Modelling and spectral analysis of the planar multipole resonance probe

Michael Friedrichs, Jens Oberrath, Ralf Peter Brinkmann

WELT­PP-16, Kerk­ra­de, The Nether­lands, 21-22 No­vem­ber


Abstract

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density [1]. However, the influence of the probe on the plasma by its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP.

Coupling the cold plasma model with the Maxwell equations for electrostatic approximation an analytical model for the system response of the plasma is derived and solved analytically for an arbitrary geometry of the planar MRP. Based on a square geometry of the planar MRP the analytical term of the system response is solved numerically and presented for different electron densities. The variation of the resonance frequencies matches the drift of the electron densities and shows the monitoring ability of the probe.

[1]: „The Multipole-Resonance-Probe: Characterization of a prototype “, M. Lapke et al., Appl. Phys. Lett. 93, 051502 (2008)

Tags: analysis;, Modelling;, Multipole, Planar, probe, resonance, spectral