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This study presents a comprehensive examination of the development of TiN/SiO$_\mathrm{x}$/Cu/SiO$_\mathrm{x}$/TiN memristive devices, engineered for neuromorphic applications using a wedge-type deposition technique and Monte Carlo simulations. Identifying critical parameters for the desired device characteristics can be challenging with conventional trial-and-error approaches, which often obscure the effects of varying layer compositions. By employing an \textit{off-center} thermal evaporation method, we created a thickness gradient of SiO$_\mathrm{x}$ and Cu on a 4-inch wafer, facilitating detailed resistance map analysis through semiautomatic measurements. This allows to investigate in detail the influence of layer composition and thickness on single wafers, thus keeping every other process condition constant. Combining experimental data with simulations provides a precise understanding of the layer thickness distribution and its impact on device performance. Optimizing the SiO$_\mathrm{x}$ layers to be below 12.5 nm, coupled with a discontinuous Cu layer with a nominal thickness lower than 0.6 nm, exhibits analog switching properties with an R$_\mathrm{on}$/R$_\mathrm{off}$ ratio of $>$100, suitable for neuromorphic applications, whereas R $\times$ A analysis shows no clear signs of filamentary switching. Our findings highlight the significant role of carefully choosing the SiO$_\mathrm{x}$ and Cu thickness in determining the switching behavior and provide insights that could lead to the more systematic development of high-performance analog switching components for bio-inspired computing systems., Comment: Manuscript, 11 pages, 6 figures, not published

This study presents the computational modeling and simulation of silver nanoparticle networks (NPNs), which, in the realm of neuromorphic computation, suggest to be a promising candidate for nontraditional computation methods. The modeling of the networks construction, its electrical properties and model parameters are derived from well-established physical principles.

Nonlinearity is a crucial characteristic for implementing hardware security primitives or neuromorphic computing systems. The main feature of all memristive devices is this nonlinear behavior observed in their current-voltage characteristics. To comprehend the nonlinear behavior, we have to understand the coexistence of resistive, capacitive, and inertia (virtual inductive) effects in these devices. These effects originate from corresponding physical and chemical processes in memristive devices. A physics-inspired compact model is employed to model and simulate interface-type RRAMs such as Au/BiFeO$_{3}$/Pt/Ti, Au/Nb$_{\rm x}$O$_{\rm y}$/Al$_{2}$O$_{3}$/Nb, while accounting for the modeling of capacitive and inertia effects. The simulated current-voltage characteristics align well with experimental data and accurately capture the non-zero crossing hysteresis generated by capacitive and inductive effects. This study examines the response of two devices to increasing frequencies, revealing a shift in their nonlinear behavior characterized by a reduced hysteresis range and increased chaotic behavior, as observed through internal state attractors. Fourier series analysis utilizing a sinusoidal input voltage of varying amplitudes and frequencies indicates harmonics or frequency components that considerably influence the functioning of RRAMs. Moreover, we propose and demonstrate the use of the frequency spectra as one of the fingerprints for memristive devices.

This paper examines the coexistence of resistive, capacitive, and inertia (virtual inductive) effects in memristive devices, focusing on ReRAM devices, specifically the interface-type or non-filamentary analog switching devices. A physics-inspired compact model is used to effectively capture the underlying mechanisms governing resistive switching in NbO$_{\rm x}$ and BiFeO$_{3}$ based on memristive devices. The model includes different capacitive components in metal-insulator-metal structures to simulate capacitive effects. Drift and diffusion of particles are modeled and correlated with particles' inertia within the system. Using the model, we obtain the I-V characteristics of both devices that show good agreement with experimental findings and the corresponding C-V characteristics. This model also replicates observed non-zero crossing hysteresis in perovskite-based devices. Additionally, the study examines how the reactance of the device changes in response to variations in the device area and length., Comment: 4 pages, 7 figures

A number of memristive devices, mainly ReRAMs, have been reported to exhibit a unique non-zero crossing hysteresis attributed to the interplay of resistive and not yet fully understood `capacitive', and `inductive' effects. This work exploits a kinetic simulation model based on the stochastic cloud-in-a-cell method to capture these effects. The model, applied to Au/BiFeO$_{3}$/Pt/Ti interface-type devices, incorporates vacancy transport and capacitive contributions. The resulting nonlinear response, characterized by hysteresis, is analyzed in detail, providing an in-depth physical understanding of the virtual effects. Capacitive effects are modeled across different layers, revealing their significant role in shaping the non-zero crossing hysteresis behavior. Results from kinetic simulations demonstrate the impact of frequency-dependent impedance on the non-zero crossing phenomenon. This model provides insights into the effects of various device material properties, such as Schottky barrier height, device area and oxide layer on the non-zero crossing point., Comment: 7 pages, 5 figures

Machine learning has had an enormous impact in many scientific disciplines. Also in the field of low-temperature plasma modeling and simulation it has attracted significant interest within the past years. Whereas its application should be carefully assessed in general, many aspects of plasma modeling and simulation have benefited substantially from recent developments within the field of machine learning and data-driven modeling. In this survey, we approach two main objectives: (a) We review the state-of-the-art focusing on approaches to low-temperature plasma modeling and simulation. By dividing our survey into plasma physics, plasma chemistry, plasma-surface interactions, and plasma process control, we aim to extensively discuss relevant examples from literature. (b) We provide a perspective of potential advances to plasma science and technology. We specifically elaborate on advances possibly enabled by adaptation from other scientific disciplines. We argue that not only the known unknowns, but also unknown unknowns may be discovered due to the inherent propensity of data-driven methods to spotlight hidden patterns in data.

This feature article presents insights concerning the correlation of PECVD and PEALD thin film structures with their barrier or membrane properties. While in principle similar precursor gases and processes can be applied, the adjustment of deposition parameters for different polymer substrates can lead to either an effective diffusion barrier or selective permeabilities. In both cases the understanding of the film growth and the analysis of the pore size distribution and the pore surface chemistry is of utmost importance for the understanding of the related transport properties of small molecules. In this regard the article presents both concepts of thin film engineering and analytical as well as theoretical approaches leading to a comprehensive description of the state of the art in this field. Moreover, based on the presented correlation of film structure and molecular transport properties perspectives of future relevant research in this area is presented., Comment: 26 pages, 18 figures

This feature article considers the analysis of the initial states of film growth on polymer substrates. The assembled results are based on the cooperation between research groups in the field of plasma physics, chemistry, electric as well as mechanical engineering over the last years, mostly within the frame of the transregional project SFB-TR 87 ("Pulsed high power plasmas for the synthesis of nanostructured functional layers"). This feature article aims at bridging the gap between the understanding of plasma processes in the gas phase and the resulting surface and interface processes of the polymer. The results show that interfacial adhesion and initial film growth can be well controlled and even predicted based on the combination of analytical approaches., Comment: 22 pages, 16 figures

Poisson's equation plays an important role in modeling many physical systems. In electrostatic self-consistent low-temperature plasma (LTP) simulations, Poisson's equation is solved at each simulation time step, which can amount to a significant computational cost for the entire simulation. In this paper, we describe the development of a generic machine-learned Poisson solver specifically designed for the requirements of LTP simulations in complex 2D reactor geometries on structured Cartesian grids. Here, the reactor geometries can consist of inner electrodes and dielectric materials as often found in LTP simulations. The approach leverages a hybrid CNN-transformer network architecture in combination with a weighted multiterm loss function. We train the network using highly-randomized synthetic data to ensure the generalizability of the learned solver to unseen reactor geometries. The results demonstrate that the learned solver is able to produce quantitatively and qualitatively accurate solutions. Furthermore, it generalizes well on new reactor geometries such as reference geometries found in the literature. To increase the numerical accuracy of the solutions required in LTP simulations, we employ a conventional iterative solver to refine the raw predictions, especially to recover the high-frequency features not resolved by the initial prediction. With this, the proposed learned Poisson solver provides the required accuracy and is potentially faster than a pure GPU-based conventional iterative solver. This opens up new possibilities for developing a generic and high-performing learned Poisson solver for LTP systems in complex geometries.

Understanding and modeling plasma-surface interactions frame a multi-scale as well as multi-physics problem. Scale-bridging machine learning surface surrogate models have been demonstrated to perceive the fundamental atomic fidelity for the physical vapor deposition of pure metals. However, the immense computational cost of the data-generating simulations render a practical application with predictions on relevant timescales impracticable. This issue is resolved in this work for the sputter deposition of AlN in Ar/N$_2$ discharges by developing a scheme that populates the parameter spaces effectively. Hybrid reactive molecular dynamics / time-stamped force-bias Monte Carlo simulations of randomized plasma-surface interactions / diffusion processes are used to setup a physics-separating artificial neural network. The application of this generic machine learning model to a specific experimental reference case study enables the systematic analysis of the particle flux emission as well as underlying system state (e.g., composition, mass density, stress, point defect structure) evolution within process times of up to 45 minutes.

Simulations of Al thin film sputter depositions rely on accurate plasma and surface interaction models. Establishing the latter commonly requires a higher level of abstraction and means to dismiss the fundamental atomic fidelity. Previous works on sputtering processes addressed this issue by establishing machine learning surrogate models, which include a basic surface state (i.e., stoichiometry) as static input. In this work, an evolving surface state and defect structure are introduced to jointly describe sputtering and growth with physics-separating artificial neural networks. The data describing the plasma-surface interactions stem from hybrid reactive molecular dynamics/time-stamped force bias Monte Carlo simulations of Al neutrals and Ar$^+$ ions impinging onto Al(001) surfaces. It is demonstrated that the fundamental processes are comprehensively described by taking the surface state as well as defect structure into account. Hence, a machine learning plasma-surface interaction surrogate model is established that resolves the inherent kinetics with high physical fidelity. The resulting model is not restricted to input from modeling and simulation, but may similarly be applied to experimental input data.

Plasma-surface interactions during AlN thin film sputter deposition could be studied by means of reactive molecular dynamics (RMD) methods. This requires an interaction potential that describes all species as well as wall interactions (e.g., particle emission, damage formation) appropriately. However, previous works focused on the establishment of AlN bulk potentials. Although for the third-generation charge-optimized many-body (COMB3) potential at least a single reference surface was taken into account, surface interactions are subject to limited reliability only. The demand for a revised COMB3 AlN potential is met in two steps: First, the Ziegler-Biersack-Littmark potential is tapered and the variable charge model QTE$^+$ is implemented to account for high-energy collisions and distant charge transport, respectively. Second, the underlying parameterization is reworked by applying a self-adaptive evolution strategy implemented in the GARFfield software. Four wurtzite, three zinc blende and three rock salt surfaces are considered. An example study on the ion bombardment induced particle emission and point defect formation reveals that the revised COMB3 AlN potential is appropriate for the accurate investigation of plasma-surface interactions by means of RMD simulations.

Data science and technology offer transformative tools and methods to science. This review article highlights latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS). A large amount of data and machine learning algorithms go hand in hand. Most plasma data, whether experimental, observational or computational, are generated or collected by machines today. It is now becoming impractical for humans to analyze all the data manually. Therefore, it is imperative to train machines to analyze and interpret (eventually) such data as intelligently as humans but far more efficiently in quantity. Despite the recent impressive progress in applications of data science to plasma science and technology, the emerging field of DDPS is still in its infancy. Fueled by some of the most challenging problems such as fusion energy, plasma processing of materials, and fundamental understanding of the universe through observable plasma phenomena, it is expected that DDPS continues to benefit significantly from the interdisciplinary marriage between plasma science and data science into the foreseeable future., Comment: 112 pages (including 700+ references), 44 figures, submitted to IEEE Transactions on Plasma Science as a part of the IEEE Golden Anniversary Special Issue

A large number of simulation models have been proposed over the years to mimic the electrical behaviour of memristive devices. The models are based either on sophisticated mathematical formulations that do not account for physical and chemical processes responsible for the actual switching dynamics or on multi-physical spatially resolved approaches that include the inherent stochastic behaviour of real-world memristive devices but are computationally very expensive. In contrast to the available models, we present a computationally inexpensive and robust spatially 1D model for simulating interface-type memristive devices. The model efficiently incorporates the stochastic behaviour observed in experiments and can be easily transferred to circuit simulation frameworks. The ion transport, responsible for the resistive switching behaviour, is modelled using the kinetic Cloud-In-a-Cell scheme. The calculated current-voltage characteristics obtained using the proposed model show excellent agreement with the experimental findings., Comment: 10 pages, 8 figures

Molecular dynamics simulations are often used to study sputtering and thin film growth. Compressive stresses in these thin films are generally assumed to be caused by a combination of forward sputtered (peened) built-in particles and entrapped working gas atoms. While the former are assumed to hold a predominant role, the effect of the latter on the interaction dynamics as well as thin film properties are scarcely clarified (concurrent or causative). The inherent overlay of the ion bombardment induced processes render an isolation of their contribution impracticable. In this work, this issue is addressed by comparing the results of two case studies on the sputter deposition of Al thin films in Ar working gas. In the first run Ar atoms are fully retained. In the second run they are artificially neglected, as implanted Ar atoms are assumed to outgas anyhow and not alter the ongoing dynamics significantly. Both case studies have in common that the consecutive impingement of 100 particles (i.e., Ar$^+$ ions, Al atoms) onto Al(001) surfaces for ion energies in the range of 3 eV to 300 eV as well as Al/Ar$^+$ flux ratios from 0 to 1 are considered. The surface interactions are simulated by means of hybrid reactive molecular dynamics/force-biased Monte Carlo simulations and characterized in terms of mass density, Ar concentration, biaxial stress, shear stress, ring statistical connectivity profile, Ar gas porosity, Al vacancy density, and root-mean-squared roughness. Ultimately, implanted Ar atoms are found to form subnanometer sized eventually outgassing clusters for ion energies exceeding 100 eV. They fundamentally govern a variety of surface processes (e.g., forward sputtering/peening) and surface properties (e.g., compressive stresses) in the considered operating regime.

Simulations of thin film sputter deposition require the separation of the plasma and material transport in the gas-phase from the growth/sputtering processes at the bounding surfaces. Interface models based on analytic expressions or look-up tables inherently restrict this complex interaction to a bare minimum. A machine learning model has recently been shown to overcome this remedy for Ar ions bombarding a Ti-Al composite target. However, the chosen network structure (i.e., a multilayer perceptron) provides approximately 4 million degrees of freedom, which bears the risk of overfitting the relevant dynamics and complicating the model to an unreliable extend. This work proposes a conceptually more sophisticated but parameterwise simplified regression artificial neural network for an extended scenario, considering a variable instead of a single fixed Ti-Al stoichiometry. A convolutional $\beta$-variational autoencoder is trained to reduce the high-dimensional energy-angular distribution of sputtered particles to a latent space representation of only two components. In addition to a primary decoder which is trained to reconstruct the input energy-angular distribution, a secondary decoder is employed to reconstruct the mean energy of incident Ar ions as well as the present Ti-Al composition. The mutual latent space is hence conditioned on these quantities. The trained primary decoder of the variational autoencoder network is subsequently transferred to a regression network, for which only the mapping to the particular latent space has to be learned. While obtaining a competitive performance, the number of degrees of freedom is drastically reduced to 15,111 and 486 parameters for the primary decoder and the remaining regression network, respectively. The underlying methodology is general and can easily be extended to more complex physical descriptions with a minimal amount of data required.

For the measurement of the dynamics of fusion-born alpha particles $E_\alpha \leq 3.5$ MeV in ITER using collective Thomson scattering (CTS), safe transmission of a gyrotron beam at mm-wavelength (1 MW, 60 GHz) passing the electron cyclotron resonance (ECR) in the in-vessel tokamak `port plug' vacuum is a prerequisite. Depending on neutral gas pressure and composition, ECR-assisted gas breakdown may occur at the location of the resonance, which must be mitigated for diagnostic performance and safety reasons. The concept of a split electrically biased waveguide (SBWG) has been previously demonstrated in [C.P. Moeller, U.S. Patent 4,687,616 (1987)]. The waveguide is longitudinally split and a kV bias voltage applied between the two halves. Electrons are rapidly removed from the central region of high radio frequency electric field strength, mitigating breakdown. As a full scale experimental investigation of gas and electromagnetic field conditions inside the ITER equatorial port plugs is currently unattainable, a corresponding Monte Carlo simulation study is presented. Validity of the Monte Carlo electron model is demonstrated with a prediction of ECR breakdown and the mitigation pressure limits for the above quoted reference case with $^1$H$_2$ (and pollutant high $Z$ elements). For the proposed ITER CTS design with a 88.9 mm inner diameter SBWG, ECR breakdown is predicted to occur down to a pure $^1$H$_2$ pressure of 0.3 Pa, while mitigation is shown to be effective at least up to 10 Pa using a bias voltage of 1 kV. The analysis is complemented by results for relevant electric/magnetic field arrangements and limitations of the SBWG mitigation concept are addressed.

Variable charge models (e.g., EEM, QEq, ES+) in reactive molecular dynamics simulations often inherently impose a global charge transfer between atoms (approximating each system as ideal metal). Consequently, most surface processes (e.g., adsorption, desorption, deposition, sputtering) are affected, potentially causing dubious dynamics. This issue is meant to be addressed by the ACKS2 and QTPIE model, which are based on the Kohn-Sham density functional theory as well as a charge transfer restricting extension to the QEq model (approximating each system as ideal insulator), respectively. In a brief review of the QEq and the QTPIE model, their applicability for studying surface interactions is assessed in this work. Following this reasoning, the demand for a revised generalization of the QEq and QTPIE model is proposed, called charge transfer equilibration model or in short QTE model. This method is derived from the equilibration of constrained charge transfer variables, instead of considering atomic charge variables. The latter, however, are obtained by a respective transformation, employing an extended Lagrangian method. We moreover propose a mirror boundary condition and its implementation to accelerate surface investigations. The models proposed in this work facilitate reactive molecular dynamics simulations which describe various materials and surface phenomena appropriately.

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 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 as well as more complex spatially resolved Particle-in-Cell simulations.

Thin film processing by means of sputter deposition inherently depends on the interaction of energetic particles with a target surface and the subsequent particle transport. The length and time scales of the underlying physical phenomena span orders of magnitudes. A theoretical description which bridges all time and length scales is not practically possible. Advantage can be taken particularly from the well-separated time scales of the fundamental surface and plasma processes. Initially, surface properties may be calculated from a surface model and stored for a number of representative cases. Subsequently, the surface data may be provided to gas-phase transport simulations via appropriate model interfaces (e.g., analytic expressions or look-up tables) and utilized to define insertion boundary conditions. During run-time evaluation, however, the maintained surface data may prove to be not sufficient. In this case, missing data may be obtained by interpolation (common), extrapolation (inaccurate), or be supplied on-demand by the surface model (computationally inefficient). In this work, a potential alternative is established based on machine learning techniques using artificial neural networks. As a proof of concept, a multilayer perceptron network is trained and verified with sputtered particle distributions obtained from transport of ions in matter based simulations for Ar projectiles bombarding a Ti-Al composite. It is demonstrated that the trained network is able to predict the sputtered particle distributions for unknown, arbitrarily shaped incident ion energy distributions. It is consequently argued that the trained network may be readily used as a machine learning based model interface (e.g., by quasi-continuously sampling the desired sputtered particle distributions from the network), which is sufficiently accurate also in scenarios which have not been previously trained.

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 ionflux 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.

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 electric external 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 real plasma systems, i.e., the discharge itself, the matching network, the power generator as well as stray loss elements. While the main results 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 real plasma systems and, furthermore, may be applied to synthesize optimal matching networks.

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 low pressures 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.

The negative power absorption in low pressure plasmas is investigated by means of an analyical model which couples Boltzmann's equation and the quasi-stationary Maxwell's equation. 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 has been found for the first time. The model is applied to a low pressure inductively coupled plasma 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.

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 actually needed and which numerical concepts allow for the inherent 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 the conceptual details in the context of the sputtering scenario are elaborated on. Finally, two in the context of sputtering transport simulations often exploited assumptions, namely on the energy distribution of impinging ions as well as on the test particle approach, are validated for the proposed example discharge.

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 which is in contradiction to the widely acknowledged picture of filament growth, but consistent with recent experimental findings.

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=0.5 Pa. 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.

This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and 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.

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.

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.

In this work we investigate a numerical model of a coaxial RF-driven plasma jet operated at atmospheric pressure. Due to the cylindrical symmetry an adequate 2-D representation of the otherwise 3-dimensional structure is used. A helium-oxygen chemistry reaction scheme is applied. We study the effect of secondary electrons emitted at the inner electrode as well as the inserted dielectric tube and discuss their impact on the discharge behavior. We conclude that a proper choice of materials can improve the desired mode of operation of such plasma jets in terms of materials and surface processing.