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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.

This study investigates the correlation between flow fields induced by a surface dielectric barrier discharge (SDBD) system and its application for the volatile organic compound (VOC) gas conversion process. As a benchmark molecule, the conversion of n-butane is monitored using flame ionization detectors, while the flow field is analysed using planar particle image velocimetry. Two individual setups are developed to facilitate both conversion measurement and investigation of induced fluid dynamics. Varying the gap distance between two SDBD electrode plates for three different n-butane mole fractions reveals local peaks in relative conversion around gap distances of 16 mm to 22 mm, indicating additional spatially dependent effects. The lowest n-butane mole fractions exhibit the highest relative conversion, while the highest n-butane mole fraction conversion yields the greatest number of converted molecules per unit time. Despite maintaining constant energy density, the relative conversion exhibits a gradual decrease with increasing distances. The results of the induced flow fields reveal distinct vortex structures at the top and bottom electrodes, which evolve in size and shape as the gap distances increase. These vortices exhibit gas velocity magnitudes approximately seven times higher than the applied external gas flow velocity. Vorticity and turbulent kinetic energy analyses provide insights into these structures' characteristics and their impact on gas mixing. A comparison of line profiles through the centre of the vortices shows peaks in the middle gap region for the same gap distances, correlating with the observed peaks in conversion. These findings demonstrate a correlation between induced flow dynamics and the gas conversion process, bridging plasma actuator studies with the domain of chemical plasma gas conversion., Comment: 16 pages, 10 figures

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

This study investigates the flow field induced by a surface dielectric barrier discharge (SDBD) system, known for its efficient pollution remediation of volatile organic compounds (VOCs). We aim to understand the flow dynamics that contribute to the high conversion observed in similar systems. Experimental techniques, including schlieren imaging and particle image velocimetry (PIV), applied with high temporal resolution, were used to analyse the flow field. Complementary, fluid simulations are employed to investigate the coupling between streamer and gas dynamics. Results show distinct fluid field behaviours for different electrode configurations, which differ in geometric complexity. The fluid field analysis of the most basic electrode design revealed behaviours commonly observed in actuator studies. The simulation results indicate the local information about the electron density as well as different temporal phases of the fluid flow. The electrode design with mostly parallel grid line structures exhibits confined vortices near the surface. In contrast, an electrode design also used in previous studies, is shown to promote strong gas transport through extended vortex structures, enhancing gas mixing and potentially explaining the high conversion observed., Comment: submitted to Plasma Chemistry and Plasma Processing by Springer Nature

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

In capacitively coupled radio frequency (CCRF) discharges, the interaction of the plasma and the surface boundaries is linked to a variety of highly relevant phenomena for technological processes. One possible plasma-surface interaction is the generation of secondary electrons (SEs), which significantly influence the discharge when accelerated in the sheath electric field. However, SEs, in particular electron-induced SEs ($\updelta$-electrons), are frequently neglected in theory and simulations. Due to the relatively high threshold energy for the effective generation of $\updelta$-electrons at surfaces, their dynamics are closely connected and entangled with the dynamics of the ion-induced SEs ($\upgamma$-electrons). Thus, a fundamental understanding of the electron dynamics has to be achieved on a nanosecond timescale, and the effects of the different electron groups have to be segregated. This work utilizes $1d3v$ Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations of a symmetric discharge in the low-pressure regime ($p\,=\, 1\,\rm{Pa}$) with the inclusion of realistic electron-surface interactions for silicon dioxide. A diagnostic framework is introduced that segregates the electrons into three groups ("bulk-electrons", "$\upgamma$-electrons", and "$\updelta$-electrons") in order to analyze and discuss their dynamics. A variation of the electrode gap size $L_\mathrm{gap}$ is then presented as a control tool to alter the dynamics of the discharge significantly. It is demonstrated that this control results in two different regimes of low and high plasma density, respectively. The fundamental electron dynamics of both regimes are explained, which requires a complete analysis starting at global parameters (e.g., densities) down to single electron trajectories.

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.

With the advent of the Internet of Things, nanoelectronic devices or memristors have been the subject of significant interest for use as new hardware security primitives. Among the several available memristors, BiFe$\rm O_{3}$ (BFO)-based electroforming-free memristors have attracted considerable attention due to their excellent properties, such as long retention time, self-rectification, intrinsic stochasticity, and fast switching. They have been actively investigated for use in physical unclonable function (PUF) key storage modules, artificial synapses in neural networks, nonvolatile resistive switches, and reconfigurable logic applications. In this work, we present a physics-inspired 1D compact model of a BFO memristor to understand its implementation for such applications (mainly PUFs) and perform circuit simulations. The resistive switching based on electric field-driven vacancy migration and intrinsic stochastic behaviour of the BFO memristor are modelled using the cloud-in-a-cell scheme. The experimental current-voltage characteristics of the BFO memristor are successfully reproduced. The response of the BFO memristor to changes in electrical properties, environmental properties (such as temperature) and stress are analyzed and consistent with experimental results., Comment: 13 pages and 8 figures

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.

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.

Bounded plasmas are characterized by a rapid but smooth transition from quasi-neutrality in the volume to electron depletion close to the electrodes and chamber walls. The thin non-neutral region, the boundary sheath, comprises only a small fraction of the discharge domain but controls much of its macroscopic behavior. Insights into the properties of the sheath and its relation to the plasma are of high practical and theoretical interest. The recently proposed smooth step model provides a closed analytical expression for the electric field in a planar, radio-frequency modulated sheath. It represents (i) the space charge field in the depletion zone, (ii) the generalized Ohmic and ambipolar field in the quasi-neutral zone, and (iii) a smooth interpolation for the transition in between. This investigation compares the smooth step model with the predictions of a more fundamental particle-in-cell/Monte Carlo collisions simulation and finds good quantitative agreement when the assumed length and time scale requirements are met. A second simulation case illustrates that the model remains applicable even when the assumptions are only marginally fulfilled

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.

Based on Tunable Diode Laser Absorption Spectroscopy (TDLAS) measurements of the spatially averaged and peak helium metastable atom densities in a capacitively coupled micro atmospheric pressure plasma jet operated in He/N$_2$ mixtures, the energy efficiency of metastable species (He-I 2$^3$S$_1$) generation is compared for three different scenarios: single frequency operation at (i) 13.56 MHz and (ii) 54.12 MHz, and Voltage Waveform Tailoring (VWT) at (iii) "valleys"-waveforms synthesized from four consecutive harmonics of 13.56 MHz. For each case, the dissipated power is measured based on a careful calibration procedure of voltage and current measurements. The results are compared to PIC/MCC simulation results and very good agreement is found. The computational results show that the choice of the surface coefficients in the simulation is important to reproduce the experimental data correctly. Due to the enhanced control of the spatio-temporal electron power absorption dynamics and, thus, of the electron energy distribution function by VWT, this approach does not only provide better control of the generation of excited and reactive species compared to single frequency excitation, but in case of helium metastables the energy efficiency is also shown to be significantly higher in case of VWT.

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 O$_2$ 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 O$_2$ concentration. The increase of the electronegativity with the increasing O$_2$ 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.

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.

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.

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 either solely conductive, non-reactive or insulating materials, with thicknesses in the order of the potential cutoff radius, i.e., 10 \r{A}. 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-SiO$_2$/Cu are in agreement with fundamental field theoretical expectations.

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.

Memristors based on a double barrier design have been analysed by various nano spectroscopic methods to unveil details about its microstructure and conduction mechanism. The device consists of an AlOx tunnel barrier and a NbOy/Au Schottky barrier sandwiched between Nb bottom electrode and 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, have a major influence on electronic conduction, these factors were carefully analysed. 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 strong deviations between observed and originally sought layout, this study highlights the robustness in terms of structural deviations of the double barrier memristor device.

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/TiO$_{\text{x}}$/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.

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.

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 the role of ion transport for the dynamic behavior of a double barrier quantum mechanical Al/Al$_2$O$_3$/Nb$_{\text{x}}$O$_{\text{y}}$/Au memristive device based on numerical simulations in conjunction with experimental measurements. The device consists of an ultra-thin Nb$_{\text{x}}$O$_{\text{y}}$ 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 for potential applications 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$_{\text{x}}$O$_{\text{y}}$ 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 of the double barrier device.

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.

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 $\gamma$ 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 drfit-diffusion model, noting that the suggested numerical scheme for the former model implies only a small additional computational cost.

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 term "Active Plasma Resonance Spectroscopy" refers to 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: An signal in the GHz range is coupled to the plasma via an electrical probe; the spectral response is recorded, and then evaluated with a mathematical model to obtain information on the electron density and other plasma parameters. In recent years, the concept has found renewed interest as a basis of industry compatible plasma diagnostics. This paper analyzes the diagnostics technique in terms of a general description based on functional analytic (or Hilbert Space) methods which hold for arbitrary probe geometries. It is shown that the response function of the plasma-probe system can be expressed as a matrix element of the resolvent of an appropriately defined dynamical operator. A specialization of the formalism for a symmetric probe desing is given, as well as an interpreation in terms of a lumped circuit model consisting of series resonators. We present ideas for an optimized probe design based on geometric and electrical symmetry.