Prof. Dr.-Ing. Thomas Mussenbrock
Applied Electrodynamics and Plasma Technology
- Atomic oxygen generation in atmospheric pressure RF plasma jets driven by tailored voltage waveforms in mixtures of He and O2
Korolov, I. and Steuer, D. and Bischoff, L. and Hübner, G. and Liu, Y. and Schulz-Von der Gathen, V. and Böke, M. and Mussenbrock, T. and Schulze, J.
Journal of Physics D: Applied Physics 54 (2021)Absolute atomic oxygen densities measured space resolved in the active plasma volume of a COST microplasma reference jet operated in He/O2 and driven by tailored voltage waveforms are presented. The measurements are performed for different shapes of the driving voltage waveform, oxygen admixture concentrations, and peak-to-peak voltages. Peaks- and valleys-waveforms constructed based on different numbers of consecutive harmonics, N, of the fundamental frequency f 0 =13.56 MHz, different relative phases and amplitudes are used. The results show that the density of atomic oxygen can be controlled and optimized by voltage waveform tailoring (VWT). It is significantly enhanced by increasing the number of consecutive driving harmonics at fixed peak-to-peak voltage. The shape of the measured density profiles in the direction perpendicular to the electrodes can be controlled by VWT as well. For N >1 and peaks-/valleys-waveforms, it exhibits a strong spatial asymmetry with a maximum at one of the electrodes due to the spatially asymmetric electron power absorption dynamics. Thus, the atomic oxygen flux can be directed primarily towards one of the electrodes. The generation of atomic oxygen can be further optimized by changing the reactive gas admixture and by tuning the peak-to-peak voltage amplitude. The obtained results are understood based on a detailed analysis of the spatio-temporal dynamics of energetic electrons revealed by phase resolved optical emission spectroscopy. © 2021 Institute of Physics Publishing. All rights reserved.
view abstract 10.1088/1361-6463/abd20e
- Control of electron velocity distributions at the wafer by tailored voltage waveforms in capacitively coupled plasmas to compensate surface charging in high-aspect ratio etch features
Hartmann, P. and Wang, L. and Nösges, K. and Berger, B. and Wilczek, S. and Brinkmann, R.P. and Mussenbrock, T. and Juhasz, Z. and Donkó, Z. and Derzsi, A. and Lee, E. and Schulze, J.
Journal of Physics D: Applied Physics 54 (2021)Low pressure single- or dual-frequency capacitively coupled radio frequency (RF) plasmas are frequently used for high-aspect ratio (HAR) dielectric etching due to their capability to generate vertical ion bombardment of the wafer at high energies. Electrons typically reach the wafer at low energies and with a wide angular distribution during the local sheath collapse. Thus, in contrast to positive ions, electrons cannot propagate deeply into HAR etch features and the bottom as well as the sidewalls of such trenches can charge up positively, while the mask charges negatively. This causes etch stops and distortion of profile shapes. Here, we investigate low pressure, high voltage capacitively coupled RF argon gas discharges by Particle-In-Cell/Monte Carlo collisions simulations and demonstrate that this problem can be solved by Voltage Waveform Tailoring, i.e. the velocity and angular distribution of electrons impacting on the electrodes can be tuned towards high velocities and small angles to the surface-normal, while keeping the energies of the impacting ions high. The applied voltage waveforms consist of a base frequency of 400 kHz with 10 kV amplitude and a series of higher harmonics. A high frequency component at 40 or 60 MHz is used additionally. Square voltage waveforms with different rise-times are examined as well. We show that high fluxes of electrons towards the wafer at normal velocities of up to 2.2 × 107 m s-1 (corresponding to 1.4 keV energy) can be realized. © 2021 The Author(s). Published by IOP Publishing Ltd.
view abstract 10.1088/1361-6463/abf229
- Electron heating mode transitions in radio-frequency driven micro atmospheric pressure plasma jets in He/O2: A fluid dynamics approach
Liu, Y. and Korolov, I. and Hemke, T. and Bischoff, L. and Hübner, G. and Schulze, J. and Mussenbrock, T.
Journal of Physics D: Applied Physics 54 (2021)A two-dimensional fluid model is used to investigate the electron heating dynamics and the production of neutral species in a capacitively coupled radio-frequency micro atmospheric pressure helium plasma jet - specifically the COST jet - with a small oxygen admixture. Electron heating mode transitions are found to be induced by varying the driving voltage amplitude and the O2 concentration numerically and experimentally. The helium metastable density, and the charged species densities are highly relevant to the electron heating dynamics. By analyzing the creation and destruction mechanisms of the negative ions, we find that the generation of negative ions strongly depends on the O2 concentration. The increase of the electronegativity with the increasing O2 concentration leads to an enhancement of the bulk drift electric field. The distributions of the different neutral species densities along the direction of the gas flow inside the jet, as well as in the effluent differ a lot due to the relevant chemical reaction rates and the effect of the gas flow. The simulated results show that a fluid model can be an effective tool for qualitative investigations of micro atmospheric pressure plasma jets. © 2021 The Author(s). Published by IOP Publishing Ltd.
view abstract 10.1088/1361-6463/abf370
- Non-linear effects and electron heating dynamics in radio-frequency capacitively coupled plasmas with a non-uniform transverse magnetic field
Liu, Y. and Trieschmann, J. and Berger, B. and Schulze, J. and Mussenbrock, T.
Physics of Plasmas 28 (2021)A non-uniform transverse magnetic field is used to increase the plasma density and create an asymmetry in radio frequency capacitively coupled plasmas for plasma sputtering and plasma vapor deposition. Based on one-dimensional particle-in-cell/Monte Carlo collision simulations, the effect of the magnetic field magnitude on the non-linear behavior and the electron heating dynamics is studied for a pure helium plasma at a pressure of 30 mTorr. The results show that increasing the magnetic field magnitude can generate a more positive DC self-bias. As a result, non-linear oscillations of the electron current density and the electric field close to the grounded electrode are enhanced. An electric field reversal is induced when the powered electrode sheath collapses to balance electron and ion fluxes toward this boundary due to the strong confinement of electrons. Anomalous energetic electron beams are observed propagating from the collapsed sheath toward the plasma bulk. It is shown that such beams are reflections of the beams originating from the opposite expanding sheath based on the analysis of single particle motions. We show that energetic electron beams can be reflected by the transverse magnetic field. © 2021 Author(s).
view abstract 10.1063/5.0045947
- Charged particle dynamics and distribution functions in low pressure dual-frequency capacitively coupled plasmas operated at low frequencies and high voltages
Hartmann, P. and Wang, L. and Nösges, K. and Berger, B. and Wilczek, S. and Brinkmann, R.P. and Mussenbrock, T. and Juhasz, Z. and Donkó, Z. and Derzsi, A. and Lee, E. and Schulze, J.
Plasma Sources Science and Technology 29 (2020)In high aspect ratio (HAR) dielectric plasma etching, dual-frequency capacitively coupled radio-frequency plasmas operated at low pressures of 1 Pa or less are used. Such plasma sources are often driven by a voltage waveform that includes a low-frequency component in the range of hundreds of kHz with a voltage amplitude of 10 kV and more to generate highly energetic vertical ion bombardment at the wafer. In such discharges, the energetic positive ions can overcome the repelling potential created by positive wall charges inside the etch features, which allows high aspect ratios to be reached. In order to increase the plasma density a high-frequency driving component at several 10 MHz is typically applied simultaneously. Under such discharge conditions, the boundary surfaces are bombarded by extremely energetic particles, of which the consequences are poorly understood. We investigate the charged particle dynamics and distribution functions in this strongly non-local regime in argon discharges by particle-in-cell simulations. By including a complex implementation of plasma-surface interactions, electron induced secondary electron emission (δ-electrons) is found to have a strong effect on the ionization dynamics and the plasma density. Due to the high ion energies at the electrodes, very high yields of the ion induced secondary electron emission (γ-electrons) are found. However, unlike in classical capacitive plasmas, these γ-electrons do not cause significant ionization directly, since upon acceleration in the high voltage sheaths, these electrons are too energetic to ionize the neutral gas efficiently. These γ- and δ-electrons as well as electrons created in the plasma bulk and accelerated towards the electrodes to high energies by reversed electric fields during the local sheath collapse are found to induce the emission of a high number of δ-electrons, when they hit boundary surfaces. This regime is understood fundamentally based on the following approach: first, dual-frequency discharges with identical electrode materials are studied at different pressures and high-frequency driving voltages. Second, the effects of using electrodes made of different materials and characterized by different secondary electron emission coefficients are studied. The electron dynamics and charged particle distribution functions at boundary surfaces are determined including discharge asymmetries generated by using different materials at the powered and grounded electrodes. © 2020 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/ab9374
- Electron dynamics in low pressure capacitively coupled radio frequency discharges
Wilczek, S. and Schulze, J. and Brinkmann, R.P. and Donkó, Z. and Trieschmann, J. and Mussenbrock, T.
Journal of Applied Physics 127 (2020)In low temperature plasmas, the interaction of the electrons with the electric field is an important current research topic that is relevant for many applications. Particularly, in the low pressure regime (≤ 10 Pa), electrons can traverse a distance that may be comparable to the reactor dimensions without any collisions. This causes "nonlocal,"dynamics which results in a complicated space- and time-dependence and a strong anisotropy of the distribution function. Capacitively coupled radio frequency (CCRF) discharges, which operate in this regime, exhibit extremely complex electron dynamics. This is because the electrons interact with the space- and time-dependent electric field, which arises in the plasma boundary sheaths and oscillates at the applied radio frequency. In this tutorial paper, the fundamental physics of electron dynamics in a low pressure electropositive argon discharge is investigated by means of particle-in-cell/Monte Carlo collisions simulations. The interplay between the fundamental plasma parameters (densities, fields, currents, and temperatures) is explained by analysis (aided by animations) with respect to the spatial and temporal dynamics. Finally, the rendered picture provides an overview of how electrons gain and lose their energy in CCRF discharges. © 2020 Author(s).
view abstract 10.1063/5.0003114
- Helium metastable species generation in atmospheric pressure RF plasma jets driven by tailored voltage waveforms in mixtures of He and N2
Korolov, I. and Leimkühler, M. and Böke, M. and Donkó, Z. and Schulz-Von Der Gathen, V. and Bischoff, L. and Hübner, G. and Hartmann, P. and Gans, T. and Liu, Y. and Mussenbrock, T. and Schulze, J.
Journal of Physics D: Applied Physics 53 (2020)Spatially resolved tunable diode-laser absorption measurements of the absolute densities of He-I (23S1) metastables in a micro atmospheric pressure plasma jet operated in He/N2 and driven by 'peaks'- and 'valleys'-type tailored voltage waveforms are presented. The measurements are performed at different nitrogen admixture concentrations and peak-to-peak voltages with waveforms that consist of up to four consecutive harmonics of the fundamental frequency of 13.56 MHz. Comparisons of the measured metastable densities with those obtained from particle-in-cell/Monte Carlo collision simulations show a good quantitative agreement. The density of helium metastables is found to be significantly enhanced by increasing the number of consecutive driving harmonics. Their generation can be further optimized by tuning the peak-to-peak voltage amplitude and the concentration of the reactive gas admixture. These findings are understood based on detailed fundamental insights into the spatio-temporal electron dynamics gained from the simulations, which show that voltage waveform tailoring allows to control the electron energy distribution function to optimize the metastable generation. A high degree of correlation between the metastable creation rate and the electron impact excitation rate from the helium ground state into the He-I ((3s)3S1) level is observed for some conditions which may facilitate an estimation of the metastable densities based on phase resolved optical emission spectroscopy measurements of the 706.5 nm He-I line originating from the above level and metastable density values at proper reference conditions. © 2020 The Author(s). Published by IOP Publishing Ltd.
view abstract 10.1088/1361-6463/ab6d97
- A generic method for equipping arbitrary rf discharge simulation frameworks with external lumped element circuits
Schmidt, F. and Trieschmann, J. and Gergs, T. and Mussenbrock, T.
Journal of Applied Physics 125 (2019)External electric circuits attached to radio-frequency plasma discharges are essential for the power transfer into the discharge and are, therefore, a key element for plasma operation. Many plasma simulations, however, simplify or even neglect the external network. This is because a solution of the circuit's auxiliary differential equations following Kirchhoff's laws is required, which can become a tedious task especially for large circuits. This work proposes a method which allows one to include electric circuits in any desired radio-frequency plasma simulation. Conceptually, arbitrarily complex external networks may be incorporated in the form of a simple netlist. The suggested approach is based on the harmonic balance concept, which splits the whole system into the nonlinear plasma and the linear circuit contribution. A mathematical formulation of the influence of the applied voltage on the current for each specific harmonic is required and proposed. It is demonstrated that this method is applicable for both simple global plasma models and more complex spatially resolved Particle-in-Cell simulations. © 2019 Author(s).
view abstract 10.1063/1.5091965
- Control of electron dynamics, radical and metastable species generation in atmospheric pressure RF plasma jets by Voltage Waveform Tailoring
Korolov, I. and Donkó, Z. and Hübner, G. and Bischoff, L. and Hartmann, P. and Gans, T. and Liu, Y. and Mussenbrock, T. and Schulze, J.
Plasma Sources Science and Technology 28 (2019)Atmospheric pressure capacitively coupled radio frequency discharges operated in He/N2 mixtures and driven by tailored voltage waveforms are investigated experimentally using a COST microplasma reference jet and by means of kinetic simulations as a function of the reactive gas admixture and the number of consecutive harmonics used to drive the plasma. Pulse-type 'peaks'-waveforms, that consist of up to four consecutive harmonics of the fundamental frequency (f = 13.56 MHz), are used at a fixed peak-to-peak voltage of 400 V. Based on an excellent agreement between experimental and simulation results with respect to the DC self-bias and the spatio-temporal electron impact excitation dynamics, we demonstrate that Voltage Waveform Tailoring allows for the control of the dynamics of energetic electrons, the electron energy distribution function in distinct spatio-temporal regions of interest, and, thus, the generation of atomic nitrogen as well as helium metastables, which are highly relevant for a variety of technological and biomedical applications. By tuning the number of driving frequencies and the reactive gas admixture, the generation of these important species can be optimised. The behaviour of the DC self-bias, which is different compared to that in low pressure capacitive radio frequency plasmas, is understood based on an analytical model. © 2019 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/ab38ea
- Correlation between sputter deposition parameters and I-V characteristics in double-barrier memristive devices
Zahari, F. and Schlichting, F. and Strobel, J. and Dirkmann, S. and Cipo, J. and Gauter, S. and Trieschmann, J. and Marquardt, R. and Haberfehlner, G. and Kothleitner, G. and Kienle, L. and Mussenbrock, T. and Ziegler, M. and Kersten, H. and Kohlstedt, H.
Journal of Vacuum Science and Technology B: Nanotechnology and Microelectronics 37 (2019)Sputter deposition is one of the most important techniques for the fabrication of memristive devices. It allows us to adjust the concentration of defects within the fabricated metal-oxide thin film layers. The defect concentration is important for those memristive devices whose resistance changes during device operation due to the drift of ions within the active layer while an electric field is applied. Reversible change of the resistance is an important property for devices used in neuromorphic circuits to emulate synaptic behavior. These novel bioinspired hardware architectures are ascertained in terms of advantageous features such as lower power dissipation and improved cognitive capabilities compared to state-of-the-art digital electronics. Thus, memristive devices are intensively studied with regard to neuromorphic analog systems. Double-barrier memristive devices with the layer sequence Nb/Al/Al2O3/NbOx/Au are promising candidates to emulate analog synaptic behavior in hardware. Here, the niobium oxide acts as the active layer, in which charged defects can drift due to an applied electric field causing analog resistive switching. In this publication, crucial parameters of the process plasma for thin film deposition, such as floating potential, electron temperature, and the energy flux to the substrate, are correlated with the I-V characteristics of the individual memristive devices. The results from plasma diagnostics are combined with microscopic and simulation methods. Strong differences in the oxidation state of the niobium oxide layers were found by transmission electron microscopy. Furthermore, kinetic Monte Carlo simulations indicate the impact of the defect concentration within the NbOx layer on the I-V hysteresis. The findings may enable a new pathway for the development of plasma-engineered memristive devices tailored for specific application. © 2019 Author(s).
view abstract 10.1116/1.5119984
- Disrupting the spatio-temporal symmetry of the electron dynamics in atmospheric pressure plasmas by voltage waveform tailoring
Gibson, A.R. and Donkó, Z. and Alelyani, L. and Bischoff, L. and Hübner, G. and Bredin, J. and Doyle, S. and Korolov, I. and Niemi, K. and Mussenbrock, T. and Hartmann, P. and Dedrick, J.P. and Schulze, J. and Gans, T. and O'Connell, D.
Plasma Sources Science and Technology 28 (2019)Single frequency, geometrically symmetric Radio-Frequency (RF) driven atmospheric pressure plasmas exhibit temporally and spatially symmetric patterns of electron heating, and consequently, charged particle densities and fluxes. Using a combination of phase-resolved optical emission spectroscopy and kinetic plasma simulations, we demonstrate that tailored voltage waveforms consisting of multiple RF harmonics induce targeted disruption of these symmetries. This confines the electron heating to small regions of time and space and enables the electron energy distribution function to be tailored. © 2019 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aaf535
- Erratum: Multi frequency matching for voltage waveform tailoring (Plasma Sources Science and Technology (2018) 27 (095012) DOI: 10.1088/1361-6595/aad2cd)
Schmidt, F. and Schulze, J. and Johnson, E. and Booth, J.-P. and Keil, D. and French, D.M. and Trieschmann, J. and Mussenbrock, T.
Plasma Sources Science and Technology 28 (2019)Due to an error in the production process, the equation on should read: page (Formula Presented) is incorrect. The correct equation (Formula Presented). © 2019 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aaeb4b
- Mitigation of EC breakdown in the gyrotron transmission line of the ITER Collective Thomson Scattering diagnostic via a Split Biased Waveguide
Larsen, A.W. and Korsholm, S.B. and Gonçalves, B. and Gutierrez, H.E. and Henriques, E. and Infante, V. and Jensen, T. and Jessen, M. and Klinkby, E.B. and NonbØl, E. and Luis, R. and Vale, A. and Lopes, A. and Naulin, V. and Nielsen, S.K. and Salewski, M. and Rasmussen, J. and Taormina, A. and MØllsØe, C. and Mussenbrock, T. and Trieschmann, J.
Journal of Instrumentation 14 (2019)In this paper we present the results of the R&D work that has been performed on avoiding electron cyclotron (EC) gas breakdown inside the launcher transmission line (TL) of the ITER collective Thomson scattering (CTS) diagnostic, due to encountering the fundamental EC resonance, which is located inside the port plug vacuum for the baseline ITER magnetic field scenario. If an EC breakdown occurs, this can lead to strong local absorption of the CTS gyrotron beam, as well as arcing inside the ITER vacuum vessel, which must be avoided. Due to the hostile, restrictive, and nuclear environment in ITER, it is not possible to implement the standard method for avoiding EC breakdown - a controlled atmosphere at the EC resonance. Instead, the CTS diagnostic will include a longitudinally-split electrically-biased corrugated waveguide (SBWG) in the launcher transmission line. The SBWG works by applying a transverse DC bias voltage across the two electrically-isolated waveguide halves, causing free electrons to diffuse out of the EC resonant region before they can cause an electron-impact ionisation-avalanche, and thus an EC breakdown. Due to insufficient experimental facilities, the functionality of the SBWG is validated through Monte Carlo electron modelling. © 2019 IOP Publishing Ltd and Sissa Medialab.
view abstract 10.1088/1748-0221/14/11/C11009
- Voltage waveform tailoring in radio frequency plasmas for surface charge neutralization inside etch trenches
Krüger, F. and Wilczek, S. and Mussenbrock, T. and Schulze, J.
Plasma Sources Science and Technology 28 (2019)The etching of sub micrometer high-aspect-ratio (HAR) features into dielectric materials in low pressure radio frequency technological plasmas is limited by the accumulation of positive surface charges inside etch trenches. These are, at least partially, caused by highly energetic positive ions that are accelerated by the sheath electric field to high velocities perpendicular to the wafer. In contrast to these anisotropic ions, thermal electrons typically reach the electrode only during the sheath collapse and cannot penetrate deeply into HAR features to compensate the positive surface charges. This problem causes significant reductions of the etch rate and leads to deformations of the features due to ion deflection, i.e. the aspect ratio is limited. Here, we demonstrate that voltage waveform tailoring can be used to generate electric field reversals adjacent to the wafer during sheath collapse to accelerate electrons towards the electrode to allow them to penetrate deeply into HAR etch features to compensate positive surface charges and to overcome this process limitation. Based on 1D3V particle-in-cell/Monte Carlo collision simulations of a capacitively coupled plasma operated in argon at 1 Pa, we study the effects of changing the shape, peak-to-peak voltage, and harmonics' frequencies of the driving voltage waveform on this electric field reversal as well as on the electron velocity and angular distribution function at the wafer. We find that the angle of incidence of electrons relative to the surface normal at the wafer can be strongly reduced and the electron velocity perpendicular to the wafer can be significantly increased by choosing the driving voltage waveform in a way that ensures a fast and short sheath collapse. This is caused by the requirement of flux compensation of electrons and ions at the electrode on time average in the presence of a short and steep sheath collapse. © 2019 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/ab2c72
- Combined experimental and theoretical description of direct current magnetron sputtering of Al by Ar and Ar/N2 plasma
Trieschmann, J. and Ries, S. and Bibinov, N. and Awakowicz, P. and Mráz, S. and Schneider, J.M. and Mussenbrock, T.
Plasma Sources Science and Technology 27 (2018)Direct current magnetron sputtering of Al by Ar and Ar/N2 low pressure plasmas was characterized by experimental and theoretical means in a unified consideration. Experimentally, the plasmas were analyzed by optical emission spectroscopy, while the film deposition rate was determined by weight measurements and laser optical microscopy, and the film composition by energy dispersive x-ray spectroscopy. Theoretically, a global particle and power balance model was used to estimate the electron temperature T e and the electron density n e of the plasma at constant discharge power. In addition, the sputtering process and the transport of the sputtered atoms were described using Monte Carlo models - TRIDYN and dsmcFoam, respectively. Initially, the non-reactive situation is characterized based on deposition experiment results, which are in agreement with predictions from simulations. Subsequently, a similar study is presented for the reactive case. The influence of the N2 addition is found to be twofold, in terms of (i) the target and substrate surface conditions (e.g., sputtering, secondary electron emission, particle sticking) and (ii) the volumetric changes of the plasma density n e governing the ion flux to the surfaces (e.g., due to additional energy conversion channels). It is shown that a combined experimental/simulation approach reveals a physically coherent and, in particular, quantitative understanding of the properties (e.g., electron density and temperature, target surface nitrogen content, sputtered Al density, deposited mass) involved in the deposition process. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aac23e
- Consistent simulation of capacitive radio-frequency discharges and external matching networks
Schmidt, F. and Mussenbrock, T. and Trieschmann, J.
Plasma Sources Science and Technology 27 (2018)External matching networks are crucial and necessary for operating capacitively coupled plasmas in order to maximize the absorbed power. Experiments show that external circuits in general heavily interact with the plasma in a nonlinear way. This interaction has to be taken into account in order to be able to design suitable networks, e.g., for plasma processing systems. For a complete understanding of the underlying physics of this coupling, a nonlinear simulation approach which considers both the plasma and the circuit dynamics can provide useful insights. In this work, the coupling of an equivalent circuit plasma model and an external electric circuit composed of lumped elements is discussed. The plasma model itself is self-consistent in the sense that the plasma density and the electron temperature is calculated from the absorbed power based on a global plasma chemistry model. The approach encompasses all elements present in plasma systems, i.e., the discharge itself, the matching network, the power generator as well as stray loss elements. While the main result of this work is the conceptual approach itself, at the example of a single-frequency capacitively coupled discharge its applicability is demonstrated. It is shown that it provides an effective and efficient way to analyze and understand the nonlinear dynamics of plasma systems including the external circuit and, furthermore, may be applied to synthesize optimal matching networks. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aae429
- Disparity between current and voltage driven capacitively coupled radio frequency discharges
Wilczek, S. and Trieschmann, J. and Schulze, J. and Donkó, Z. and Brinkmann, R.P. and Mussenbrock, T.
Plasma Sources Science and Technology 27 (2018)In simulation as well as analytical modeling studies of low-pressure capacitively coupled radio frequency (CCRF) discharges, the assumption of both a driving voltage source or a driving current source is commonly used. It is unclear, however, how and to what extent the choice of the mode of driving, that prescribes either a sinusoidal discharge voltage or a sinusoidal discharge current, itself defines the discharge dynamics that results from these studies. To address this issue, 1d3v cylindrical particle-in-cell/Monte Carlo collisions simulations of asymmetric CCRF discharges are performed in the low pressure regime (p < 2 Pa). We study the nonlocal and nonlinear dynamics of these discharges on a nanosecond timescale. We find that the excitation of the plasma series resonance in the voltage driven case strongly enhances the nonlinear electron power dissipation. However, this resonance is suppressed when a current source is used, because the excitation of harmonics in the RF current is not allowed. Consequently, significant differences between both driving sources are observed in the plasma density as well as in the electron and the power coupling dynamics. We conclude that caution is advised in comparisons between simulations and experiments, as in the former the discharge dynamics is partly defined by the method of driving of the plasma source, while in the latter the addressed resonance phenomena are inherently present at low pressures, since experiments are typically voltage driven. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aae5c1
- Experimental and computational investigations of electron dynamics in micro atmospheric pressure radio-frequency plasma jets operated in He/N 2 mixtures
Bischoff, L. and Hübner, G. and Korolov, I. and Donkó, Z. and Hartmann, P. and Gans, T. and Held, J. and Schulz-Von Der Gathen, V. and Liu, Y. and Mussenbrock, T. and Schulze, J.
Plasma Sources Science and Technology 27 (2018)The electron power absorption dynamics in radio frequency driven micro atmospheric pressure capacitive plasma jets are studied based on experimental phase resolved optical emission spectroscopy and the computational particle in cell simulations with Monte Carlo treatment of collisions. The jet is operated at 13.56 MHz in He with different admixture concentrations of N 2 and at several driving voltage amplitudes. We find the spatio-temporal dynamics of the light emission of the plasma at various wavelengths to be markedly different. This is understood by revealing the population dynamics of the upper levels of selected emission lines/bands based on comparisons between experimental and simulation results. The populations of these excited states are sensitive to different parts of the electron energy distribution function and to contributions from other excited states. Mode transitions of the electron power absorption dynamics from the Ω- to the Penning-mode are found to be induced by changing the N 2 admixture concentration and the driving voltage amplitude. Our numerical simulations reveal details of this mode transition and provide novel insights into the operation details of the Penning-mode. The characteristic excitation/emission maximum at the time of maximum sheath voltage at each electrode is found to be based on two mechanisms: (i) a direct channel, i.e. excitation/emission caused by electrons generated by Penning ionization inside the sheaths and (ii) an indirect channel, i.e. secondary electrons emitted from the electrode due to the impact of positive ions generated by Penning ionization at the electrodes. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aaf35d
- Filament Growth and Resistive Switching in Hafnium Oxide Memristive Devices
Dirkmann, S. and Kaiser, J. and Wenger, C. and Mussenbrock, T.
ACS Applied Materials and Interfaces 10 (2018)We report on the resistive switching in TiN/Ti/HfO2/TiN memristive devices. A resistive switching model for the device is proposed, taking into account important experimental and theoretical findings. The proposed switching model is validated using 2D and 3D kinetic Monte Carlo simulation models. The models are consistently coupled to the electric field and different current transport mechanisms such as direct tunneling, trap-assisted tunneling, ohmic transport, and transport through a quantum point contact have been considered. We find that the numerical results are in excellent agreement with experimentally obtained data. Important device parameters, which are difficult or impossible to measure in experiments, are calculated. This includes the shape of the conductive filament, width of filament constriction, current density, and temperature distribution. To obtain insights in the operation of the device, consecutive cycles have been simulated. Furthermore, the switching kinetics for the forming and set process for different applied voltages is investigated. Finally, the influence of an annealing process on the filament growth, especially on the filament growth direction, is discussed. © 2018 American Chemical Society.
view abstract 10.1021/acsami.7b19836
- Improved homogeneity of plasma and coating properties using a lance matrix gas distribution in MW-PECVD
Kirchheim, D. and Wilski, S. and Jaritz, M. and Mitschker, F. and Oberberg, M. and Trieschmann, J. and Banko, L. and Brochhagen, M. and Schreckenberg, R. and Hopmann, C. and Böke, M. and Benedikt, J. and de los Arcos, T. and Grundmeier, G. and Grochla, D. and Ludwig, Al. and Mussenbrock, T. and Brinkmann, R.P. and Awakowicz, P. and Dahlmann, R.
Journal of Coatings Technology and Research (2018)Plasma reactors for the application of silicon oxide coatings (SiOx) are often customized to optimize the processes regarding substrate properties and targeted functionalities. The design of these reactors is often based on qualitative considerations. This paper evaluates the use of a numerical, free simulation software for continuous mechanical problems (OpenFOAM) as a tool to evaluate reactor design options. As demonstrator for this purpose serves a given reactor for large-area pulsed microwave plasmas with a precursor inlet in the form of a shower ring. Previous results indicate that the shower ring may lead to an inhomogeneity in plasma and coatings properties along the substrate surface. Thus, a new precursor inlet design shall be developed. For this, the distribution of the process gases in the reactor for a variety of gas inlet designs and gas flows was simulated and a design chosen based on the results. The reactor was modified accordingly, and the simulations correlated with experimental results of plasma and coating properties. The results show that, despite many simplifications, a simulation of the neutral gas distribution using an open-access software can be a viable tool to support reactor and process design development. © 2018, American Coatings Association.
view abstract 10.1007/s11998-018-0138-4
- Integration of external electric fields in molecular dynamics simulation models for resistive switching devices
Gergs, T. and Dirkmann, S. and Mussenbrock, T.
Journal of Applied Physics 123 (2018)Resistive switching devices emerged a huge amount of interest as promising candidates for non-volatile memories as well as artificial synapses due to their memristive behavior. The main physical and chemical phenomena which define their functionality are driven by externally applied voltages and the resulting electric fields. Although molecular dynamics simulations are widely used in order to describe the dynamics on the corresponding atomic length and time scales, there is a lack of models which allow for the actual driving force of the dynamics, i.e., externally applied electric fields. This is due to the restriction of currently applied models to solely conductive, non-reactive, or insulating materials, with thicknesses on the order of the potential cutoff radius, i.e., 10 Å. In this work, we propose a generic model, which can be applied in particular to describe the resistive switching phenomena of metal-insulator-metal systems. It has been shown that the calculated electric field and force distribution in case of the chosen example system Cu/a-SiO2/Cu are in agreement with the fundamental field theoretical expectations. © 2018 Author(s).
view abstract 10.1063/1.5029877
- Kinetic bandgap analysis of plasma photonic crystals
Trieschmann, J. and Mussenbrock, T.
Journal of Applied Physics 124 (2018)The dispersion relation of plasma and plasma-dielectric photonic multilayer structures is approached in terms of a one-dimensional Particle-in-Cell simulation. For several plasma-dielectric configurations, the system response is obtained using a pulsed excitation and a subsequent two-dimensional frequency analysis. It is first shown that the dispersion relation of a single, homogeneous plasma slab is well described by the cold-plasma model even at a low pressure of 1 Pa. The study is extended to the simulation of plasma photonic crystals with a variety of configurations based on the work of Hojo and Mase [J. Plasma Fusion Res. 80, 89 (2004)]. Considering a one-dimensional plasma photonic crystal made from alternating layers of dielectric and homogeneous plasma slabs, it is shown that the assumption of a cold-plasma description is well justified also in this case. Moreover, in this work, the results are reformatted and analyzed in a band diagram representation, in particular, based on the lattice constant a. Based on these considerations, a scaling invariant representation is presented, utilizing a generalized set of parameters. The study is completed with an exemplary comparison of three plasma-dielectric photonic crystal configurations and their corresponding band diagrams. © 2018 Author(s).
view abstract 10.1063/1.5055282
- Multi frequency matching for voltage waveform tailoring
Schmidt, F. and Schulze, J. and Johnson, E. and Booth, J.-P. and Keil, D. and French, D.M. and Trieschmann, J. and Mussenbrock, T.
Plasma Sources Science and Technology 27 (2018)Customized voltage waveforms composed of a number of frequencies and used as the excitation of radio-frequency plasmas can control various plasma parameters such as energy distribution functions, homogeneity of the ion flux, or ionization dynamics. So far this technology, while being extensively studied in academia, has yet to be established in applications. One reason for this is the lack of a suitable multi frequency matching network that allows for maximum power absorption for each excitation frequency that is generated and transmitted via a single broadband amplifier. In this work, a method is introduced for designing such a network based on network theory and synthesis. Using this method, a circuit simulation is established that connects an exemplary matching network to an equivalent circuit plasma model of a capacitive radio-frequency discharge. It is found that for a range of gas pressures and number of excitation frequencies the matching conditions can be satisfied, which proves the functionality and feasibility of the proposed concept. Based on the proposed multi frequency impedance matching, tailored voltage waveforms can be used at an industrial level. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aad2cd
- Observation of the generation of multiple electron beams during a single sheath expansion phase in capacitive RF plasmas
Berger, B. and You, K. and Lee, H.-C. and Mussenbrock, T. and Awakowicz, P. and Schulze, J.
Plasma Sources Science and Technology 27 (2018)The fundamental investigation of different electron heating modes is important in order to fully understand the generation of plasmas, as well as to optimize their technological applications. In this study, a capacitively coupled radio-frequency discharge is operated at its limit of comparably low plasma density. Phase resolved optical emission spectroscopy provides insights into the electron dynamics on a nanosecond time scale under these conditions. At low applied voltage amplitudes, it is observed that more than one electron beam is generated within a single phase of sheath expansion at a given electrode. When the voltage amplitude is increased these beams merge in time to a single electron beam. This effect has been predicted by particle in cell/Monte-Carlo collision simulations before and contradicts existing models that assume the generation of a single beam per sheath expansion phase by stochastic heating (Wilczek et al 2015 Plasma Sources Sci. Technol. 24 024002; Wilczek et al 2016 Phys. Plasmas 23 063514). In this study, results from a systematic experimental study of the effect are presented, which support the theoretically predicted phenomenon. © 2018 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aaefc7
- An enhanced lumped element electrical model of a double barrier memristive device
Solan, E. and Dirkmann, S. and Hansen, M. and Schroeder, D. and Kohlstedt, H. and Ziegler, M. and Mussenbrock, T. and Ochs, K.
Journal of Physics D: Applied Physics 50 (2017)The massive parallel approach of neuromorphic circuits leads to effective methods for solving complex problems. It has turned out that resistive switching devices with a continuous resistance range are potential candidates for such applications. These devices are memristive systems - nonlinear resistors with memory. They are fabricated in nanotechnology and hence parameter spread during fabrication may aggravate reproducible analyses. This issue makes simulation models of memristive devices worthwhile. Kinetic Monte-Carlo simulations based on a distributed model of the device can be used to understand the underlying physical and chemical phenomena. However, such simulations are very time-consuming and neither convenient for investigations of whole circuits nor for real-time applications, e.g. emulation purposes. Instead, a concentrated model of the device can be used for both fast simulations and real-time applications, respectively. We introduce an enhanced electrical model of a valence change mechanism (VCM) based double barrier memristive device (DBMD) with a continuous resistance range. This device consists of an ultra-thin memristive layer sandwiched between a tunnel barrier and a Schottky-contact. The introduced model leads to very fast simulations by using usual circuit simulation tools while maintaining physically meaningful parameters. Kinetic Monte-Carlo simulations based on a distributed model and experimental data have been utilized as references to verify the concentrated model. © 2017 IOP Publishing Ltd.
view abstract 10.1088/1361-6463/aa69ae
- Enhanced power coupling efficiency in inductive discharges with RF substrate bias driven at consecutive harmonics with adjustable phase
Berger, B. and Steinberger, T. and Schüngel, E. and Koepke, M. and Mussenbrock, T. and Awakowicz, P. and Schulze, J.
Applied Physics Letters 111 (2017)Inductive discharges with radio-frequency (RF) substrate bias are frequently used for various technological applications. We operate such a hybrid discharge with a phase-locked RF substrate bias at twice the frequency of the inductive coupling with fixed but adjustable phase between both RF sources in neon at low pressures of a few Pa. The ion flux to the substrate is found to be a function of this relative phase in the H-mode at constant RF powers as long as some residual capacitive coupling of the planar coil is present. For distinct choices of the phase, Phase Resolved Optical Emission Spectroscopy measurements show that energetic beam electrons generated by the expanding boundary sheaths (i) are well confined, (ii) are accelerated efficiently, and (iii) propagate vertically through the inductive skin layer at the times of maximum azimuthal induced electric field within the fundamental RF period. This enhances the inductive stochastic electron heating, the power coupling efficiency, and finally the ion flux. © 2017 Author(s).
view abstract 10.1063/1.5000144
- In depth nano spectroscopic analysis on homogeneously switching double barrier memristive devices
Strobel, J. and Hansen, M. and Dirkmann, S. and Neelisetty, K.K. and Ziegler, M. and Haberfehlner, G. and Popescu, R. and Kothleitner, G. and Chakravadhanula, V.S.K. and Kübel, C. and Kohlstedt, H. and Mussenbrock, T. and Kienle, L.
Journal of Applied Physics 121 (2017)Memristors based on a double barrier design have been analyzed by various nanospectroscopic methods to unveil details about their microstructure and conduction mechanism. The device consists of an AlOx tunnel barrier and a NbOy/Au Schottky barrier sandwiched between the Nb bottom electrode and the Au top electrode. As it was anticipated that the local chemical composition of the tunnel barrier, i.e., oxidation state of the metals as well as concentration and distribution of oxygen ions, has a major influence on electronic conduction, these factors were carefully analyzed. A combined approach was chosen in order to reliably investigate electronic states of Nb and O by electron energy-loss spectroscopy as well as map elements whose transition edges exhibit a different energy range by energy-dispersive X-ray spectroscopy like Au and Al. The results conclusively demonstrate significant oxidation of the bottom electrode as well as a small oxygen vacancy concentration in the Al oxide tunnel barrier. Possible scenarios to explain this unexpected additional oxide layer are discussed and kinetic Monte Carlo simulations were applied in order to identify its influence on conduction mechanisms in the device. In light of the deviations between observed and originally sought layout, this study highlights the robustness of the memristive function in terms of structural deviations of the double barrier memristor device. © 2017 Author(s).
view abstract 10.1063/1.4990145
- Kinetic analysis of negative power deposition in inductive low pressure plasmas
Trieschmann, J. and Mussenbrock, T.
Plasma Sources Science and Technology 26 (2017)Negative power deposition in low pressure inductively coupled plasmas (ICPs) is investigated by means of an analytical model which couples Boltzmann's equation and the quasi-stationary Maxwell's equations. Exploiting standard Hilbert space methods an explicit solution for both, the electric field and the distribution function of the electrons for a bounded discharge configuration subject to an unsymmetrical excitation is found for the first time. The model is applied to a low pressure ICP discharge. In this context particularly the anomalous skin effect and the effect of phase mixing is discussed. The analytical solution is compared with results from electromagnetic full wave particle in cell simulations. Excellent agreement between the analytical and the numerical results is found. © 2017 IOP Publishing Ltd.
view abstract 10.1088/1361-6595/aa51f2
- Kinetic investigation of the ion angular distribution in capacitive radio-frequency plasmas
Shihab, M. and Mussenbrock, T.
Physics of Plasmas 24 (2017)One of the key parameters in the context of plasma assisted processing in semiconductor fabrication using capacitive radio-frequency plasmas is the ion flux distribution at the substrate. Whereas the ion energy distribution function determines the etching rate and selectivity, the ion angular distribution controls the etching profile. In this contribution, we reveal the effect of the ion flux and the sheath potential on the ion angular distribution and the direct ion heat flux at the bottom of etching profiles in geometrically symmetric plasma reactors. The ion angular distribution and the direct ion heat flux are calculated as a function of the sheath potential, the driving frequency, and the phase shift between the two distinct harmonics of the driving voltage of dual frequency discharges. For this task, self-consistent particle-in-cell simulations subject to Monte Carlo collision are carried out. The results from particle-in-cell simulations which are computationally very expensive are compared and verified with those from the novel ensemble-in-spacetime model. It is confirmed that increasing the voltage of the high-frequency component, the high-frequency component, and/or make a phase shift of π/2 between the dual frequency, narrow the ion angular distribution and increase the direct ion heat flux to the etching profile bottom. In all simulation cases, a correlation between the narrowing of the ion angular distribution and the increase of the sheath potential and the sheath ion flux is found. © 2017 Author(s).
view abstract 10.1063/1.4994754
- Observations of Surface Mode Influence on Plasma Uniformity in PIC/MCC Simulations of Large Capacitive Discharges
Eremin, D. and Brinkmann, R.P. and Mussenbrock, T.
Plasma Processes and Polymers 14 (2017)Capacitively coupled plasmas with large electrodes, driven at high frequencies, exhibit new physics compared to small scale CCP devices or at low frequencies. This is due to excitation of two types of surface modes which arise as a result of interaction between the bulk plasma and the plasma sheaths separating the plasma from electrodes. Based on the physical effects that these modes cause, they are labeled as “self-bias” (SB) and “plasma-series resonance” (PSR) modes. Results of electrostatic 2d3v PIC/MCC simulations for a model geometry are used to selectively study the SB modes and demonstrate that they lead to non-uniformities of the plasma density profile owing to the influence of the SB modes on the heating of high- and low-energy electrons. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
view abstract 10.1002/ppap.201600164
- Particle-in-Cell/Test-Particle Simulations of Technological Plasmas: Sputtering Transport in Capacitive Radio Frequency Discharges
Trieschmann, J. and Schmidt, F. and Mussenbrock, T.
Plasma Processes and Polymers 14 (2017)The paper provides a tutorial to the conceptual layout of a self-consistently coupled Particle-In-Cell/Test-Particle model for the kinetic simulation of sputtering transport in capacitively coupled plasmas at low gas pressures. It explains when a kinetic approach is needed and which numerical concepts allow for capturing the often observed nonequilibrium behavior of the charged and neutral particles. At the example of a generic sputtering discharge, both the fundamentals of the applied Monte Carlo methods as well as their conceptual details are elaborated on. Finally, two assumptions that are often exploited in the context of sputtering transport simulations, namely on the energy distribution of impinging ions as well as on the test particle approach, are validated for the proposed example discharge. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
view abstract 10.1002/ppap.201600140
- Resistive switching in memristive electrochemical metallization devices
Dirkmann, S. and Mussenbrock, T.
AIP Advances 7 (2017)We report on resistive switching of memristive electrochemical metallization devices using 3D kinetic Monte Carlo simulations describing the transport of ions through a solid state electrolyte of an Ag/TiOx/Pt thin layer system. The ion transport model is consistently coupled with solvers for the electric field and thermal diffusion. We show that the model is able to describe not only the formation of conducting filaments but also its dissolution. Furthermore, we calculate realistic current-voltage characteristics and resistive switching kinetics. Finally, we discuss in detail the influence of both the electric field and the local heat on the switching processes of the device. © 2017 Author(s).
view abstract 10.1063/1.4985443
- The effect of realistic heavy particle induced secondary electron emission coefficients on the electron power absorption dynamics in single- and dual-frequency capacitively coupled plasmas
Daksha, M. and Derzsi, A. and Wilczek, S. and Trieschmann, J. and Mussenbrock, T. and Awakowicz, P. and Donkó, Z. and Schulze, J.
Plasma Sources Science and Technology 26 (2017)
view abstract 10.1088/1361-6595/aa7c88
- A computational analysis of the vibrational levels of molecular oxygen in low-pressure stationary and transient radio-frequency oxygen plasma
Kemaneci, E. and Booth, J.-P. and Chabert, P. and Van Dijk, J. and Mussenbrock, T. and Brinkmann, R.P.
Plasma Sources Science and Technology 25 (2016)Vibrational levels of molecular oxygen, O2(v < 42), are investigated in continuous and pulse-modulated low-pressure radio-frequency oxygen plasma with a global modelling approach. The model is benchmarked against a variety of pressure-, power- and time-resolved measurements of several inductive and asymmetric capacitive discharges available in the literature, and a good agreement is obtained. The sensitivity of the model with respect to the vibrational kinetics, the wall reactions and the spatial inhomogeneity of the charged particles are presented. The simulations without the vibrational levels are also shown for the sake of comparison. © 2016 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/25/2/025025
- Electron heating in technological plasmas
Schulze, J. and Mussenbrock, T.
Plasma Sources Science and Technology 25 (2016)The Special Issue of Plasma Sources Science and Technology is devoted to merging the state of knowledge and gather new ideas from theory and experiment. It aims to bridge the gap between fundamental research and application. The old, yet unresolved, issue of collisionless electron heating in capacitive RF low pressure plasmas is discussed computationally by Lafleur and Chabert. They find that the level of true collisionless/stochastic electron heating is small under typical operating conditions. Franek and colleagues focus on diagnostics aspects by applying Optical Emission Spectroscopy (OES) to correlate metastable densities, reduced electric fields, and EEDFs. Schweigert and colleagues analyze plasma breakdown in high voltage open discharges. Gosh and colleagues and Siddiqui and colleagues discuss electron heating in helicon plasma sources with and without microwave assistance. Campanell and colleagues introduce a fundamentally new effect of the self-amplification of electrons emitted from surfaces in plasmas with E?B fields, while Tian and Kushner discuss the control and relevance of VUV photon fluxes in ICPs.
view abstract 10.1088/0963-0252/25/2/020401
- Kinetic interpretation of resonance phenomena in low pressure capacitively coupled radio frequency plasmas
Wilczek, S. and Trieschmann, J. and Eremin, D. and Brinkmann, R.P. and Schulze, J. and Schuengel, E. and Derzsi, A. and Korolov, I. and Hartmann, P. and Donkó, Z. and Mussenbrock, T.
Physics of Plasmas 23 (2016)Low pressure capacitive radio frequency (RF) plasmas are often described by equivalent circuit models based on fluid approaches that predict the self-excitation of resonances, e.g., high frequency oscillations of the total current in asymmetric discharges, but do not provide a kinetic interpretation of these effects. In fact, they leave important questions open: How is current continuity ensured in the presence of energetic electron beams generated by the expanding sheaths that lead to a local enhancement of the conduction current propagating through the bulk? How do the beam electrons interact with cold bulk electrons? What is the kinetic origin of resonance phenomena? Based on kinetic simulations, we find that the energetic beam electrons interact with cold bulk electrons (modulated on a timescale of the inverse local electron plasma frequency) via a time dependent electric field outside the sheaths. This electric field is caused by the electron beam itself, which leaves behind a positive space charge, that attracts cold bulk electrons towards the expanding sheath. The resulting displacement current ensures current continuity by locally compensating the enhancement of the conduction current. The backflow of cold electrons and their interaction with the nonlinear plasma sheath cause the generation of multiple electron beams during one phase of sheath expansion and contribute to a strongly non-sinusoidal RF current. These kinetic mechanisms are the basis for a fundamental understanding of the electron power absorption dynamics and resonance phenomena in such plasmas, which are found to occur in discharges of different symmetries including perfectly symmetric plasmas. © 2016 Author(s).
view abstract 10.1063/1.4953432
- On the physics of a large CCP discharge
Eremin, D. and Bienholz, S. and Szeremley, D. and Trieschmann, J. and Ries, S. and Awakowicz, P. and Mussenbrock, T. and Brinkmann, R.P.
Plasma Sources Science and Technology 25 (2016)Demands of the plasma processing industry gradually lead to an increase in electrode areas and driving frequency of the commonly used capacitively coupled reactors. This brings about new phenomena which differ from the well known physics of smaller capacitively coupled plasma (CCP) devices. In this work we compare experimental data and results of numerical modeling for a large CCP discharge having a GEC cell-like geometry currently studied in context of a possible use as a sputtering device. Using an electrostatic implicit particle-in-cell code with Monte-Carlo collisions (PIC/MCC), we have been capable of reproducing all main features of the experimental discharges, which have strong relevance for the processing applications, such as the plasma uniformity and the self-bias. The side chamber proves to play an essential role in defining the physics of the whole device, featuring substantial production of plasma particles and participating in establishing the self-bias due to the telegraph effect observed for higher frequencies. © 2016 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/25/2/025020
- The role of ion transport phenomena in memristive double barrier devices
Dirkmann, S. and Hansen, M. and Ziegler, M. and Kohlstedt, H. and Mussenbrock, T.
Scientific Reports 6 (2016)In this work we report on the role of ion transport for the dynamic behavior of a double barrier quantum mechanical Al/Al 2 O 3 /Nb x O y /Au memristive device based on numerical simulations in conjunction with experimental measurements. The device consists of an ultra-Thin Nb x O y solid state electrolyte between an Al 2 O 3 tunnel barrier and a semiconductor metal interface at an Au electrode. It is shown that the device provides a number of interesting features such as an intrinsic current compliance, a relatively long retention time, and no need for an initialization step. Therefore, it is particularly attractive for applications in highly dense random access memories or neuromorphic mixed signal circuits. However, the underlying physical mechanisms of the resistive switching are still not completely understood yet. To investigate the interplay between the current transport mechanisms and the inner atomistic device structure a lumped element circuit model is consistently coupled with 3D kinetic Monte Carlo model for the ion transport. The simulation results indicate that the drift of charged point defects within the Nb x O y is the key factor for the resistive switching behavior. It is shown in detail that the diffusion of oxygen modifies the local electronic interface states resulting in a change of the interface properties. © The Author(s) 2016.
view abstract 10.1038/srep35686
- Wave digital emulation of a double barrier memristive device
Ochs, K. and Solan, E. and Dirkmann, S. and Mussenbrock, T.
Midwest Symposium on Circuits and Systems (2016)A memristor is a novel elementary passive device which is essentially a resistor with memory. This new device is capable of different technical applications like non-volatile memory, reconfigurable logic, and neuromorphic computation. Unfortunately, the commercial use of memristors is not common, which complicates the fabrication of devices with an arbitrarily desired functionality. This makes an investigation and development of real memristive circuits dedicated to a specific utilization very cumbersome. In order to circumvent these problems, we propose a wave digital memristor emulator, which is inherently passive like its analog counterpart. Due to its passivity even stable neuromorphic computation circuits with unpredictable interconnection structure can reliably be emulated. © 2016 IEEE.
view abstract 10.1109/MWSCAS.2016.7869946
- A double barrier memristive device
Hansen, M. and Ziegler, M. and Kolberg, L. and Soni, R. and Dirkmann, S. and Mussenbrock, T. and Kohlstedt, H.
Scientific Reports 5 (2015)We present a quantum mechanical memristive Nb/Al/Al2O3/NbxOy/Au device which consists of an ultra-thin memristive layer (NbxOy) sandwiched between an Al2O3 tunnel barrier and a Schottkylike contact. A highly uniform current distribution for the LRS (low resistance state) and HRS (high resistance state) for areas ranging between 70 μm2 and 2300 μm2 were obtained, which indicates a non-filamentary based resistive switching mechanism. In a detailed experimental and theoretical analysis we show evidence that resistive switching originates from oxygen diffusion and modifications of the local electronic interface states within the NbxOy layer, which influences the interface properties of the Au (Schottky) contact and of the Al2O3 tunneling barrier, respectively. The presented device might offer several benefits like an intrinsic current compliance, improved retention and no need for an electric forming procedure, which is especially attractive for possible applications in highly dense random access memories or neuromorphic mixed signal circuits.
view abstract 10.1038/srep13753
- A new hybrid scheme for simulations of highly collisional RF-driven plasmas
Eremin, D. and Hemke, T. and Mussenbrock, T.
Plasma Sources Science and Technology 25 (2015)This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using particle-in-cell/Monte-Carlo (PIC/MCC) scheme, whereas the heavy species are modeled within a fluid description. Validity of the popular drift-diffusion approximation is verified against a 'full' fluid model accounting for the ion inertia and a fully kinetic PIC/MCC code for ions as well as electrons. The fluid models require knowledge of the momentum exchange frequency and dependence of the ion mobilities on the electric field when the ions are in equilibrium with the latter. To this end an auxiliary Monte-Carlo scheme is constructed. It is demonstrated that the drift-diffusion approximation can overestimate ion transport in simulations of RF-driven discharges with heavy ion species operated in the γ mode at the atmospheric pressure or in all discharge simulations for lower pressures. This can lead to exaggerated plasma densities and incorrect profiles provided by the drift-diffusion models. Therefore, the hybrid code version featuring the full ion fluid model should be favored against the more popular drift-diffusion model, noting that the suggested numerical scheme for the former model implies only a small additional computational cost. © 2016 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/25/1/015009
- Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas
Gallian, S. and Trieschmann, J. and Mussenbrock, T. and Brinkmann, R.P. and Hitchon, W.N.G.
Journal of Applied Physics 117 (2015)This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and high power impulse magnetron sputtering (HiPIMS) systems, where secondary electrons enter the plasma after being accelerated in the cathode fall and encounter a nearly uniform bulk. An analytic calculation of the distribution function of hot electrons is presented; these are described as an initially monoenergetic beam that slows down by Coulomb collisions with a Maxwellian distribution of bulk (cold) electrons, and by inelastic collisions with neutrals. Although this analytical solution is based on a steady-state assumption, a comparison of the characteristic time-scales suggests that it may be applicable to a variety of practical time-dependent discharges, and it may be used to introduce kinetic effects into models based on the hypothesis of Maxwellian electrons. The results are verified for parameters appropriate to HiPIMS discharges, by means of time-dependent and fully kinetic numerical calculations. © 2015 AIP Publishing LLC.
view abstract 10.1063/1.4905943
- Experimental investigations of electron heating dynamics and ion energy distributions in capacitive discharges driven by customized voltage waveforms
Berger, B. and Brandt, S. and Franek, J. and Schüngel, E. and Koepke, M. and Mussenbrock, T. and Schulze, J.
Journal of Applied Physics 118 (2015)Capacitively coupled radio frequency plasmas driven by customized voltage waveforms provide enhanced opportunities to control process-relevant energy distributions of different particle species. Here, we present an experimental investigation of the spatio-temporal electron heating dynamics probed by Phase-Resolved Optical Emission Spectroscopy (PROES) in an argon discharge driven by up to three consecutive harmonics of 13.56 MHz with individually adjustable harmonics' amplitudes and phases. PROES and voltage measurements are performed at fixed total voltage amplitudes as a function of the number of driving harmonics, their relative phases, and pressure to study the effects of changing the applied voltage waveform on the heating dynamics in collisionless and collisional regimes. Additionally, the ion energy distribution function (IEDF) is measured at low pressure. In this collisionless regime, the discharge is operated in the α-mode. The velocity of energetic electron beams generated by the expanding sheaths is found to be affected by the number of driving harmonics and their relative phases. This is understood based on the sheath dynamics obtained from a model that determines sheath voltage waveforms. The formation of the measured IEDFs is understood and found to be directly affected by the observed changes in the electron heating dynamics. It is demonstrated that the mean ion energy can be controlled by adjusting the harmonics' phases. In the collisional regime at higher pressures changing the number of harmonics and their phases at fixed voltage is found to induce heating mode transitions from the α- to the γ-mode. Finally, a method to use PROES as a non-invasive diagnostic to monitor and detect changes of the ion flux to the electrodes is developed. © 2015 AIP Publishing LLC.
view abstract 10.1063/1.4937403
- Global modeling of hiPIMS systems: Transition from homogeneous to self organized discharges
Gallian, S. and Trieschmann, J. and Mussenbrock, T. and Hitchon, W.N.G. and Brinkmann, R.P.
ICOPS/BEAMS 2014 - 41st IEEE International Conference on Plasma Science and the 20th International Conference on High-Power Particle Beams (2015)
view abstract 10.1109/PLASMA.2014.7012495
- Kinetic simulation of filament growth dynamics in memristive electrochemical metallization devices
Dirkmann, S. and Ziegler, M. and Hansen, M. and Kohlstedt, H. and Trieschmann, J. and Mussenbrock, T.
Journal of Applied Physics 118 (2015)In this work, we report on kinetic Monte-Carlo calculations of resistive switching and the underlying growth dynamics of filaments in an electrochemical metallization device consisting of an Ag/TiO2/Pt sandwich-like thin film system. The developed model is not limited to (i) fast time scale dynamics and (ii) only one growth and dissolution cycle of metallic filaments. In particular, we present results from the simulation of consecutive cycles. We find that the numerical results are in excellent agreement with experimentally obtained data. Additionally we observe an unexpected filament growth mode that is in contradiction to the widely acknowledged picture of filament growth but consistent with recent experimental findings. © 2015 AIP Publishing LLC.
view abstract 10.1063/1.4936107
- Nonlocal behavior of the excitation rate in highly collisional RF discharges
Eremin, D. and Hemke, T. and Mussenbrock, T.
Plasma Sources Science and Technology 24 (2015)The present work focuses on the fundamental aspects of atmospheric pressure plasma electropositive discharges operated in the ohmically heated Ω mode, the electron heating and the excitation (ionization) rate. We find that the two do not necessarily have similar profiles and can show peaks at different locations, the ionization rate being much more sensitive to the electric field compared to the sensitivity to the electric field of the electron heating. This suggests an explanation for the discrepancies between the profiles of the power absorbed by electrons and the excitation patterns previously reported in the literature and observed in the present study. The excitation rate profile can then be explained by analyzing overlapping of the electron heating and the electric field profiles. Surprisingly, it has been discovered that the excitation dynamics exhibits nonlocal behavior having maxima spatially separated from the maxima of the electric field and the electron heating rate, a new effect in discharges operated in the Ω mode. The strong electric field in such discharges leads to large displacements of the electron component. This can produce significant charge separation close to the sheath or even in the bulk plasma because electrons are not able to follow the electric field adiabatically and maintain quasineutrality owing to the high collisionality. In particular, this leads to a significant distortion of the sheath structure and increase in the electric field there. © 2015 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/24/4/044004
- Pattern recognition with TiOx-based memristive devices
Zahari, F. and Hansen, M. and Mussenbrock, T. and Ziegler, M. and Kohlstedt, H.
AIMS Materials Science 2 (2015)We report on the development of TiOx-based memristive devices for bio-inspired neuromorphic systems. In particular, capacitor like structures of Al/AlOx/TiOx/Al with, respectively 20 nm and 50 nm thick TiOx-layers were fabricated and analyzed in terms of their use in neural network circuits. Therefore, an equivalent circuit model is presented which mimics the observed device properties on a qualitative level and relies on mobile oxygen ions by taking electronic transport through local conducting filaments and hopping between TiOx defect states into account. The model also comprises back diffusion of oxygen ions and allows for a realistic description of the experimental recorded device characteristics. The in Refs. [1-3] reported computing paradigms for pattern recognition have been used as guidelines for a device performance investigation at the network level. In particular, simulations of a spiking neural network are presented which allows for pattern recognition. As input patterns hand written digits taken from the MNIST Data base have been used. Within the network the memristive devices are arranged in a cross-bar array connected by 196 input neurons and ten output neurons. While, each input neuron corresponds to a specific pixel of the image of the input pattern, the output neurons were implemented as spiking neurons. In addition, the output neurons were inhibitory linked within an winner-take-it-all network and consist of a homeostasis-like behavior for their spiking thresholds. Based on the network simulation essential requirements for the development of optimal memristive device for neuromorphic circuits are discussed. © 2015 Martin Ziegler, et al.
view abstract 10.3934/matersci.2015.3.203
- The effect of the driving frequency on the confinement of beam electrons and plasma density in low-pressure capacitive discharges
Wilczek, S. and Trieschmann, J. and Schulze, J. and Schuengel, E. and Brinkmann, R.P. and Derzsi, A. and Korolov, I. and Donkó, Z. and Mussenbrock, T.
Plasma Sources Science and Technology 24 (2015)The effect of changing the driving frequency on the plasma density and the electron dynamics in a capacitive radio-frequency argon plasma operated at low pressures of a few Pa is investigated by particle-in-cell/Monte-Carlo collision simulations and analytical modeling. In contrast to previous assumptions, the plasma density does not follow a quadratic dependence on the driving frequency in this non-local collisionless regime. Instead, a step-like increase at a distinct driving frequency is observed. Based on an analytical power balance model, in combination with a detailed analysis of the electron kinetics, the density jump is found to be caused by an electron heating mode transition from the classical -mode into a low-density resonant heating mode characterized by the generation of two energetic electron beams at each electrode per sheath expansion phase. These electron beams propagate through the bulk without collisions and interact with the opposing sheath. In the low-density mode, the second beam is found to hit the opposing sheath during its collapse. Consequently, a large number of energetic electrons is lost at the electrodes resulting in a poor confinement of beam electrons in contrast to the classical -mode observed at higher driving frequencies. Based on the analytical model this modulated confinement quality and the related modulation of the energy lost per electron lost at the electrodes is demonstrated to cause the step-like change of the plasma density. The effects of a variation of the electrode gap, the neutral gas pressure, the electron sticking and secondary electron emission coefficients of the electrodes on this step-like increase of the plasma density are analyzed based on the simulation results. © 2015 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/24/2/024002
- Transport of sputtered particles in capacitive sputter sources
Trieschmann, J. and Mussenbrock, T.
Journal of Applied Physics 118 (2015)The transport of sputtered aluminum inside a multi frequency capacitively coupled plasma chamber is simulated by means of a kinetic test multi-particle approach. A novel consistent set of scattering parameters obtained for a modified variable hard sphere collision model is presented for both argon and aluminum. An angular dependent Thompson energy distribution is fitted to results from Monte Carlo simulations and used for the kinetic simulation of the transport of sputtered aluminum. For the proposed configuration, the transport of sputtered particles is characterized under typical process conditions at a gas pressure of p=0.5Pa. It is found that - due to the peculiar geometric conditions - the transport can be understood in a one dimensional picture, governed by the interaction of the imposed and backscattered particle fluxes. It is shown that the precise geometric features play an important role only in proximity to the electrode edges, where the effect of backscattering from the outside chamber volume becomes the governing mechanism. © 2015 AIP Publishing LLC.
view abstract 10.1063/1.4926878
- Complex electron heating in capacitive multi-frequency plasmas
Schulze, J. and Schungel, E. and Derzsi, A. and Korolov, I. and Mussenbrock, T. and Donko, Z.
IEEE Transactions on Plasma Science 42 (2014)Complex spatio-temporal electron heating dynamics are observed in kinetic simulations of geometrically symmetric low-pressure capacitive argon plasmas driven by multiple consecutive harmonics of 13.56 MHz. These dynamics are caused by an electrically induced asymmetry that leads to the self-excitation of plasma series resonance oscillations of the current. Such oscillations cause a nonsinusoidal movement of the boundary sheath edges and multiple phases of fast sheath expansions. These expansion phases lead to the generation of negative space charges that propagate into the bulk, where they affect the heating rate significantly and relax quickly. © 2014 IEEE.
view abstract 10.1109/TPS.2014.2306265
- On the OES line-ratio technique in argon and argon-containing plasmas
Siepa, S. and Danko, S. and Tsankov, T.V. and Mussenbrock, T. and Czarnetzki, U.
Journal of Physics D: Applied Physics 47 (2014)Optical emission spectroscopy is used to investigate capacitively coupled argon and argon-hydrogen-silane plasmas. The argon collisional-radiative model (CRM) used to extract the electron density and temperature from the spectra is presented. The electron energy distribution function, which is an input parameter to the model, is discussed in detail. Its strong variation with pressure is found to significantly influence the results for the (effective) temperature. For the analysis of the spectra the common line-ratio technique is applied. Special attention is paid to the choice of lines and a pair of line-ratios for optimum accuracy is suggested. For the argon gas mixture at high partial pressure of the admixed molecular gases the CRM reduces to a corona-like model, extended by a quenching term. The line-ratio method is found to fail under these conditions due to the strong depopulation of the argon 1s states. As a consequence, individual line intensities have to be used and an absolute calibration is required. An easy calibration method, which relies on the results obtained by the line-ratio method in pure argon, is proposed and applied. © 2014 IOP Publishing Ltd.
view abstract 10.1088/0022-3727/47/44/445201
- A phenomenological model for the description of rotating spokes in HiPIMS discharges
Gallian, S. and Hitchon, W.N.G. and Eremin, D. and Mussenbrock, T. and Brinkmann, R.P.
Plasma Science and Technology 22 (2013)In the ionization region above circular planar magnetrons, well-defined regions of high emissivity are observed, when the discharge is driven in the HiPIMS regime. These regions are characterized by high plasma density and are often referred to as 'spokes'. Once their mode is stabilized, these structures rotate in the E × B direction with a constant rotation frequency in the hundreds of kHz range. A phenomenological model of the phenomenon is developed, in the form of a system of nonlinear coupled partial differential equations. The system is solved analytically in a frame co-moving with the structure, and its solution gives the neutral density and the plasma density once the electron density shape is imposed. From the balance of ionization, electron loss and constant neutral refilling, a steady-state configuration in the rotating frame is achieved for the electron and neutral densities. Therefore, the spoke experimentally observed can be sustained simply by the combination of this highly reduced number of phenomena. Finally, a study of the sensitivity of neutral and plasma densities to the physical parameters is also given. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/22/5/055012
- Active plasma resonance spectroscopy: A functional analytic description
Lapke, M. and Oberrath, J. and Mussenbrock, T. and Brinkmann, R.P.
Plasma Sources Science and Technology 22 (2013)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. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/22/2/025005
- Continuum and kinetic simulations of the neutral gas flow in an industrial physical vapor deposition reactor
Bobzin, K. and Brinkmann, R.P. and Mussenbrock, T. and Bagcivan, N. and Brugnara, R.H. and Schäfer, M. and Trieschmann, J.
Surface and Coatings Technology 237 (2013)Magnetron sputtering used for physical vapor deposition processes often requires gas pressures well below 1. Pa. Under these conditions the gas flow in the reactor is usually determined by a Knudsen number of about one, i.e., a transition regime between the hydrodynamic and the rarefied gas regime. In the first, the gas flow is well described by the Navier-Stokes equations, while in the second a kinetic approach via the Boltzmann equation is necessary. In this paper the neutral gas flow of argon and molecular nitrogen gas inside an industrial scale plasma reactor was simulated using both a fluid model and a fully kinetic Direct Simulation Monte Carlo model.By comparing both model results the validity of the fluid model was checked. Although in both models a Maxwell-Boltzmann energy distribution of the neutral particles is the natural outcome, the results of the gas flow differ significantly. The fluid model description breaks down, due to the inappropriate assumption of a fluid continuum. This is due to exclusion of non-local effects in the multi dimensional velocity space, as well as invalid gas/wall interactions. Only the kinetic model is able to provide an accurate physical description of the gas flow in the transition regime. Our analysis is completed with a brief investigation of different definitions of the local Knudsen number. We conclude that the most decisive parameter - the spatial length scale L - has to be very careful chosen in order to obtain a reasonable estimate of the gas flow regime. © 2013 Elsevier B.V.
view abstract 10.1016/j.surfcoat.2013.08.018
- Ion energy distribution functions behind the sheaths of magnetized and non-magnetized radio frequency discharges
Trieschmann, J. and Shihab, M. and Szeremley, D. and Elgendy, A.E. and Gallian, S. and Eremin, D. and Brinkmann, R.P. and Mussenbrock, T.
Journal of Physics D: Applied Physics 46 (2013)The effect of a magnetic field on the characteristics of capacitively coupled radio frequency discharges is investigated and found to be substantial. A one-dimensional particle-in-cell simulation shows that geometrically symmetric discharges can be asymmetrized by applying a spatially inhomogeneous magnetic field. This effect is similar to the recently discovered electrical asymmetry effect. Both effects act independently, they can work in the same direction or compensate each other. Also the ion energy distribution functions at the electrodes are strongly affected by the magnetic field, although only indirectly. The field influences not the dynamics of the sheath itself but rather its operating conditions, i.e. the ion flux through it and voltage drop across it. To support this interpretation, the particle-in-cell results are compared with the outcome of the recently proposed ensemble-in-spacetime algorithm. Although that scheme resolves only the sheath and neglects magnetization, it is able to reproduce the ion energy distribution functions with very good accuracy, regardless of whether the discharge is magnetized or not. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0022-3727/46/8/084016
- Ionization by bulk heating of electrons in capacitive radio frequency atmospheric pressure microplasmas
Hemke, T. and Eremin, D. and Mussenbrock, T. and Derzsi, A. and Donkó, Z. and Dittmann, K. and Meichsner, J. and Schulze, J.
Plasma Sources Science and Technology 22 (2013)Electron heating and ionization dynamics in capacitively coupled radio frequency (RF) atmospheric pressure microplasmas operated in helium are investigated by particle-in-cell simulations and semi-analytical modeling. A strong heating of electrons and ionization in the plasma bulk due to high bulk electric fields are observed at distinct times within the RF period. Based on the model the electric field is identified to be a drift field caused by a low electrical conductivity due to the high electron-neutral collision frequency at atmospheric pressure. Thus, the ionization is mainly caused by ohmic heating in this 'Ω-mode'. The phase of strongest bulk electric field and ionization is affected by the driving voltage amplitude. At high amplitudes, the plasma density is high, so that the sheath impedance is comparable to the bulk resistance. Thus, voltage and current are about 45° out of phase and maximum ionization is observed during sheath expansion with local maxima at the sheath edges. At low driving voltages, the plasma density is low and the discharge becomes more resistive, resulting in a smaller phase shift of about 4°. Thus, maximum ionization occurs later within the RF period with a maximum at the discharge center. Significant analogies to electronegative low-pressure macroscopic discharges operated in the drift-ambipolar mode are found, where similar mechanisms induced by a high electronegativity instead of a high collision frequency have been identified. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/22/1/015012
- Kinetic simulation of the sheath dynamics in the intermediate radio frequency regime
Shihab, M. and Elgendy, A.T. and Korolov, I. and Derzsi, A. and Schulze, J. and Eremin, D. and Mussenbrock, T. and Donkó, Z. and Brinkmann, R.P.
Plasma Science and Technology 22 (2013)The dynamics of temporally modulated plasma boundary sheaths is studied in the intermediate radio frequency regime where the applied radio frequency and the ion plasma frequency (or the reciprocal of the ion transit time) are comparable. Two fully kinetic simulation algorithms are employed and their results are compared. The first is a realization of the well-known particle-in-cell technique with Monte Carlo collisions and simulates the entire discharge, a planar radio frequency capacitively coupled plasma with an additional ionization source. The second code is based on the recently published scheme Ensemble-in-Spacetime (EST); it resolves only the sheath and requires the time-resolved voltage across and the ion flux into the sheath as input. Ion inertia causes a temporal asymmetry (hysteresis) of the charge-voltage relation; other ion transit time effects are also found. The two algorithms are in good agreement, both with respect to the spatial and temporal dynamics of the sheath and with respect to the ion energy distributions at the electrodes. It is concluded that the EST scheme may serve as an efficient post-processor for fluid or global simulations and for measurements: it can rapidly and accurately calculate ion distribution functions even when no genuine kinetic information is available. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/22/5/055013
- Simulation benchmarks for low-pressure plasmas: Capacitive discharges
Turner, M.M. and Derzsi, A. and Donkó, Z. and Eremin, D. and Kelly, S.J. and Lafleur, T. and Mussenbrock, T.
Physics of Plasmas 20 (2013)Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We, therefore, claim that the results of these simulations represent strong benchmarks, which can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in the Appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena. © 2013 American Institute of Physics.
view abstract 10.1063/1.4775084
- Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation
Eremin, D. and Hemke, T. and Brinkmann, R.P. and Mussenbrock, T.
Journal of Physics D: Applied Physics 46 (2013)The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high-frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that the Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity. © 2013 IOP Publishing Ltd.
view abstract 10.1088/0022-3727/46/8/084017
- The multipole resonance probe: Evolution of a plasma sensor
Schulz, C. and Rolfes, I. and Styrnoll, T. and Awakowicz, P. and Oberrath, J. and Mussenbrock, T. and Brinkmann, R.P. and Storch, R. and Musch, T.
Proceedings of IEEE Sensors (2013)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 MRP's 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. © 2013 IEEE.
view abstract 10.1109/ICSENS.2013.6688324
- A novel radio-frequency plasma probe for monitoring systems in dielectric deposition processes
Schulz, C. and Styrnoll, T. and Lapke, M. and Oberrath, J. and Storch, R. and Awakowicz, P. and Brinkmann, R.P. and Musch, T. and Mussenbrock, T. and Rolfes, I.
Proceedings of the 2012 International Conference on Electromagnetics in Advanced Applications, ICEAA'12 (2012)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. © 2012 IEEE.
view abstract 10.1109/ICEAA.2012.6328725
- Modeling and Simulation of Ion Energy Distribution Functions in Technological Plasmas
Contributions to Plasma Physics 52 (2012)The highly advanced treatment of surfaces as etching and deposition is mainly enabled by the extraordinary properties of technological plasmas. The primary factors that influence these processes are the flux and the energy of various species, particularly ions, that impinge the substrate surface. These features can be theoretically described using the ion energy distribution function (IEDF). The article is intended to summarize the fundamental concepts of modeling and simulation of IEDFs from simplified models to self-consistent plasma simulations. Finally, concepts for controlling the IEDF are discussed. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
view abstract 10.1002/ctpp.201210053
- The electrical asymmetry effect in geometrically asymmetric capacitive radio frequency plasmas
Schüngel, E. and Eremin, D. and Schulze, J. and Mussenbrock, T. and Czarnetzki, U.
Journal of Applied Physics 112 (2012)The electrical asymmetry effect (EAE) allows an almost ideal separate control of the mean ion energy, 〈E i〉 , and flux, Γ i, at the electrodes in capacitive radio frequency discharges with identical electrode areas driven at two consecutive harmonics with adjustable phase shift, θ. In such geometrically symmetric discharges, a DC self bias is generated as a function of θ. Consequently, 〈E i〉 can be controlled separately from Γ i by adjusting the phase shift. Here, we systematically study the EA〈E i〉n low pressure dual-frequency discharges with different electrode areas operated in argon at 13.56 MHz and 27.12 MHz by experiments, kinetic simulations, and analytical modeling. We find that the functional dependence of the DC self bias on θ is similar, but its absolute value is strongly affected by the electrode area ratio. Consequently, the ion energy distributions change and 〈E i〉 can be controlled by adjusting θ, but its control range is different at both electrodes and determined by the area ratio. Under distinct conditions, the geometric asymmetry can be compensated electrically. In contrast to geometrically symmetric discharges, we find the ratio of the maximum sheath voltages to remain constant as a function of θ at low pressures and Γ i to depend on θ at the smaller electrode. These observations are understood by the model. Finally, we study the self-excitation of non-linear plasma series resonance oscillations and its effect on the electron heating. © 2012 American Institute of Physics.
view abstract 10.1063/1.4747914
- Fine-sorting one-dimensional particle-in-cell algorithm with Monte-Carlo collisions on a graphics processing unit
Mertmann, P. and Eremin, D. and Mussenbrock, T. and Brinkmann, R.P. and Awakowicz, P.
Computer Physics Communications 182 (2011)Particle-in-cell (PIC) simulations with Monte-Carlo collisions are used in plasma science to explore a variety of kinetic effects. One major problem is the long run-time of such simulations. Even on modern computer systems, PIC codes take a considerable amount of time for convergence. Most of the computations can be massively parallelized, since particles behave independently of each other within one time step. Current graphics processing units (GPUs) offer an attractive means for execution of the parallelized code. In this contribution we show a one-dimensional PIC code running on NVIDIA^TM GPUs using the CUDA^TM environment. A distinctive feature of the code is that size of the cells that the code uses to sort the particles with respect to their coordinates is comparable to size of the grid cells used for discretization of the electric field. Hence, we call the corresponding algorithm "fine-sorting". Implementation details and optimization of the code are discussed and the speed-up compared to classical CPU approaches is computed. © 2011 Elsevier B.V. All rights reserved.
view abstract 10.1016/j.cpc.2011.05.012
- Ignition of a microcavity plasma array
Wollny, A. and Hemke, T. and Gebhardt, M. and Brinkmann, R.P. and Mussenbrock, T.
IEEE Transactions on Plasma Science 39 (2011)Microcavity plasma arrays are regular arrays of inverse pyramidal cavities created on positively doped silicon wafers. Each cavity acts as a microscopic dielectric barrier discharge. It has an opening of 50 μm × 50 μm and a depth of 45 μm. The separation of the cavities is 50 μm. Operated at atmospheric pressure in argon and excited with a 100-kHz RF voltage, each cavity develops a localized microplasma. Experiments show a strong interaction of the individual cavities, leading, for example, to the propagation of ionization waves along the array surface. This paper studies the ignition of a microcavity plasma array by means of a numerical simulation. The propagation of an ionization wave is observed. Its propagation speed matches experimental findings. © 2006 IEEE.
view abstract 10.1109/TPS.2011.2128350
- Ionization wave propagation on a micro cavity plasma array
Wollny, A. and Hemke, T. and Gebhardt, M. and Peter Brinkmann, R. and Boettner, H. and Winter, J. and Schulz-Von Der Gathen, V. and Xiong, Z. and Kushner, M.J. and Mussenbrock, T.
Applied Physics Letters 99 (2011)Microcavity plasma arrays of inverse pyramidal cavities fabricated on p-Si wafers act as localized dielectric barrier discharges. When operated at atmospheric pressure in argon and excited with high voltage at 10 kHz, a strong interaction between individual cavities is observed leading to wave-like optical emission propagating along the surface of the array. This phenomenon is numerically investigated. The computed ionization wave propagates with a speed of 5 km/s, which agrees well with experiments. The wave propagation is due to the sequential drift of electrons followed by drift of ions between cavities seeded by photoemission of electrons by the plasma in adjacent cavities. © 2011 American Institute of Physics.
view abstract 10.1063/1.3647978
- Making a geometrically asymmetric capacitive rf discharge electrically symmetric
Schulze, J. and Schüngel, E. and Czarnetzki, U. and Gebhardt, M. and Brinkmann, R.P. and Mussenbrock, T.
Applied Physics Letters 98 (2011)The electrical asymmetry effect in a spherical, geometrically asymmetric capacitive argon discharge driven by two consecutive harmonics is investigated using particle in cell simulations and analytical modeling. We find that the discharge asymmetry can be reduced electrically by tuning the phase shift between the driving frequencies, i.e., the absolute value of the dc self-bias voltage can be completely reduced and the mean ion energies at both electrodes can be adapted. © 2011 American Institute of Physics.
view abstract 10.1063/1.3544541
- Spatial dynamics of helium metastables in sheath or bulk dominated rf micro-plasma jets
Niermann, B. and Hemke, T. and Babaeva, N.Y. and Böke, M. and Kushner, M.J. and Mussenbrock, T. and Winter, J.
Journal of Physics D: Applied Physics 44 (2011)Space resolved concentrations of helium He (3S1) metastable atoms in an atmospheric pressure radio-frequency micro-plasma jet were measured using tunable diode laser absorption spectroscopy. The spatial profile of metastable atoms in the volume between the electrodes was deduced for various electrode gap distances. Density profiles reveal the sheath structure and reflect the plasma excitation distribution, as well as the dominance of the α-mode discharge. Gap width variations show the transition from a normal glow plasma to a pure sheath discharge. In order to analyse and verify the experimentally observed profiles of the metastable atoms, a two-dimensional simulation model was set up. Applying an appropriate He/N2/O 2 chemistry model, the correlation between the metastable profiles and the underlying excitation mechanisms was obtained. © 2011 IOP Publishing Ltd.
view abstract 10.1088/0022-3727/44/48/485204
- Spatially resolved simulation of a radio-frequency driven micro-atmospheric pressure plasma jet and its effluent
Hemke, T. and Wollny, A. and Gebhardt, M. and Brinkmann, R.P. and Mussenbrock, T.
Journal of Physics D: Applied Physics 44 (2011)Radio-frequency driven plasma jets are frequently employed as efficient plasma sources for surface modification and other processes at atmospheric pressure. The radio-frequency driven micro-atmospheric pressure plasma jet (μAPPJ) is a particular variant of that concept whose geometry allows direct optical access. In this work, the characteristics of the μAPPJ operated with a helium-oxygen mixture and its interaction with a helium environment are studied by numerical simulation. The density and temperature of the electrons, as well as the concentration of all reactive species are studied both in the jet itself and in its effluent. It is found that the effluent is essentially free of charge carriers but contains a substantial amount of activated oxygen (O, O3 and O2(1Δ)). The simulation results are verified by comparison with experimental data. © 2011 IOP Publishing Ltd.
view abstract 10.1088/0022-3727/44/28/285206
- The multipole resonance probe: Characterization of a prototype
Lapke, M. and Oberrath, J. and Schulz, C. and Storch, R. and Styrnoll, T. and Zietz, C. and Awakowicz, P. and Brinkmann, R.P. and Musch, T. and Mussenbrock, T. and Rolfes, I.
Plasma Sources Science and Technology 20 (2011)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. © 2011 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/20/4/042001
- The influence of the relative phase between the driving voltages on electron heating in asymmetric dual frequency capacitive discharges
Ziegler, D. and Trieschmann, J. and Mussenbrock, T. and Brinkmann, R.P. and Schulze, J. and Czarnetzki, U. and Semmler, E. and Awakowicz, P. and O'Connell, D. and Gans, T.
Plasma Sources Science and Technology 19 (2010)The influence of the relative phase between the driving voltages on electron heating in asymmetric phase-locked dual frequency capacitively coupled radio frequency plasmas operated at 2 and 14 MHz is investigated. The basis of the analysis is a nonlinear global model with the option to implement a relative phase between the two driving voltages. In recent publications it has been reported that nonlinear electron resonance heating can drastically enhance the power dissipation to electrons at moments of sheath collapse due to the self-excitation of nonlinear plasma series resonance (PSR) oscillations of the radio frequency current. This work shows that depending on the relative phase of the driving voltages, the total number and exact moments of sheath collapse can be influenced. In the case of two consecutive sheath collapses a substantial increase in dissipated power compared with the known increase due to a single PSR excitation event per period is observed. Phase resolved optical emission spectroscopy (PROES) provides access to the excitation dynamics in front of the driven electrode. Via PROES the propagation of beam-like energetic electrons immediately after the sheath collapse is observed. In this work we demonstrate that there is a close relation between moments of sheath collapse, and thus excitation of the PSR, and beam-like electron propagation. A comparison of simulation results to experiments in a single and dual frequency discharge shows good agreement. In particular the observed influence of the relative phase on the dynamics of a dual frequency discharge is described by means of the presented model. Additionally, the analysis demonstrates that the observed gain in dissipation is not accompanied by an increase in the electrode's dc-bias voltage which directly addresses the issue of separate control of ion flux and ion energy in dual frequency capacitively coupled radio frequency plasmas. © 2010 IOP Publishing Ltd.
view abstract 10.1088/0963-0252/19/4/045001
- The multipole resonance probe: Realization of an optimized radio-frequency plasma probe based on active plasma resonance spectroscopy
Schulz, C. and Lapke, M. and Oberrath, J. and Storch, R. and Styrnoll, T. and Zietz, C. and Awakowicz, P. and Brinkmann, R.P. and Musch, T. and Mussenbrock, T. and Rolfes, I.
MECAP'10, 1st Middle East Conference on Antennas and Propagation (2010)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(Ï) 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 radiofrequency 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. © 2010-IEEE APS.
view abstract 10.1109/MECAP.2010.5724175
modelling and simulation