.3 Torr 之间变化时，在 25-100 W 的射频输入功率范围内研究等离子体放电，这导致电子密度和自偏置的持续增强。评估电子能量分布函数（EEDF）对放电的影响，^{分别为 15}  m ^-3和 3.3 eV，而 Maxwellian 情况下为 8.1 × 10 ¹⁵  m ^-3和 1.9 eV。整个反应堆的不对称功率分布被量化，以构建具有较低计算成本的简化域模型。评估了电浮动平行板电极的效果，与接地情况相比，导致体等离子体电位高出 42%。包含谐振和 2 p氩的激发态对放电动力学有重大影响，导致体电子密度降低一个数量级。这项研究提出了一个强大的 CCRF 氩等离子体放电数值模型，以促进未来对更复杂放电的模拟，这些放电对等离子体表面工程和材料合成具有重要意义。