Active plasma resonance spectroscopy: a functional analytic description

Lapke, Martin; Oberrath, Jens; Mussenbrock, Thomas; Brinkmann, R. P.

doi:10.1088/0963-0252/22/2/025005

Cited by 32 publications

(80 citation statements)

References 22 publications

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“…A fully kinetic generalization of the study of [20], i.e., an abstract kinetic model of electrostatic resonance valid for all pressures is presented in [21]. It turned out that the main result could directly be transferred.…”

Section: Several Years Later Morin and Balmain Compared The Kinetic Amentioning

confidence: 99%

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Kinetic damping in the spectra of the spherical impedance probe

Oberrath¹

2018

Plasma Sources Sci. Technol.

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The impedance probe is a measurement device to measure plasma parameter like electron density.It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods.These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. Within this manuscript an explicit response function of the spherical impedance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function and its corresponding spectra. These spectra show additional damping due to kinetic effects and are in good agreement with former kinetically determined spectra.

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Section: Several Years Later Morin and Balmain Compared The Kinetic Amentioning

confidence: 99%

“…Entering the basis function (20) into Poisson's equation (2) the integrals over the velocity space can be solved which yields…”

Section: Appendix A: Potential Of a Basis Functionmentioning

confidence: 99%

Kinetic damping in the spectra of the spherical impedance probe

Oberrath¹

2018

Plasma Sources Sci. Technol.

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“…In reference [26] a geometry independent APRS probe, which excites electrostatic resonance modes, was analyzed. In the general APRS model a matrix sheath with complete electron depletion and a sharp sheath edge is assumed.…”

Section: Consequences Of Symmetry In Mrp and Pmrp Designmentioning

confidence: 99%

“…1 (right). A RLC series circuit parallel to a vacuum capacitance C vac is the simplest lumped element circuit model for Z as shown in [26]. C represents the dielectric and sheath behavior, L the inertia of the electrons, and R damping due to elastic collisions of the electrons with the neutral background.…”

Section: Consequences Of Symmetry In Mrp and Pmrp Designmentioning

confidence: 99%

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The planar Multipole Resonance Probe: a functional analytic approach

Friedrichs

Oberrath

2018

EPJ Techn Instrum

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Active Plasma Resonance Spectroscopy (APRS) is a well known diagnostic method, where a radio frequency probe is immersed into a plasma and excites plasma oscillations. The response of the plasma is recorded as frequency dependent spectrum, in which resonance peaks occur. By means of a mathematical model plasma parameters like the electron density or the electron temperature can be determined from the detected resonances. The majority of all APRS probes have in common, that they are immersed into the plasma and perturb the plasma due to the physical presence of the probe. Thus, they are invasive and can at least influence the homogeneity of the plasma. To overcome this problem, the planar Multipole Resonance Probe (pMRP) was invented, which can be integrated into the chamber wall of a plasma reactor. Within this paper, the first analytic model of the pMRP is presented, which is based on a cold plasma description of the electrons. The general admittance of the probe-plasma system is derived by means of functional analytic methods and a complete orthonormal set of basis functions. Explicit spectra for an approximated admittance including a convergence study are shown. The determined resonance frequencies are in good agreement with former simulation results.

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Comparison of Langmuir probe and multipole resonance probe measurements in argon, hydrogen, nitrogen, and oxygen mixtures in a double ICP discharge

Fiebrandt

Oberberg

Awakowicz

2017

Journal of Applied Physics

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The results of a Multipole Resonance Probe (MRP) are compared to a Langmuir probe in measuring the electron density in Ar, H2, N2, and O2 mixtures. The MRP was designed for measurements in industry processes, i.e., coating or etching. To evaluate a possible influence on the MRP measurement due to molecular gases, different plasmas with increasing molecular gas content in a double inductively coupled plasma at 5 Pa and 10 Pa at 500 W are used. The determined electron densities from the MRP and the Langmuir probe slightly differ in H2 and N2 diluted argon plasmas, but diverge significantly with oxygen. In pure molecular gas plasmas, electron densities measured with the MRP are always higher than those measured with the Langmuir Probe, in particular, in oxygen containing mixtures. The differences can be attributed to etching of the tungsten wire in the Ar:O2 mixtures and rf distortion in the pure molecular discharges. The influence of a non-Maxwellian electron energy distribution function, negative ions or secondary electron emission seems to be of no or only minor importance.

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Active plasma resonance spectroscopy: a functional analytic description

Cited by 32 publications

References 22 publications

Kinetic damping in the spectra of the spherical impedance probe

Kinetic damping in the spectra of the spherical impedance probe

The planar Multipole Resonance Probe: a functional analytic approach

Comparison of Langmuir probe and multipole resonance probe measurements in argon, hydrogen, nitrogen, and oxygen mixtures in a double ICP discharge

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