Jens Oberrath

The multipole resonance probe: characterization of a prototype

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 multipole resonance probe: Realization of an optimized radio-frequency plasma probe based on active plasma resonance spectroscopy

A diagnostic concept is presented which enables the simultaneous determination of plasma density, electron temperature, and collision rate in low-pressure gas discharges. The proposed method utilizes a radio-frequency driven probe of particular spherical design which is immersed in the plasma to excite a family of spatially bounded surface resonances. An analysis of the measured absorption spectrum S(ω) of the probe provides information on the distribution of the plasma in its vicinity, from which the values of the plasma parameters can be inferred. In its simplest realization, the probe consists of two dielectrically shielded, conducting hemispheres, which are symmetrically driven by a radio-frequency source, and the excited resonances can be classified as multipole fields, which allows an analytical evaluation of the measured signal. A comparison of the analytical results, 3D-field simulations, and first measurements of a prototype show the functionality of the presented probe concept.

A novel radio-frequency plasma probe for monitoring systems in dielectric deposition processes

This paper presents a novel industry compatible plasma probe for monitoring systems in dielectric deposition processes. The probe is based on the so called active plasma resonance spectroscopy and allows an extensive evaluation of different important plasma parameters, needed for the supervision and control of the plasma deposition process. Due to its assembly, the probe is insensitive against additional dielectric coating. Hence, the measurement performance is not affected. 3D-electromagnetic field simulations of the probe in a pseudo plasma deposition process, as well as the measurement with a prototype in a real deposition process show a good agreement with the expected behaviour and confirm the applicability of the probe as a monitoring tool for dielectric deposition processes.

Active plasma resonance spectroscopy: a functional analytic description

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 diagnostic 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.

Active plasma resonance spectroscopy: eigenfunction solutions in spherical geometry

The term active plasma resonance spectroscopy 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 ?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. The mathematical model of an arbitrarily shaped probe?plasma system can be written in an abstract but very compact equation. It contains an appropriate operator, which describes the dynamical behavior and can be split into a conservative and a dissipative part. Based on the cold plasma model, this manuscript provides a solution strategy to determine the electrical admittance of a specific probe?plasma system derived from the abstract dynamical equation. Focusing on probes with a spherical-shaped probe tip the general admittance can be derived analytically. Therefore, the matrix representation of the resolvent of the dynamical operator is determined. This matrix representation is derived by means of the eigenfunctions and eigenvalues of the conservative operator. It can be shown that these eigenvalues 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 established probe designs: the spherical impedance probe and the multipole resonance probe.

Active plasma resonance spectroscopy: a kinetic functional analytic description

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 ?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 such as the electron density or the electron temperature. This paper 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 radio frequency (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.

The multipole resonance probe: Evolution of a plasma sensor

A robust and sensitive plasma probe, the multipole resonance probe (MRP), and its importance for industrial purposes is presented and discussed in this paper. Based on its innovative concept and its simple model of the system ”probe-plasma”, a novel wall-mounted sensor is introduced. This sensor represents an optimized design of one sector of the MRPs assembly and is investigated within 3D-electromagnetic field simulations and compared to measurements of the MRP in an argon plasma. The resulting wall-mounted sensor can be designed for a desired application, which operates within a limited frequency range. The presented sensor covers a density range of approximately ne = 1016 m-3... 1017 m-3, which is sufficient for the considered process.

Kinetic damping in the spectra of the spherical impedance probe

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.

Collisionless spectral-kinetic simulation of the multipole resonance probe on GPU

Summary form only given. Plasma resonance spectroscopy is a well established plasma diagnostic method realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized geometrically simplified version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development, which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation.In the simulation the potential is separation in an inner and a vacuum potential. The inner potential is influenced by the charged particles and is calculated by a specialized Poisson solver. The vacuum potential fulfills Laplaces equation and consists of the applied voltage of the probe as boundary condition. Both potentials are expanded in spherical harmonics. For a practical particle pusher implementation, the expansion must be appropriately truncated. Compared to a PIC simulation a grid is unnecessary to calculate the force on the particles. To reduce the simulation time the code is parallelized and used on a GPU. This work purpose is a collisionless kinetic simulation, which can be used to investigate kinetic effects on the resonance behavior of the MRP.

Spectral-kinetic simulation of the multipole resonance probe

Summary form only given. Plasma resonance spectroscopy is a well established plasma diagnostic method realized in several designs. One of these designs is the multipole resonance probe (MRP)1. In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development, which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation.