Electron heating in capacitive RF plasmas based on moments of the Boltzmann equation: From fundamental understanding to predictive control

电容耦合射频低温等离子体（CCP）经常用于各种具有高度社会相关性的应用，从微观尺度上的蚀刻和沉积过程到伤口愈合和癌症治疗中的生物医学应用。然而，它们产生的基本原理，即空间和时间分辨的电子功率吸收动力学，尚不清楚。这些动力学决定了中性气体的电离和解离，以及不同粒子种类的过程相关能量分布函数的形成。因此，等离子体过程通常是经验优化的，而不是基于科学的理解。这导致了过程控制的严重局限性。描述电子功率吸收的理论多种多样，但它们大多是基于对玻尔兹曼方程第一速度矩的高度简化。这包括忽略电子惯性、压力梯度、等离子体体中均匀谐波电场的假设，以及对碰撞的简化处理。欧姆和随机电子加热的经典概念就是这些简化的结果。最近的研究表明，在各种工艺相关的放电条件下，这些假设是非常值得怀疑和不正确的。结果表明，这些模型导致了对CCP操作的根本错误理解，因此，不允许实现基于知识的等离子体过程优化。相反，基于粒子在细胞模拟中的输入参数，必须对玻尔兹曼方程的完整第一矩进行时空分析。该方法已被证明可以在氩气中运行的单频低压CCP中提供完整的空间和时间分辨理解。在本项目中，这种所谓的玻尔兹曼项方法将系统地应用于在过程相关条件下运行的ccp，以获得无线电频率周期内具有高时空分辨率的电子功率吸收动力学的基本理解。单频和多频ccp（包括定制电压波形）在正电和负电气体以及反应气体混合物中工作，压力范围为0.5 Pa到大气压，将作为基本驱动频率的函数进行研究。理论/计算结果将与实验结果进行比较。阐明了不同的加热机制及其对电子能量分布函数（EEDF）形成的影响。基于这些基本见解，将开发控制EEDF的概念。最后，将重新审视现有的描述等离子体电导率和介电常数以及碰撞算子的理论概念，这些理论概念也是这些经典假设的结果，并将其替换为更准确的表达式。

Capacitively coupled radio frequency low temperature plasmas (CCP) are frequently used for a variety of applications of high societal relevance ranging from etching and deposition processes on microscopic scales to biomedical applications in wound healing and cancer therapy. However, the fundamentals of their generation, i.e. the space and time resolved electron power absorption dynamics, are not understood. These dynamics determines the ionization and dissociation of the neutral gas as well as the formation of process relevant energy distribution functions of different particle species. Consequently, plasma processes are typically optimized empirically and not based on scientific understanding. This results in strong limitations of process control.Various theories to describe the electron power absorption exist, but they are mostly based on strong simplifications of the first velocity moment of the Boltzmann equation. This includes the negligence of electron inertia, pressure gradients, the assumption of a homogeneous and harmonic electric field in the plasma bulk, and a simplified treatment of collisions. The classical concepts of ohmic and stochastic electron heating are a result of these simplifications. Recent works have demonstrated that these assumptions are highly questionable and incorrect under a variety of process relevant discharge conditions. It was shown that these models result in a fundamentally incorrect understanding of CCP operation and, thus, do not allow to realize a knowledge based optimization of plasma processes. Instead a spatio-temporal analysis of the complete first moment of the Boltzmann equation based on input parameters from Particle in Cell simulations must be performed. This approach was demonstrated to provide a complete space and time resolved understanding in a single frequency low pressure CCP operated in argon. In this project, this so-called Boltzmann term method will be applied systematically to CCPs operated under process relevant conditions to obtain a fundamental understanding of the electron power absorption dynamics with high spatial and temporal resolution within the radio frequency period. Single- and multi-frequency CCPs (including Tailored Voltage Waveforms) operated in electropositive and -negative gases as well as reactive gas mixtures and at pressures ranging 0.5 Pa to atmospheric pressure will be studied as a function of the fundamental driving frequency. The theoretical/computational results will be compared to experiments. The role of different heating mechanisms and their effects on the formation of electron energy distribution functions (EEDF) will be clarified. Based on these fundamental insights concepts to control the EEDF will be developed. Finally, the existing theoretical concepts to describe the plasma conductivity and permittivity as well as the collision operator, which are also a result of these classical assumptions, will be revisited and replaced by more accurate expressions.