Kinetic modeling and simulation of the planar multipole resonance probe

• Applicants: Professor Dr. Ralf-Peter Brinkmann; Professor Dr.-Ing. Jens Oberrath
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 360750908

To control technological plasmas, the in-situ measurement of their state variables is required, especially of the electron density and the electron temperature. This research project will contribute to this quest. It focuses on a particular diagnostic scheme, the industry-compatible diagnostic method active plasma resonance spectroscopy (APRS). APRS obtains information on a plasma by recording its response to radio frequency signal applied by an electric probe. A specific realization of the APRS concept is taken as example, the so-called planar multipole resonance probe (pMRP) which has the benefit of fitting squarely into the chamber wall. First principles are used to uncover the relation between the observed resonance and the inner plasma parameters electron density and electron temperature. In principle, the resonance is a collective effect which can be described well within a fluid dynamic model. This covers the relation between the observed resonance frequency and the electron density. The damping of the resonance is, however, strongly influenced by individual effects which can be studied only within a fully kinetic model. Although the existence of this influence is known since the 1960s, it is not yet fully understood. This is core of this research project.To turn the APRS scheme into a useful measurement scheme, the influence of the kinetic effects must be understood on a quantitative level. An experimental approach is not possible, as the responsible physics takes place in the vicinity of the probe head, i.e., on the spatial scales of millimeters, and only during the high-frequency measuring process itself, i.e., on the temporal scale of nanoseconds. This is virtually impossible to be resolved experimentally. For that reason, this research will attempt another approach for validation, namely compare two mathematically different methods which are based on two entirely different approaches. The first uses functional analysis; the second formulates an integral equation based on a linearization of the kinetic equation. The functional analytic approach has the advantage that collisions can be considered relatively easily; the integral equation approach is predestined for a collision-free dynamic. To compare the methods, they must both be extended to cover the other regime at least partially. When this is achieved, a complete understanding of the dynamic influence of the kinetic effects on the characteristics of the resonances will be available for the first time.Once the basic physical aspects of probe behavior are clarified, a comprehensive mathe-matical model will be formulated which sets the frequency and the damping of the observed resonance in relation to the electron density and the electron temperature. Such a relation will be the basis for the desired improved evaluation rule to be used for supervision and control of plasma processes.

• DFG Programme: Research Grants