用于射频电容耦合等离子体流体模拟的低存储隐式双时间有限体积框架
A Low-Storage Implicit Dual-Time Finite-Volume Framework for Radio-Frequency Capacitively Coupled Plasma Fluid Simulations
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中文总结 AI 辅助
针对射频电容耦合等离子体流体模拟，提出低存储隐式双时间有限体积框架，通过向后差分公式和解非线性系统等方法，克服数值刚性和时间步长限制，经一维和二维验证展示了其有效性和适用性。
中文摘要 AI 辅助
射频电容耦合等离子体在半导体制造中广泛应用。有效准确求解相关流体控制方程对优化等离子体反应器设计和过程控制至关重要。为克服低温等离子体建模中的数值刚性和时间步长限制，提出一种用于射频电容耦合等离子体模拟的稳健、低存储隐式双时间有限体积框架。通过向后差分公式将物理时间推进与显式稳定性限制严格解耦，用伪时间迭代有效求解非线性系统，采用局部块隐式松弛方法处理刚性输运和化学源项，对泊松方程进行半隐式处理加速静电耦合。先通过一维氩放电基准验证框架，后扩展到二维构型，结果显示了静电势的多维畸变和横向边界引起的局部电子加热区。
英文摘要
Radio-frequency (RF) capacitively coupled plasmas (CCPs) are widely utilized in semiconductor manufacturing. Efficiently and accurately solving the underlying fluid governing equations to resolve the complex multi-physics fields is crucial for optimizing plasma reactor designs and process control. To overcome the severe numerical stiffness and prohibitive time-step constraints inherent in low-temperature plasma modeling, we present a robust, low-storage implicit dual-time finite-volume framework for RF CCP simulations, establishing a highly efficient and memory-friendly pathway for the predictive modeling of multi-dimensional low-temperature plasmas. In this approach, the physical time advancement is strictly decoupled from explicit stability limits through a backward-difference formula (BDF), while the resulting nonlinear system is efficiently solved using pseudo-time iterations. A localized block-implicit relaxation method is employed to handle the stiff transport and chemical source terms at the cell level, effectively circumventing the massive memory overhead typical of conventional fully implicit solvers. Concurrently, a semi-implicit treatment of Poisson's equation is integrated to accelerate the electrostatic coupling. The framework is first verified against a standard one-dimensional argon discharge benchmark, demonstrating that a highly accurate periodic state can be achieved with satisfactory computational efficiency through the optimal selection of the physical time step, pseudo-CFL number, and inner iteration step. To further demonstrate the multidimensional applicability of the proposed method, the solver is extended to genuine two-dimensional configurations. The numerical results show the multi-dimensional distortion of the electrostatic potential and localized electron heating zones induced by the transverse boundaries.
