Active Plasma Resonance Spectroscopy Research Articles

The multipole resonance probe: simultaneous determination of electron density and electron temperature using spectral kinetic simulation

The multipole resonance probe (MRP) is an innovative sensor suitable for monitoring and control of industrial plasma processes. It is a realization of ‘active plasma resonance spectroscopy’, a class of electromagnetic diagnostic methods which employ the ability of plasmas to resonate on or near the plasma frequency. A signal in the GHz range is fed to the plasma via an electrical probe; the spectral response S(ω) is recorded, and then evaluated with a mathematical model to obtain information on the internal plasma parameters. In this study, a spectral kinetic model of the MRP is discussed. It is superior to previous analyses based on the Drude model, as it allows to determine not only the electron density n e but also the electron temperature T e from S(ω). Good agreement with independent measurements shows the suitability of the model.

Kinetic simulation of the ideal multipole resonance probe

Active plasma resonance spectroscopy (APRS) is a process-compatible plasma diagnostic method, which utilizes the natural ability of plasmas to resonate on or near the electron plasma frequency. The multipole resonance probe (MRP) is a particular design of APRS that has a high degree of geometric and electric symmetry. The principle of the MRP can be described on the basis of an idealized geometry that is particularly suited for theoretical investigations. In a pressure regime of a few Pa or lower, kinetic effects become important, which cannot be predicted by the Drude model. Therefore, in this paper, a dynamic model of the interaction of the idealized MRP with a plasma is established. The proposed scheme reveals the kinetic behavior of the plasma that is able to explain the influence of kinetic effects on the resonance structure. Similar to particle-in-cell, the spectral kinetic method iteratively determines the electric field at each particle position, however, without employing any numerical grids. The optimized analytical model ensures the high efficiency of the simulation. Eventually, the presented work is expected to cover the limitation of the Drude model, especially for the determination of the pure collisionless damping caused by kinetic effects. A formula to determine the electron temperature from the half-width Δω is proposed.

On the Multipole Resonance Probe: Current Status of Research and Development

During the last decade a new probe design for active plasma resonance spectroscopy, the multipole resonance probe (MRP), was proposed, analyzed, developed, and characterized in two different designs: the spherical MRP (sMRP) and the planar MRP (pMRP). The advantage of the latter is that it can be integrated into the chamber wall and can minimize the perturbation of the plasma. Both designs can be applied for monitoring and control purposes of plasma processes for industrial applications. As usual for this measurement technique, a mathematical model is required to determine plasma parameter (electron density, electron temperature, and collision frequency of electrons with neutral atoms) from the measured resonances. Based on the cold plasma model a simple relationship between the resonance frequency and the electron density can be derived and leads to excellent measurement results. However, a simultaneous measurement of the electron temperature in low-pressure plasmas requires a kinetic model, because the half-width of the resonance peak is broadened by kinetic effects. Such a model has been derived and first results show the broadening of the spectra as expected. Deriving a relation between the half-width and the electron temperature will allow the simultaneous measurement and an improvement of monitoring and control concepts.

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

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.

The spherical multipole resonance probe: kinetic damping in its spectrum

The multipole resonance probe is one of the more recently developed measurement devices to measure plasma parameters like electron density and temperature based on the concept of active plasma resonance spectroscopy. The dynamical interaction between the probe and the plasma in an 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 multipole resonance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows us to compute an approximated response function and its corresponding spectra, which show additional damping due to kinetic effects.

Concepts for in situ characterization and control of plasma ion assisted deposition processes

In this paper recent results on monitoring and control of plasma ion assisted deposition (PIAD) processes are presented. An industrial PIAD system equipped with diagnostics for deposition rate and optical thickness was augmented by active plasma resonance spectroscopy to access electron density near the substrate. A series of experiments implementing different schemes to control the level of plasma assistance, while depositing a model 5-layer quarterwave stack SiO2/TiO2, were conducted. Data on in situ spectral transmission of the coatings was used to reconstruct optical properties and the thickness of each layer. Conventional control of anode voltage of the assist source Advanced Plasma Source (APS) was found to exhibit remarkable variations of electron density as drifts during deposition and shifts between separate runs. We demonstrate that measuring the electron density and using that signal in the feedback loop control of the APS greatly improves the layer-to-layer repeatability and run-to-run reproducibility of coating performance. Best results were obtained combining electron density control with optical monitoring for endpoint detection.

The planar Multipole Resonance Probe: a functional analytic approach

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.

A simple and straightforward expression for curling probe electron density diagnosis in reactive plasmas

Active plasma resonance spectroscopy (APRS) refers to the family of plasma diagnostic methods which utilize the ability of plasmas to resonate at frequencies close to the plasma frequency. APRS operates by exciting the plasma with a weak RF signal by means of a small electric probe. The response of the plasma is recorded by a network analyzer (NA). A mathematical model is applied to derive characteristics like the electron density and the electron temperature. The curling probe is a promising realization of APRS. The curling probe is well-qualified for the local measurement of the electron density in reactive plasmas. This spiral probe resonates in plasma at a larger density dependent frequency than the plasma frequency. This manuscript represents a simple and straightforward expression relating this resonance frequency to the electron density of the plasma. A good agreement is observed between the proposed expression and the results obtained from previous studies and numerical simulations.

Analytical investigation of microwave resonances of a curling probe for low and high-pressure plasma diagnostics

The concept of ‘active plasma resonance spectroscopy’ (APRS) has attracted greater interest in recent years as an established plasma diagnostic technique. The APRS describes a class of related methods utilizing the intrinsic ability of plasma to resonate at or near the electron plasma frequency . The Curling probe (CP) as a novel realization of the APRS idea, is a miniaturized spiral slot embedded flatly in the chamber wall. Consequently, a plasma diagnostic technique with minimum disturbance and without metal contamination can be developed. To measure the plasma parameters the CP is fed with a weak frequency-swept signal from the exterior of the plasma chamber by a network analyzer which also records the response of the plasma versus the frequency. The resonance behavior is strongly dependent on the electron density and the gas pressure. The CP has also the advantage of resonating at a frequency greater than which is dependent on the spiral’s length. The double resonance characteristic gives the CP the ability to be applied in varying plasma regimes. Assuming that the spiralization does not have a considerable effect on the resonances, a ‘straightened’ infinite length CP has recently been investigated (Arshadi and Brinkmann 2016 Plasma Sources Sci. Technol. 25 045014) to obtain the surface wave resonances. This work generalizes the approach and models the CP by a rectangular slot-type resonator located between plasma and quartz. Cold plasma theory and Maxwell’s equations are utilized to compute the electromagnetic fields propagating into the plasma by the diffraction of an incident plane wave at the slot. A mathematical model is employed and both kinds of resonances are derived. The analytical study of this paper shows good agreement with the numerical results of the probe inventors.

Influence of kinetic effects on the spectrum of a parallel electrode probe

Active plasma resonance spectroscopy (APRS) denotes a class of diagnostic techniques which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency . One particular class of APRS can be described in an abstract notation based on functional analytic methods in electrostatic approximation. These methods allow for a general solution of the kinetic model in arbitrary geometry. This solution is given as the response function of the probe-plasma system and is defined by the resolvent of an appropriate dynamical operator. The general response predicts an additional damping due to kinetic effects. This manuscript provides the derivation of an explicit response function of the kinetic APRS model in a simple geometry. Therefore, the resolvent is determined by its matrix representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function. The resulting spectra show clearly a stronger damping due to kinetic effects.

Analytical investigation into the resonance frequencies of a curling probe

The term ‘active plasma resonance spectroscopy’ (APRS) denotes a class of closely related plasma diagnostic methods which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ; an electrical radio frequency signal (in the GHz range) is coupled into the plasma via an antenna or a probe, the spectral response is recorded and a mathematical model is employed to determine plasma parameters such as the plasma density and the electron temperature. The curling probe, recently invented by Liang et al (2011 Appl. Phys. Express 4 066101), is a novel realization of the APRS concept which has many practical advantages. In particular, it can be miniaturized and flatly embedded into the chamber wall, thus allowing the monitoring of plasma processes without contamination nor disturbance. Physically, the curling probe can be understood as a ‘coiled’ form of the hairpin probe (Stenzel 1976 Rev. Sci. Instrum. 47 603). Assuming that the spiralization of the probe has little electrical effect, this paper investigates the characteristcs of a ‘straightened’ curling probe by modeling it as an infinite slot-type resonator that is in direct contact with the plasma. The diffraction of an incident plane wave at the slot is calculated by solving the cold plasma model and Maxwell’s equations simultaneously. The resonance frequencies of the probe are derived and are found to be in good agreement with the numerical results of the probe inventors.

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 ωpe: 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 ωpe: 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.

Study on electrostatic and electromagnetic probes operated in ceramic and metallic depositing plasmas

This paper discusses plasma probe diagnostics, namely the multipole resonance probe (MRP) and Langmuir probe (LP), operated in depositing plasmas. The aim of this work is to show that the combination of both probes provides stable and robust measurements and clear determination of plasma parameters for metallic and ceramic coating processes. The probes use different approaches to determine plasma parameters, e.g. electron density ne and electron temperature Te. The LP is a well-established plasma diagnostic, and its applicability in technological plasmas is well documented. The LP is a dc probe that performs a voltage sweep and analyses the measured current, which makes it insensitive against conductive metallic coating. However, once the LP is dielectrically coated with a ceramic film, its functionality is constricted. In contrast, the MRP was recently presented as a monitoring tool, which is insensitive to coating with dielectric ceramics. It is a new plasma diagnostic based on the concept of active plasma resonance spectroscopy, which uses the universal characteristic of all plasmas to resonate on or near the electron plasma frequency. The MRP emits a frequency sweep and the absorption of the signal, the |S11| parameter, is analysed. Since the MRP concept is based on electromagnetic waves, which are able to transmit dielectrics, it is insensitive to dielectric coatings. But once the MRP is metallized with a thin conductive film, no undisturbed RF-signal can be emitted into the plasma, which leads to falsified plasma parameter.In order to compare both systems, during metallic or dielectric coating, the probes are operated in a magnetron CCP, which is equipped with a titanium target. We present measurements in metallic and dielectric coating processes with both probes and elaborate advantages and problems of each probe operated in each coating environment.

Multiscale Splitting Method for the Boltzmann-Poisson Equation: Application to the Dynamics of Electrons

We present a model based on dynamics of electrons in a plasma using a simplified Boltzmann equation coupled with Poisson’s equation. The motivation arose from simulating active plasma resonance spectroscopy, which is used for plasma diagnostic techniques; see Braithwaite and Franklin (2009), Lapke et al. (2010), and Oberrath et al. (2011). Mathematically, we are interested in designing splitting methods for the model problem. While the full Boltzmann equation is delicate to solve, we decouple it into a transport and collision part, which are then solved in different ways. First we reduce it to a simplified transport-collision equation and start to analyse the abstract Cauchy problem using semigroup methods. Second, we pass to the coupled transport and collision model and apply the splitting ideas, resecting the different discretization schemes. The results are discussed first with numerical experiments and then we verify the underlying theoretical novelties.

An iterative splitting approach for linear integro-differential equations

The motivation for this paper is to solve a model based on the dynamics of electrons in a plasma using a simplified Boltzmann equation. Such problems have arisen in active plasma resonance spectroscopy, which is used for plasma diagnostic techniques; see Braithwaite and Franklin (2009) [1] . We propose a modified iterative splitting approach to solve the Boltzmann equations as a system of integro-differential equations. To enable solution by fast and iterative computations, we first transform the integro-differential equations into second order differential equations. Second, we split each second order differential equations into two first order differential equations via a splitting approach. We carry out an error analysis of the higher order iterative approach. Numerical experiments with a simplified Boltzmann equation will be discussed, along with the benefits of computing with this splitting approach.

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.