The multipole resonance probe (MRP) was recently proposed as an economical and industry compatible plasma diagnostic device (Lapke et al 2008 Appl. Phys. Lett. 93 051502). This communication reports the experimental characterization of a first MRP prototype in an inductively coupled argon/nitrogen plasma at 10 Pa. The behavior of the device follows the predictions of both an analytical model and a numerical simulation. The obtained electron densities are in excellent agreement with the results of Langmuir probe measurements.
The term "Active Plasma Resonance Spectroscopy" denotes a class of diagnostic methods which employ the ability of plasmas to resonate on or near the plasma frequency. The basic idea dates back to the early days of discharge physics: A signal in the GHz range is coupled to the plasma via an electrical probe; the spectral response is recorded, and then evaluated with a mathematical model to obtain information on the electron density and other plasma parameters. In recent years, the concept has found renewed interest as a basis of industry compatible plasma diagnostics. This paper analyzes the diagnostics technique in terms of a general description based on functional analytic (or Hilbert Space) methods which hold for arbitrary probe geometries. It is shown that the response function of the plasma-probe system can be expressed as a matrix element of the resolvent of an appropriately defined dynamical operator. A specialization of the formalism to a symmetric probe design is given, as well as an interpretation in terms of a lumped circuit model consisting of series resonance circuits. We present ideas for an optimized probe design based on geometric and electrical symmetry.
The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency ω pe : A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature.This manuscript provides a kinetic description of APRS valid for all pressures and probe geometries.Subject of the description is the interaction of the probe with the plasma of its influence domain.In a first step, the kinetic free energy of that domain is established which has a definite time derivative with respect to the RF power. In the absence of RF excitation, it assumes the properties of a Lyapunov functional; its minimum provides the stable equilibrium of the plasma-probe system.Equipped with a scalar product motivated by the second variation of the free energy, the set of all perturbations of the equilibrium forms a Hilbert space. The dynamics of the perturbations can be cast in an evolution equation in that space. The spectral response function of the plasma-probe system consists of matrix elements of the resolvent of the dynamical operator. An interpretation in terms of an equivalent electric circuit model is given and the residual broadening of the spectrum in the collisionless regime is explained.
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.
The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency ω pe : A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature.Based on the cold plasma model, this manuscript provides the general analytic expression of the electrical admittance of a spherical shaped probe immersed into a plasma. It is derived from the matrix representation of an appropriate operator, which describes the dynamical behavior of the probe-plasma system. This dynamical operator can be split into a conservative operator and a dissipative operator. It can be shown that the eigenvalues of the conservative operator represent the resonance frequencies of the probe-plasma system which are simply connected to the electron density. As an example, the result is applied to the spherical impedance probe and the multipole resonance probe.
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