DFG project

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

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.

The project is funded by the German Research Foundation. Project leader is Dr. habil. Julian Schulze.