Kinetic investigation of the planar multipole resonance probe in the low-pressure plasma

Abstract

Active Plasma Resonance Spectroscopy (APRS) is a well-established plasma diagnostic method: a radio frequency signal is coupled into the plasma via a probe or antenna, excites it to oscillate, and the response is evaluated through a mathematical model. The majority of APRS probes are invasive and perturb the plasma by their physical presence. The planar multipole resonance probe (pMRP) solves this problem: it can be integrated into the chamber wall and minimize the perturbation. Previous work has studied the pMRP in the frame of the Drude model, but it misses important kinetic effects like collision-less damping. In this work, a collision-less kinetic model is developed to further investigate the behavior of the pMRP. This model consists of the Vlasov equation, which is coupled with the Poisson equation under electrostatic approximation. The spectral response of the probe-plasma system is found by calculating the complex admittance. This model covers the kinetic effects and overcomes the limitations of the Drude model.

Development of the Measurement of Lateral Electron Density (MOLE) Probe Applicable to Low-Pressure Plasma Diagnostics

“…In the recent attempt, they demonstrated operation of the MCRS with the wall-mounted invasive antenna. Brinkmann et al developed the planar multipole resonance probe (pMRP) based on dipole resonance; this probe measures multipole resonance frequencies in S [ 23 , 35 , 36 , 37 , 38 ]. They introduced the pMRP [ 36 ], developed it as a monitoring sensor [ 37 ], and further investigated the pMRP [ 23 , 38 ].…”

“…Brinkmann et al developed the planar multipole resonance probe (pMRP) based on dipole resonance; this probe measures multipole resonance frequencies in S [ 23 , 35 , 36 , 37 , 38 ]. They introduced the pMRP [ 36 ], developed it as a monitoring sensor [ 37 ], and further investigated the pMRP [ 23 , 38 ]. Among those probes, the MCRS and microwave interferometry show wide measurement range and short time resolution, whereas there is lack of study for measurement limitations of the PCP, the CP, and the pMRP; those planar probes would be deeply investigated in terms of its detection limitations.…”

Development of a High-Linearity Voltage and Current Probe with a Floating Toroidal Coil: Principle, Demonstration, Design Optimization, and Evaluation

“…To improve process productivity, process monitoring techniques based on plasma diagnostic methods have garnered much attention [ 15 ] since key process parameters such as etching and deposition rates are related to the plasma parameters [ 16 , 17 , 18 , 19 , 20 ]. Plasma diagnostic methods employ an analysis of (i) the current-voltage characteristics of plasma using the Langmuir probe [ 21 , 22 , 23 ], (ii) the response characteristics of plasma to microwaves using resonators (microwave probes) [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], (iii) the optical emission characteristics of plasma using an optical emission spectrometer (OES) [ 33 , 34 ], and (iv) the voltage and current (VI) waveforms on a powered electrode using VI probes with circuit modeling [ 35 , 36 , 37 ].…”

“…Some of them, however, especially the Langmuir probe and microwave probes, are not suitable for plasma process monitoring, since they are invasive and as a result would distort and be perturbed by the processing. Recently, low-frequency modulation technology and non-invasive types have been proposed and are still under development [ 27 , 31 , 32 , 38 , 39 ]. Commonly implemented plasma process monitoring tools are the OES and VI probe; they are non-invasive and easy to install in the process equipment [ 40 , 41 , 42 , 43 , 44 ].…”

Kinetic investigation of the planar multipole resonance probe under arbitrary pressure

“…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 Covers collisionless and collisional damping Yields electron density and collision frequency Yields electron density, temperature, and collision frequency [20][21][22]. These probes can be flatly embedded into the chamber wall or chuck for minimally invasive process monitoring, which is preferred in the sensitive plasma process.…”