The planar Multipole Resonance Probe: a functional analytic approach

Abstract

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.

Development of a novel plasma probe for the investigation and control of plasma‐enhanced chemical vapor deposition coating processes

“…Another advantage of the PACP is that its design is relatively simple as compared with the MRP, which typically consists of two metallic hemispheres separated by a dielectric layer, a conical balun, dielectric tube, and coaxial cable. [26] The MRP can monitor n e , T e , and electron collision frequency, [25][26][27] whereas the PACP can monitor n e and V f . Each probe can measure, respectively, the different parameters.…”

“…Several other probe methods that are effective in PECVD environments have been proposed, such as the self-excited electron resonance spectroscopy (SEERS), the surface wave probe (SWP), multipole resonance probe (MRP), and capacitive probe (CP). [19][20][21][22][23][24][25][26][27][28][29][30][31] The compact combined sensor, which is used as a heat flux sensor and a planer LP, has also been developed. [32,33] SEERS, which is a passive plasma probe based on a general hydrodynamical discharge model, can monitor n e and the electron collision rate.…”

Kinetic investigation of the planar Multipole Resonance Probe under arbitrary pressure

“…A thin dielectric layer with covers the electrodes and chamber wall. As described in [14,16], we assume that the chamber wall is infinite and the insulator is ignorable. A naturally oriented Cartesian coordinate system (x, y, z) is used, which locates the dielectric at −d < z < 0 and the plasma at z > 0.…”

“…In the past decade, several planar-type APRS probes have been developed, such as the planar multipole resonance probe (pMRP) [10][11][12][13][14][15][16], curling probe [17][18][19], and flat cutoff probe [20][21][22]. These probes can be flatly embedded into the chamber wall or chuck for minimally invasive process monitoring.…”

“…I. Previous work has studied the pMRP with the Drude model [10][11][12][13][14][15][16] and collision-less kinetic model [16]. The collision-less kinetic model ignores all collisions, and it only applies to the low-pressure plasma (a few Pa).…”