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We present a method for the treatment of the boundary conditions and the particle loading in a self-consistent semi-infinite Particle-In-Cell simulation. We assume a nonionizing, collisional plasma in contact with an electrode. The simulation is planar and one-dimensional (1d-2v), and is driven by an rf and/or DC current source. The particle loading is done by appropriate drifting velocity distributions, both for ions and electrons. Limiting the simulation to the region immediately adjacent to the electrode dramatically improves run-times and diagnostic resolution and is ideal for studying the sheath and plasma-sheath interface independently from the rest of the plasma. The method can be generalized easily to model cylindrical and spherical geometries, and surface processes can also be included. The control parameters of the simulation are the values for the current drive (Irf, ωrf, IDC), the species temperatures in the bulk plasma Ts, and the values of the ion fluxes Γs.

Low-pressure capacitive rf plasmas can be maintained chiefly by collisionless heating in the rf modulated sheaths adjacent to the electrodes. Theoretical models dealing with this mechanism are often based on a `hard wall' approximation where the electrons are considered to collide elastically with the oscillating sheath edge. The power transfer is then calculated by averaging forward and reverse power fluxes over an rf period. There are, however, several drawbacks to this approach: the models are sensitive to assumptions regarding the incident electron distribution, transit time effects in the sheath electric field are neglected, electron loss is not considered and current conservation is not satisfied. In order to examine the validity of the theoretical models, we use a Monte Carlo approach to study electron interactions with the model and self-consistent fields providing modifications that can lead to a more consistent treatment of the electron dynamics inside the sheath. Of particular importance is the presence of a small field behind the moving electron sheath edge which maintains quasi-neutrality between the electron sheath position and the bulk plasma. In addition, a semi-infinite particle-in-cell (PIC) simulation is used to investigate in detail sheath dynamics. The errors that the `hard wall' approximation gives are calculated and power deposition scalings with current drive, frequency and electron temperature are provided. Our results indicate that collisionless heating cannot be attributed to the stochastic heating mechanism based on the `hard wall' approximation and that in contrast electron inertia plays a dominant role as far as collisionless heating is concerned.

Computer simulations can be carried out with various aims. Perhaps the most challenging is prediction under conditions where experiments are difficult or inaccessible, especially when failure to predict adequately may have unhappy consequences. There is, probably, not much confidence at present in the capability of low-temperature plasma physics simulations in such a context. Other fields have attempted to meet this challenge using a collection of techniques collectively known as “Verification and Validation,” or “V&V.” These are methods for enhancing confidence in the correctness and fidelity of computer simulations. This paper surveys these techniques and discusses their application to improvements of simulation capability in low-temperature plasma physics.

By using a self-consistent particle-in-cell simulation we investigated the effect of driving frequency (27.12–70 MHz) on the electron energy distribution function (EEDF) and electron-sheath interaction in a low pressure (5 mTorr) capacitively coupled Ar discharge for a fixed discharge voltage. We observed a mode transition with driving frequency, changing the shape of EEDF from a strongly bi-Maxwellian at a driving frequency of 27.12 MHz, to a convex type distribution at an intermediate frequency, 50 MHz, and finally becomes a weak bi-Maxwellian at a higher driving frequency i.e. above 50 MHz. The transition is caused by the electric field transients which is of the order of electron plasma frequency caused by the energetic ‘beams’ of electrons ejected from near the sheath edge. Below the transition frequency, 50 MHz, these high energy electrons redistributes their energy with low energy electrons thereby increasing the effective electron temperature in the plasma, whereas, the plasma density remains nearly-constant. Above the transition frequency high-energy electrons are confined between opposite sheaths which increases the ionization probability and therefore the plasma density increases drastically.

Electrodeless radiofrequency discharges exhibit two modes of operation: a low-density mode in which the power is capacitively coupled to the plasma and which is known as the E-mode, and a higher density mode which is an inductive discharge known as the H-mode. The transition between these modes exhibits hysteresis, i.e. the E to H transition occurs at a different coil current than the reverse H to E transition. Recent theoretical results show that the hysteresis can be qualitatively understood in terms of electron power balance assuming that either the power dissipated or the power absorbed by the plasma electrons has a nonlinear dependence on the electron density. Experiments have been carried out to examine this hypothesis, both by characterizing steady-state E- and H-mode plasmas with a Langmuir probe, and by using a new approach consisting of measuring the internal plasma parameters in a pulsed discharge. In the latter case, the power is time modulated with increasing and decreasing power ramps. This approach allows us to investigate the hysteresis in detail and to study the dynamics of the transition. A number of time-resolved diagnostics including Langmuir probes, current and voltage sensors, optical emission and B-dot probes have been used.

Typical inductive discharges, such as are used for plasma processing, exhibit two modes of operation: the true inductive discharge known as the H mode, and a weak capacitive discharge known as the E mode. Experimentally, the transition between these modes as the coil current is increased is clear and is marked by a large increase in discharge power, plasma density and optical emission occurring as the H mode appears. According to simple theory, this transition and the reverse transition occur at a single well defined current. In practice, this is usually not the case. The E-to-H transition occurs at a larger coil current than the H-to-E transition, and a range of currents between these values supports either E or H mode. This effect is called hysteresis. In this paper we show that hysteresis can be understood to arise from nonlinear effects, most notably in the electron power balance equation. We survey various mechanisms that can produce hysteresis and attempt to provide quantitative estimates of their significance.

Inductively coupled rf discharges typically exhibit two modes of operation, namely, a low-density mode known as the E mode and a higher density mode known as the H mode. The transition between these modes exhibits hysteresis. Experimental observations of these transitions are presented. By means of a mixture of electromagnetic theory and circuit analysis and by invoking the requirement that the power absorbed and lost by the electrons should balance, the possible working points of an inductively coupled rf plasma source are identified in (P, ) space, where P is the power absorbed by the electrons, is the peak rf current in the induction coil and is the electron number density. Once the loci of the operating points have been identified in this manner, it is possible to construct a consistent explanation for all the experimental observations reported in the first part of the paper. In particular, it is possible to present an explanation for the hysteresis-like behaviour manifested by the mode transitions. Basically, the transitions occur when it is no longer possible to balance the power absorbed and lost by electrons.

A "plasma needle" is a cold plasma source operating at atmospheric pressure. Such sources interact strongly with living cells, but experimental studies on bacterial samples show that this interaction has a surprising pattern resulting in circular or annular killing structures. This paper presents numerical simulations showing that this pattern occurs because biologically active reactive oxygen and nitrogen species are produced dominantly where effluent from the plasma needle interacts with ambient air. A novel solution strategy is utilised coupling plasma produced neutral (uncharged) reactive species to the gas dynamics solving for steady state profiles at the treated biological surface. Numerical results are compared with experimental reports corroborating evidence for atomic oxygen as a key bactericidal species. Surface losses are considered for interaction of plasma produced reactants with reactive solid and liquid interfaces. Atomic oxygen surface reactions on a reactive solid surface with adsorption probabilities above 0.1 are shown to be limited by the flux of atomic oxygen from the plasma. Interaction of the source with an aqueous surface showed hydrogen peroxide as the dominant species at this interface. (C) 2013 AIP Publishing LLC.

Results are presented of a search for the production of new particles decaying to pairs of partons (quarks, antiquarks, or gluons), in the dijet mass spectrum in proton-proton collisions at sqrt(s) = 8 TeV. The data sample corresponds to an integrated luminosity of 4.0 inverse femtobarns, collected with the CMS detector at the LHC in 2012. No significant evidence for narrow resonance production is observed. Upper limits are set at the 95% confidence level on the production cross section of hypothetical new particles decaying to quark-quark, quark-gluon, or gluon-gluon final states. These limits are then translated into lower limits on the masses of new resonances in specific scenarios of physics beyond the standard model. The limits reach up to 4.8 TeV, depending on the model, and extend previous exclusions from similar searches performed at lower collision energies. For the first time mass limits are set for the Randall-Sundrum graviton model in the dijet channel.

International audience; 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.

International audience; We develop a semi-analytical theory for the self-bias formation in capacitively coupled plasmas excited by arbitrary radio-frequency (rf) waveforms. The requirement of rf current continuity and voltage balance across the discharge results in the need for a self-bias voltage to develop with non-sinusoidal excitations, even in geometrically symmetric systems. The theory is compared extensively with a wide range of experimental and particle-in-cell (PIC) simulation data within the literature, and is found to be in excellent agreement. Furthermore, it is shown that the present theory is formally equivalent to the original model proposed by Heil et al (2008 J. Phys. D: Appl. Phys. 41 165202), but goes further by explicitly allowing the time-varying sheath voltages and symmetry parameter to be evaluated without input from PIC simulations.

Actinometry is a non-invasive optical technique that can be used to quantitatively monitor atomic oxygen number densities [O] in gas discharges under certain operating conditions. However, careless application of the technique can lead to erroneous conclusions regarding the behaviour of atomic oxygen in plasma. One limitation on this technique is an accurate knowledge of the various rate constants required, which in turn is hampered by an insufficiently precise knowledge of the electron energy distribution function (EEDF) in the plasma. In this work, particle-in-cell (PIC) simulations are used to generate theoretical EEDFs. To validate a simulation the electron density n(e) produced by the PIC code is compared with experimental n(e) values measured using a hairpin probe. The PIC input parameters are adjusted to optimize agreement between the PIC and experimental ne results. This approach should in principle yield an EEDF that more accurately reflects the true EEDF in the plasma. The PIC EEDF is then used to generate rate constants for the actinometry model which should improve the accuracy of the quantitative [O] result for that particular set of plasma conditions. The actinometry [O] results are then compared with [O] results obtained using two-photon absorption laser-induced fluorescence (TALIF) to validate the approach.

International audience; Based on a theoretical argument from fundamental kinetic theory, by way of simple worked examples, and through the use of particle-in-cell simulations of capacitively coupled plasmas, we demonstrate that conventional methods for calculating the momentum transfer collision frequency in low-pressure plasmas can be seriously erroneous. This potentially plays an important and previously unconsidered role in many low-pressure discharges, and at least in part provides a possible explanation for anomalous behaviour often encountered in these plasmas.

We show that a recently proposed pressure model of collisionless heating in capacitive rf discharges predicts that a small magnetic field ({approximately}10 G) applied transverse to the electric field will induce a heating mode transition from a pressure-heating dominated state to an Ohmic-heating dominated state. This prediction is confirmed by kinetic simulations and experiments. {copyright} {ital 1996 The American Physical Society.}

Widespread recent interest in techniques for demonstrating that computer simulation programs are correct ('verification') has been motivated by evidence that traditional development and testing procedures are disturbingly ineffective. Reproducing an exact solution of the relevant model equations is generally accepted as the strongest available verification procedure, but this technique depends on the availability of suitable exact solutions. In this paper we consider verification of a particle-in-cell simulation with Monte Carlo collisions. We know of no exact solutions that simultaneously exercise all of the functions of this code. However, we show here that there can be found in the literature a number of non-trivial exact solutions, each of which exercises a substantial subset of these functions, and which in combination exercise all of the functions of the code. That the code is able to reproduce these solutions is correctness evidence of a stronger kind than has hitherto been elucidated.

Atomic oxygen number density [O] is measured in an air atmospheric pressure plasma jet (APPJ) using two-photon absorption laser induced fluorescence (TALIF). Gas flow is fixed at 8 slpm, the RF power coupled into the plasma jet varied between 5 W and 20 W, and the resulting changes in atomic oxygen density measured. Photolysis of molecular oxygen is employed to allow in situ calibration of the TALIF system. During calibration, O2 photo-dissociation and two-photon excitation of the resulting oxygen atoms are achieved within the same laser pulse. The atomic oxygen density produced by photolysis is time varying and spatially non-uniform which needs to be corrected for to calibrate the TALIF system for measurement of atomic oxygen density in plasma. Knowledge of the laser pulse intensity I 0(t), wavelength, and focal spot size allows correction factors to be determined using a rate equation model. Atomic oxygen is used for calibration and measurement, so the laser intensity can be increased outside the TALIF quadratic laser power dependence region without affecting the calibration reliability as the laser power dependence will still be the same for both. The atomic O density results obtained are not directly benchmarked against other known density measurement techniques. The results show that the plasma jet atomic oxygen content increases as the RF power coupled into the plasma increases.

The European negative ion based neutral beam development programme consists presently of experiments on high energy electrostatic accelerators and high current D − sources, and of neutral beam physics and system design studies. At CEA-Cadarache the source test bed MANTIS started operation last June, and the 1 MV, 0.1 A, D − acceleration project SINGAP will be operational by the end of 1994. Additionally, negative ion source physics-oriented experiments will be conducted at Dublin City University. A Pagoda source, developed for the SINGAP experiment, recently produced more than 1 A D − beams and j (D − ) of 10 mA cm −2 , with Cs seeding, at 0.6 Pa operating pressure. 1.3 A H − and 0.5 A D − beams have also been obtained without the use of Cs during the first experiments on MANTIS. Studies on neutral beam heating (NBH) for a next step machine have been conducted during 1993, mainly at JET and CEA-Cadarache. NBH physics studies based on the RLW model indicate that ignition on ITER-EDA should be reached with about 40 MW of 0.4–1 MeV D 0 beams. The outlines of an NBH system for ITER-EDA, based on SINGAP, have been studied.

A capacitively-coupled RF argon discharge at a pressure of 10 mTorr with a plate separation of 7.5 cm has been studied both experimentally and using a one-dimensional particle in cell simulation with Monte Carlo collisions. A magnetic field of 0 to 60 G is applied in the direction parallel to the capacitor plates. In the simulation it was found that as the magnetic field was increased such that the electron cyclotron orbit radius of the hot electrons became smaller than of the order of the discharge length, the electron heating in the bulk of the discharge increased. The dominant electron heating mechanism was observed to change from a stochastic sheath to a bulk ohmic electron heating mode, with a variation of field from a to 10 G. This was accompanied by a drop in the plasma density at small magnetic fields, which was also observed experimentally. At higher magnetic fields the plasma density was found to increase, A detailed discussion of the simulation results is presented drawing comparisons with the experimental results, with which there is good agreement, and a simple magnetohydrodynamic model for the bulk heating. >

Summary form only given. Atmospheric pressure plasma jet sources2 provide plasmas that are not spatially bound to any electrode and overcome the need for vacuum systems. Typically plasma is generated internally and then convected to an ambient environment via a gas flow. Applications for non-thermal atmospheric pressure plasma jets range from material processing3 to recent applications in medical physics4. The finite element numerical approach allows for simulation of the non-uniform geometries often used in atmospheric plasma systems. In this work we discuss models for mass transport of plasma species for nonthermal atmospheric pressure plasma jet sources employing dielectric barrier on the electrode. Fluid models using a drift diffusion approximation for the species flux are solved for the electron and heavy gas species along with the electron energy. This is coupled with a mixing gas model of a low density gas jet in the quiescent environment employing the Navier Stokes equations and a mass balance equation for gas mixing5. Two dimensional axi-symmetric models of Argon and Helium-Nitrogen jets for a cross-section of cylindrical dielectric barrier geometries with AC and pulsed DC power sources will be discussed. The commercial finite element partial differential equation solver Comsol Multiphysics6 is used for simulation in this work.

Summary form only given. Non-equilibrium atmospheric pressure discharges provide an attractive area of industrial interest, largely due to their relative ease of operation and usefulness in fields such as surface treatment of plastics, medical surfaces or even tissue1. In recent years there has therefore been a mounting interest in characterising these types of discharges numerically through simulation, as well as through experiment. However due to the computational intensity and complex physics of atmospheric pressure discharges most of the simulation work has been done using the fluid approximation, as opposed to the directly kinetic treatment of the Particle-In-Cell/Monte Carlo collisions approach2. As a result of these simplifications, the quantitative validity of these simulations has been previously questioned in the literature3,4.

Summary form only given. Capacitively coupled plasma discharges that are driven by two frequencies have been of interest in recent years because the low frequency source can control the sheath voltage and the mean ion bombarding energy while the high frequency source can sustain the plasma and control the ion flux. Thus the independent control of ion energy and ion flux is the motivation of dual frequency discharges. An analytical model for dual frequency case to study stochastic heating is given by Kawamura et al.1 and has been investigated here using particle-in-cell simulation. Benchmarking of this analytical model has been done by Kawamura et al. using particle-in-cell simulation but the data points are rather small. Turner and Chabert 2 developed an alternative model to study stochastic heating using fluid equations for dual-frequency capacitive discharges.

Summary form only given. The important phenomenon in low pressure radio-frequency capacitive discharges is stochastic heating. Ohmic heating is not the main source of power absorption. The electrons gain energy by interacting with the high voltage oscillating sheath. This phenomenon has been investigated by different analytical models2,3,4 using several different approaches and has produced results that are broadly in agreement insofar as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect. Benchmarking of these analytical models has been done by Kawamura et al.1, using particle-in-cell simulation but the data points are rather small.

Summary form only given. Electro-negative plasmas are widely used in plasma processing, ion source for neutral beam heating in fusion devices, plasma etching and ion Hall thrusters. Presence of negative ions principally modifies the sheath thereby affecting the direct transport of charged particle toward the wall or substrate. In some scenarios they lead to discharge instabilities. They are also responsible for various plasma chemistries. While conventional method of measuring negative ion is based on laser photodetachment in conjunction with Langmuir probe, recently we have demonstrated application of a hairpin probe with laser photodetachment for measuring negative ion density and temperature in an ICP Oxygen discharge1. This paper presents the novel technique in which pulsed bias hairpin is used against pulsed laser photodetachment for the measurement of negative ions. The principle remains the same except that a strong transient negative potential of the order of few 100 Volts allows to discriminate electrons and negative ions responding to the probe at distinct time scales. This results in observing peak electron density immediately post stimulation of the applied negative pulse. Some preliminary results are presented in the oxygen ICP discharge and results are compared with those obtained by hairpin probe assisted laser photo-detachment.

Summary form only given. As a direct solution of the Boltzmann equation, particle-in-cell simulation potentially yields highly accurate descriptions of low-temperature plasma. However, this accuracy is realised only with correct implementation and appropriately chosen numerical parameters. Particle-in-cell simulation is a computationally intensive procedure. Consequently, efficient implementations that take full advantage of the resources of modern computer hardware are highly desirable. Such hardware typically offers some degree of parallelisation, such as is found in multicored processors and graphical processing units. Implementations exploiting these facilities can be orders of magnitude faster than traditional serialized approaches. However, parallelisation introduces a great increase in algorithmic complexity, and thereby intensifies concerns about correct implementation. In this report we describe a suite of benchmark calculations for particle-in-cell simulations, making use of LXcat cross section data. These bench marks have three aims: (1) verification, i.e, to demonstrate correct implementation (2) to facilitate performance comparisons of different implementations and (3) to provide a baseline for other simulation methods. We will discuss the benchmarks, which include measurements of plasma kinetic properties, transport coefficients and discharge simulations, together with the results obtained from a variety of particle-in-cell implementations.

Uniform high density electronegative plasmas find important application for plasma heating by neutral beams in fusion devices and in material processing. In this work we present a constricted hollow anode plasma source (CHAPS) for the investigation of electronegative Ar/O 2 discharge. The source consists of a series of equidistant stainless steel parallel plates acting as cathode with a small stainless steel tube as the anode. The plasma comprise of highly uniform density outside the cathode plates and an intense glow near the anode1. The negative oxygen ion fraction is determined by measuring the electron density by hairpin probe and ion density using a planer Langmuir probe. The negative ion density in the bulk plasma is typically 1016 m−3 and increases monotonically as a function of pressure and power. The electronegativity of the discharge is typically close to 0.5 and remains constant with the applied power. Whereas the negative ion density in the anode region varies from 1016 m−3 to 1017 m−3 with electronegativity of 3.0 near the edge of the anodic glow and decreases to 1.0 with the distance from the anode glow.

A well-defined sharp drop in the amplitude of the reflected signal characterizes the resonance signal of the hairpin probe (HP) when the frequency is varied over a given range typically of the order of electron plasma frequency. A quantity that defines the ratio of width of the resonance signal, Δf (f upper - f lower ) to the central frequency, f central is the quality/Q factor of the HP. For lower Q it is difficult to resolve the f central against the background noise1. The factors governing the Q are the losses of the energy stored in the resonator due to the resistive heating of the probe that depends on the probes temperature and the specific resistivity of the wire material as shown in figure. The coupling between the adjacent loop antenna and the hairpin also determines the shape of the resonance peak. In the plasma, the losses are further enhanced due to resistive heating of the oscillating electrons influenced by the electric field between the probe tips and the presence of external magnetic field. In this work, we present an analytical model based on the transmission line theory of the hairpin resonator circuit that explains the physical factors responsible for the observation of broad resonance peaks.

Neutral beam injection based on a negative ion source is one of the most promising candidates for heating and current drive in future fusion reactors. The physical and chemical processes involved in the filter field region of an ion sources are especially important to investigate, as this is the region where the negative ions are mainly generated and extracted. The externally applied magnetic/filter field around 0.012T cools the high-energy electrons in order to avoid collisional destruction of the negative ions. The electron density (n e ) measurements using conventional diagnostic techniques such as Langmuir Probe (LP) and Optical Emission Spectroscopy becomes complicated in presence of negative ions as well as magnetic field and gives a qualitative result. For accurate det ermination of n e in such complex plasma, the floating resonance hairpin probe1 (HP) is applied in KAMABOKO-III negative ion source, at the MANTIS test bed in CEA Cadarache, France. The technique is based on measuring the plasma permittivity using a U-shaped microwave resonating structure whose relative shift of characteristics frequency in plasma from that in vacuum directly gives the n e without rely on any other plasma parameter. However, in the presence of magnetic field the plasma density becomes anisotropic and thus the HP gives an effective n e measurement within its spatial resolution. The measured n e is compared with the positive ion density measured by planar LP. The n e is studied as a function operating source parameters such as arc power, pressure, applied magnetic field and the plasma grid bias exclusively in the filter field region. The effect of probe orientation to the B-field on the resonant properties is also studied under given plasma conditions. The performance of the HP shows that the technique is more reliable, sensitive and accurate diagnostic tool for such ion source.

We have determined the electron energy distribution function (EEDF) in a low pressure nitrogen rf discharge both experimentally and using a computer simulation. The EEDFs show unusual structures, which can be interpreted in terms of a sheath-oscillation electron heating mechanism. However, the simulation shows that contrary to the conventional model, the electrons are heated in part by retreating sheaths. We present an analytical treatment of this phenomenon.

Radio-frequency discharges are practically and scientifically interesting. A practical understanding of such discharges requires, among other things, a quantitative appreciation of the mechanisms involved in heating electrons, since this heating is the proximate cause of the ionization that sustains the plasma. When these discharges are operated at sufficiently low pressure, collisionless electron heating can be an important and even the dominant mechanism. Since the low pressure regime is important for many applications, understanding collisionless heating is both theoretically and practically important. This review is concerned with the state of theoretical knowledge of collisionless heating in both inductive and capacitive discharges.

The dynamics of high energetic electrons (11.7 eV) in a modified industrial confined dual-frequency capacitively coupled RF discharge (Exelan, Lam Research Inc.), operated at 1.937 MHz and 27.118 MHz, is investigated by means of phase resolved optical emission spectroscopy. Operating in a He–O2 plasma with small rare gas admixtures the emission is measured, with one-dimensional spatial resolution along the discharge axis. Both the low and high frequency RF cycle are resolved. The diagnostic is based on time dependent measurements of the population densities of specifically chosen excited rare gas states. A time dependent model, based on rate equations, describes the dynamics of the population densities of these levels. Based on this model and the comparison of the excitation of various rare gas states, with different excitation thresholds, time and space resolved electron temperature, propagation velocity and qualitative electron density as well as electron energy distribution functions are determined. This information leads to a better understanding of the dual-frequency sheath dynamics and shows, that separate control of ion energy and electron density is limited. (Some figures in this article are in colour only in the electronic version)

Gas and heat dynamics of the 'Cooperation on Science and Technology (COST) Reference Microplasma Jet' (COST-jet), a European lead reference device for low temperature atmospheric pressure plasma application, are investigated. Of particular interest to many biomedical application scenarios, the temperature characteristics of a surface impacted by the jet are revealed. Schlieren imaging, thermocouple measurements, infrared thermal imaging and numerical modelling are employed. Temperature spatial profiles in the gas domain reveal heating primarily of the helium fraction of the gas mixture. Thermocouple and model temporal data show a bounded exponential temperature growth described by a single characteristic time parameter to reach ~63% or (1-1/e) fraction of the temperature increase. Peak temperatures occurred in the gas domain where the carrier jet exits the COST-jet, with values ranging from ambient temperatures to in excess of 100 °C in 'α-mode' operation. In a horizontal orientation of the COST-jet a curved trajectory of the helium effluent at low gas flows results from buoyant forces. Gas mixture profiles reveal significant containment of the helium concentrations for a surface placed in close proximity to the COST-jet. Surface heating of a quartz plate follows a similar bounded exponential temporal temperature growth as device heating. Spatial profiles of surface heating are found to correlate strongly to the impacting effluent where peak temperatures occur in regions of maximum surface helium concentration.

Collisionless heating of the electrons in the vicinity of the sheath region corresponding to higher order sinusoidal signals in a current-driven radio-frequency capacitively coupled plasma discharge has been investigated analytically and further verified by particle-in-cell simulation. The simulation results for collisionless sheath heating are found to be in good agreement with analytical predictions. In contrast to the voltage driven case, it is demonstrated that a pure sinusoidal waveform gives maximum electron sheath heating with a current-driven configuration and the ion energy can be controlled by varying the pulse width.

The sheath around the cylindrical pins of a resonance hairpin probe is modulated by applying a train of negative pulse voltages with respect to the grounded chamber. This phenomenon leads to the creation of a conjugate dielectric due to the electron-free sheath around the probe surface and the ambient plasma outside the sheath region. Synchronous measurement of electron density, ne, with respect to pulse waveform finds an overshoot in ne during the withdrawal of the negative pulses in the electronegative oxygen plasma. The physical reason behind this observation is presented together with a qualitative model for interpreting the density and temperature of negative ions based on this method.

The particle-in-cell method with Monte Carlo collisions is frequently used when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization (i.e., relaxation of the velocity distribution toward a Maxwellian), and consequently distortion of the true velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This article shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining strictly converged simulation results difficult in many cases of practical interest.

We discuss collisionless electron heating in capacitive discharges excited by a combination of two disparate frequencies. By developing an analytical model, we find, contrary to expectation, that the net heating in this case is much larger than the sum of the effects occurring when the two frequencies act separately. This prediction is substantiated by kinetic simulations, which are also in excellent general quantitative agreement with the model for discharge parameters that are typical of recent experiments.

The quarter wave resonator immersed in a strongly magnetized plasma displays two possible resonances occurring either below or above its resonance frequency in vacuum, fo. This fact was demonstrated in our recent articles [G. S. Gogna and S. K. Karkari, Appl. Phys. Lett. 96, 151503 (2010); S. K. Karkari, G. S. Gogna, D. Boilson, M. M. Turner, and A. Simonin, Contrib. Plasma Phys. 50(9), 903 (2010)], where the experiments were carried out over a limited range of magnetic fields at a constant electron density, ne. In this paper, we present the observation of dual resonances occurring over the frequency scan and find that ne calculated by considering the lower resonance frequency is 25%–30% smaller than that calculated using the upper resonance frequency with respect to fo. At a given magnetic field strength, the resonances tend to shift away from fo as the background density is increased. The lower resonance tends to saturate when its value approaches electron cyclotron frequency, fce. Interpretation of the...

Summary form only given. It is generally accepted that capacitive radio frequency discharges can be sustained predominantly by a non Ohmic heating process involving the interaction of electrons with the oscillating sheaths. It has usually been supposed that such heating is localized at the sheath edge, and can be computed by considering the interaction of an assumed electron flux with the moving sheath edge, which is considered to be a rigid barrier. This approach is commonly called a 'hard wall' model. In this paper we show that models of this character are not selfconsistent, in that current is not conserved through the sheath region. Moreover, attempts to repair such 'hard wall' models have the side effect of causing the heating to vanish identically. Therefore, it seems to us that it is impossible to to construct a self-consistent heating model of this type. We will also show that an alternative model based on moments of the Vlasov equation with a simple kinetic closure assumption can be used to calculate the heating effect, and this model is in good agreement with particle in cell simulations. In some parts of the parameter space, there are substantial differences between the heating predicted by this model and the earlier 'hard wall' model. The effect of electron collisions will also be discussed.

Summary form only given, as follows. Capacitive discharges have been used in the manufacture of microchips and in related applications for many years. A typical aim in these applications is to effect a surface modification by delivering a flux of energetic ions onto the surface. Consequently, the ion flux and ion energy are critical process parameters. For the most part, such discharges have been excited by a single frequency which has almost invariably been 13.56 MHz. Recently, there has been interest in exciting this type of discharge with two frequencies, where typically one frequency is smaller than 13.56 MHz and the other larger. The point of this complication is to separately control the plasma density and sheath voltage, and thereby independently control the ion flux and average energy. Since the impedance of the plasma is usually dominated by the capacitance of the sheaths, it is reasonable to expect that an appropriately high frequency will drive a large current through the plasma bulk without dropping a large voltage across the sheaths. Conversely, a suitably low frequency will drive a low current through the bulk while dropping a large voltage across the sheaths. Therefore, the hope is that the higher frequency will couple primarily to the electrons, while the lower frequency couples to the ions. This ideal picture is not exactly realised in practice, and the aim of the present work is to apply self-consistent kinetic simulation to the problem of discovering what conditions must be satisfied in order that a dual frequency discharge will operate in the way intended. For this purpose we use an electrostatic particle in cell simulation with Monte Carlo collisions. We do not consider electromagnetic effects, which may well be significant in some parts of the parameter space of practical interest.

Summary form only given. It is usually assumed that capacitive discharges are a strictly electrostatic phenomenon, so that magnetic fields are negligible unless externally applied and the only electric fields are those determined by solving Poisson's equation. These are reasonable assumptions for the relatively low frequencies (e.g., 13.56 MHz) and moderate areas (e.g. 20 cm electrode diameter) discharges that are in wide use. However, there is now interest in the use of substantially higher frequencies (e.g. 100 MHz) and larger areas (e.g. 50 cm electrode diameter). In this paper we show that it is generally not safe to neglect electromagnetic effects in these cases. We make use of a predominantly analytic model in which the capacitive discharge is modelled as a plasma loaded waveguide, with vacuum regions adjacent to the electrodes representing the sheaths. In this model, the excitation is applied at the outer periphery of the planar electrodes, and the fields propagate inwards as a surface wave. Provided the wave length of the surface wave is large compared with the electrode diameter, and skin effects in the bulk plasma are not significant, this model predicts a uniform current density directed normal to the electrode surfaces. The onset of either skin effects or finite wavelength effects introduces currents in the plasma parallel to the electrode surfaces, and under these conditions there is also non-uniform power deposition, which may be expected to produce non-uniform plasma density.

Summary form only given. Striations are a class of ionization instability that affects the positive column of direct current discharges in many gases over a wide range of pressure and current density. The origin of this effect was for long a mystery, which was substantially resolved during the course of the nineteen-sixties when the observed phenomena where shown to be qualitatively explained in terms of hydrodynamic theories of ionization waves. A kinetic theory has been given subsequently. These works are mainly analytic. In this paper, we discuss the application of a modern kinetic simulation technique-namely particle in cell simulation with Monte Carlo collisions-to instabilities of positive columns. We use a simplified one dimensional treatment. Where the axial direction is explicitly represented while plasma loss to the walls in the radial direction is modelled by removing electron-ion pairs at a given rate, which is determined a priori as a function of the pressure-radius product. When a pair of particles is removed in this way, both are selected from within a single simulation cell, so that the noise level in the simulation is not appreciably increased. This procedure may be used either with periodic boundary conditions to simulate a finite section of the positive column, or with finite boundary conditions to simulate a complete positive column including the structure at the anode and the cathode. We will present examples of both cases.

We report a combined experimental and computational study of a low‐pressure radio frequency discharge in argon. We have determined the electron energy distribution function experimentally using a Langmuir probe system and by simulation using the particle in cell method. A close comparison of these data shows good agreement over pressures from 20 to 200 mTorr. This pressure range encompasses the putative transition from a stochastic to an ohmic electron heating mode [V. A. Godyak and R. B. Piejak, Phys. Rev. Lett. 65, 996 (1990)]. The simulation does show such a transition, and we agree with earlier estimates of the transition pressure.

Power modulation in an atmospheric pressure capacitively coupled radio frequency plasma jet is investigated by numerical modelling. The dynamics of successively pulsing the applied power on and off for a helium–oxygen (∼0.6%) plasma is investigated. The impact of power pulsing on reactive species generation and gas heating is discussed with control opportunities emphasized. Power modulation shows linear control for reactive species and heat flux delivery to a treatment surface above an initial phase of power growth. Power is found to be coupled primarily to the electrons with electron loss rates determining the interference between successive power modulation phases. Plasma decay in the power off phase is characterized by a large initial electron loss in the first 0.5 µs followed by ambipolar decay dominated by ions of opposite charge. Power modulation effects on gas heating show a larger range of temperature control when compared with convection cooling. Reactive oxygen species reaching a treatment surface are shown to typically vary over an order of magnitude for variation in the duty cycle.

The role of gas mixing in reactive species delivery to treatment surfaces for an atmospheric pressure capacitively coupled plasma helium jet is investigated by numerical modelling. Atomic oxygen in the jet effluent is shown to quickly convert to ozone for increasing device to surface separation due to the molecular oxygen present in the gas mixture. Surface profiles of reactive oxygen species show narrow peaks for atomic oxygen and broader surface distributions for ozone and metastable species. Production efficiency of atomic oxygen to the helium plasma jet by molecular oxygen admixture is shown to be dependent on electro-negativity. Excessive molecular oxygen admixture results in negative ion dominance over electrons which eventually quenches the plasma. Interaction of the plasma jet with an aqueous surface showed hydrogen peroxide as the dominant species at this interface. Gas heating by the plasma is found to be dominated by elastic electron collisions and positive ion heating. Comparison with experimental measurements for atomic oxygen shows good agreement.

Present practice in plasma-assisted semiconductor manufacturing specifies recipes in terms of inputs such as gas flow rates, power and pressure. However, ostensibly identical chambers running identical recipes may produce very different results. Extensive chamber matching, i.e., initial iterative, empirical tuning of the process recipe, which entails time-consuming, ex situ statistical analysis of process metrics such as etch depth, uniformity, anisotropy and selectivity, is required to ensure acceptable results. Once matched, chambers are run open loop and are thus sensitive to disturbances such as actuator drift, wall seasoning and substrate loading, which may impact negatively on process reproducibility. An alternative approach, which may obviate the need for chamber matching and reduce the sensitivity of process metrics to exogenous disturbances, would be to specify a recipe in terms of quantities such as active species densities, and to regulate these in real time by adjusting the inputs with a suitable control algorithm. In this work, real time control of an electron cyclotron resonance O2/Ar plasma used for photoresist ashing has been implemented. The design of elementary, model-based algorithms for the control of the argon 750 and oxygen 844 line intensities measured by optical emission spectroscopy is described. Fluorination of the chamber walls by means of an SF6 plasma prior to ashing inhibits wall recombination of oxygen radicals resulting in an approximately 20% increase in ash rate in the open loop case. However, closed loop control almost completely attenuates the effect of fluorination, thus demonstrating the efficacy of the control algorithms in ensuring a reproducible ash rate in the face of a wall disturbance.

Dual frequency capacitively coupled discharges are widely used during fabrication of modern-day integrated circuits, because of low cost and robust uniformity over broad areas. At low pressure, stochastic or collisionless electron heating is important in such discharges. The stochastic heating occurs adjacent to the sheath edge due to energy transfer from the oscillating high voltage electron sheath to electrons. The present research discusses evidence of wave emission from the sheath in such discharges, with a frequency near the electron plasma frequency. These waves are damped very promptly as they propagate away from the sheath towards the bulk plasma, by Landau damping or some related mechanism. In this work, the occurrence of strong wave phenomena during the expanding and collapsing phase of the low frequency sheath has been investigated. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. The characteristics of waves in the dual-frequency case are entirely different from the single-frequency case studied in earlier works. The existence of a field reversal phenomenon, occurring several times within a lower frequency period in the proximity of the sheath is also reported. Electron trapping near to the field reversal regions also occurs many times during a lower frequency period. The emission of waves is associated with these field reversal regions. It is observed that the field reversal and electron trapping effects appear under conditions typical of many recent experiments, and are consequently of much greater practical interest than similar effects in single frequency discharges, which occur only under extreme conditions that are not usually realized in experiments.

High-frequency plasma discharges are often sustained by collisionless heating of electrons; the nature of these mechanisms is a central problem in the theory of such discharges. In capacitive discharges, collisionless heating occurs near boundaries, and is usually attributed to inelastic collisions of electrons with oscillating plasma sheaths, regarded as moving rigid barriers. We show that, when current conservation is required, such heating necessarily vanishes, and we conclude that this model of the heating process is not correct. We develop an alternative view that associates the heating with acoustic disturbances in the electron fluid. An analytic model, based on moments of the Vlasov equation, gives results in good agreement with particle-in-cell simulations. In terms of individual particle dynamics, this acoustic heating may be interpreted as a transit-time effect.

In this article we present an experimental study of the electron electrodynamics in an inductively coupled argon discharge. The discharge is configured in a re-entrant geometry and operates in the stochastic heating regime at pressures below 10 mTorr. The radial distribution of the induced rf electric field E and current density J were determined for a wide range of plasma parameters in argon gas from the measurement of the radial distribution of the magnetic field components and its spatial derivatives. The results show an anomalous skin effect at low pressure and high plasma densities that is characterized by a nonmonotonic spatial decay of the electromagnetic field E and current density J along with phase reversal and bifurcation of E and J and negative power absorption regions. These features are interpreted to be a result of nonlocal electrodynamics due to the electron thermal motion (which causes spatial dispersion in the conductivity). The electron thermal motion in the inhomogeneous rf induced electric field induces a phase randomization that leads to collisionless heating. The relative ratio of ohmic collisional heating to collisionless heating is estimated by comparing the total and collisional (deduced from an estimation of the electron-neutral collision frequency) power fluxes absorbed by the plasma electrons. This shows that collisionless heating dominates ohmic heating for pressures below 5 m Torr. These results are compared with the previously published work of Godyak et al. [V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, Phys. Rev. Lett. 80, 3264 (1998)] and show a surprisingly good agreement (at constant gas pressure and plasma density) despite the differing chamber geometry.

A current-free electric double-layer is created in a one-dimensional hybrid (particle ions and fluid electrons) plasma computer code by inserting a loss process along the axis of the simulation to mimic an expanding plasma. The image presented here shows a supersonic ion beam which has been accelerated downstream of the double-layer.

Particle-in-cell simulations with Monte Carlo collisions are expected to calculate the velocity distribution functions of charged species correctly, even if these distribution functions have exotic features such as gross anisotropy in velocity space, marked departures from a Maxwell–Boltzmann distribution, or failure of the local field approximation. Correct computation of the electron energy distribution function, in particular, is crucial in chemically complex plasmas, where radicals produced by electron impact processes usually have a dominant role. In such cases, accurate calculation of the rate constants for electron impact processes is a major motivation for the use of a kinetic simulation procedure, such as the particle-in-cell method. Like any numerical procedure, the particle-in-cell algorithm has limitations, and one of these limitations is that velocity space diffusion can distort the particle energy distribution functions. This paper presents examples of some conditions where such numerical distortion of particle energy distribution functions is important, and draws conclusions with implications for the choice of numerical parameters for particle-in-cell simulations. In particular, we show that the number of particles per cell that is required varies significantly with the conditions (as much as three orders of magnitude), and can sometimes be very large indeed. We suggest a heuristic for selecting the number of particles per cell, derived from the examples we discuss.

Dual-frequency capacitive discharges are widespread in the semiconductor industry and are used, for example, in etching of semiconductor materials to manufacture microchips. In low-pressure dual radio-frequency capacitive discharges, stochastic heating is an important phenomenon. Recent theoretical work on this problem using several different approaches has produced results that are broadly in agreement insofar as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect for the case of dual-frequency capacitive discharges. In this work, we investigate the dependence of stochastic heating on various discharge parameters with the help of particle-in-cell (PIC) simulation. The dual-frequency analytical models are in fair agreement with PIC results for values of the low-frequency current density amplitude Jlf (or dimensionless control parameter Hlf ~ 5) typical of many modern experiments. However, for higher values of Jlf (or higher Hlf), new physical phenomena (like field reversal, reflection of ions, etc) appear and the simulation results deviate from existing dual-frequency analytical models. On the other hand, for lower Jlf (or lower Hlf) again the simulation results deviate from analytical models. So this research work produces a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters.