Building on our previous study in argon gas, we extend our approach to helium and neon capacitively coupled plasmas, which allows the effective secondary-electron emission coefficient (SEEC, gamma) to be determined in-situ under discharge operation. The method relies on the gamma-dependence of the DC self-bias voltage, which arises due to the electrical asymmetry effect (EAE). The EAE is induced by applying two consecutive radio-frequency harmonics with a variable phase angle to excite the discharge. Experimental measurements of the DC self-bias voltage are complemented by particle-in-cell/Monte Carlo collisions simulations. A sequence of SEEC values is used in the simulations, and the actual gamma is determined by matching the computed DC self-bias to the experimental value. Applying this method at a driving frequency of 4 MHz, we obtain effective gamma values of 0.105 and 0.165 for helium at 120 Pa and 240 Pa, respectively, and 0.072 and 0.103 for neon at 80 Pa and 160 Pa, respectively, with an estimated uncertainty of +/- 0.01.

The influence of externally applied homogeneous transverse magnetic fields of up to 200 G on self-organized striations in capacitively coupled radio-frequency (RF) CF4 plasmas is investigated using kinetic simulations. The striations are known to originate from a resonance between the applied RF excitation and the eigenfrequency of the ion-ion plasma, the magnetic field is found to affect the striations indirectly through its impact on electron dynamics as ions do not get magnetized within the range of magnetic fields covered. Depending on the discharge conditions, increasing the magnetic field can either switch striations on or off and, in this way, strongly affect the spatial electron energy distribution function as well as the generation of process relevant charged and neutral species. We demonstrate that at some discharge conditions where striations form in the absence of a magnetic field, applying a moderate B-field can lead to the suppression of striations near the discharge center as a result of enhanced electron power absorption and a corresponding increase in electron density, enabling electrons to neutralize the space charge caused by the ion oscillations. We also illustrate the opposite effect that can occur at some other operating conditions, where the plasma operates close to the striation regime, but striations are absent due to insufficient ion densities, the magnetic field enhances the ion density and amplifies the local space charge formation, which can no longer be balanced by electrons. As a result, striations appear, inducing a transition from the drift ambipolar to a striation/magnetized drift ambipolar hybrid mode.

We report a comparison of inferred electron density ( n e ) in a He capacitively-coupled plasma, deduced from laser-collision induced fluorescence measurements, with values computed using a hybrid simulation framework based on particle-in-cell/Monte Carlo collisions simulations and a fluid model for excited He atoms. The studies were carried out for gas pressures between 50 mTorr and 1000 mTorr and peak-to-peak radio-frequency (13.56 MHz) voltages between 150 V and 350 V, in a highly symmetric source equipped with plane-parallel electrodes. A good agreement is found between the experimental and modeling results for n e except at the lowest operating voltages and gas pressures. The (effective) electron temperature ( T e ) values derived by the two methods agree as well reasonably within the plasma bulk. The simulation results are used to compare the density distributions of He + and various He excited levels and their major populating and de-populating channels at 100 mTorr and 1000 mTorr.

Processes at the plasma boundaries, including the electrodes, can significantly influence plasma properties, among them the plasma density, the flux-energy distribution of various particle species, etc. The emission of secondary electrons, in particular, can lead to ionization avalanches, which strongly increase the plasma density and change the discharge operation mode as a function of the operating conditions. Using reliable values to characterize the efficiency of such processes is indispensable for accurate numerical modeling. There is, however, a lack of such data for surface coefficients for arbitrary combinations of the plasma species and electrode materials and surface conditions. In this work, we investigate the alpha- to gamma-mode mode transition induced by changes of the operating conditions (voltage, pressure) in capacitively coupled argon plasmas for different electrode surface materials (copper, nickel, gold, aluminum, and stainless steel) and target the determination of the effective in-situ secondary electron emission coefficient, gamma & lowast;. The first is accomplished by phase-resolved optical emission spectroscopy applied to measure the spatio-temporal distribution of the electron-impact excitation rate from the ground state into a high-threshold-energy level of a tracer gas (neon). The studies are conducted for pressures between 50 Pa and 200 Pa and voltage amplitudes ranging from 150 V to 350 V at a driving frequency of 13.56 MHz. A transition from the alpha- to the gamma-mode is shown to take place at different pressures for different materials. The combination of these measurements with particle-in-cell / Monte Carlo collisions simulations employing a range of gamma & lowast; values allows the determination of the effective 'in-situ' electron yield for the given set of operating conditions. The simulations also shed light on the contributions of the various species, argon ions, metastable atoms, and vacuum-ultraviolet photons to electron emission from the electrodes. The findings suggest that for precise modeling individual secondary electron yields specific to different electrode surface materials should be used and multiple species should be included in the models that describe secondary electron emission at the electrodes.

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor operated in a fixed mixture gas composition, at fixed pressure and voltage amplitude, with a wide range of driving RF frequencies (2 MHz ≤ f ≤ 15 MHz). The measured and calculated spatio-temporal distributions of the electron impact excitation rates from the Ar ground state to the Ar 2p1 state (with a wavelength of 750.4 nm) show good qualitative agreement. The distributions show significant frequency dependence, which is generally considered to be predictive of transitions in the dominant discharge operating mode. Three frequency ranges can be distinguished, showing distinctly different excitation characteristics: (i) in the low frequency range (f ≤ 3 MHz), excitation is strong at the sheaths and weak in the bulk region; (ii) at intermediate frequencies (3.5 MHz ≤ f ≤ 5 MHz), the excitation rate in the bulk region is enhanced and shows striation formation; (iii) above 6 MHz, excitation in the bulk gradually decreases with increasing frequency. Boltzmann term analysis was performed to quantify the frequency dependent contributions of the Ohmic and ambipolar terms to the electron power absorption.

The electron power absorption mechanisms in electronegative capacitively coupled plasmas in CF4 are investigated using particle-in-cell/Monte Carlo collisions simulations at a pressure of p = 60 Pa, a driving frequency of f =13.56 MHz for voltage amplitudes in the interval of phi(0) =100-300 V, where pronounced self-organized density variations, i.e. striations, develop. The calculations are based on the Boltzmann term analysis, a computational diagnostic method capable of providing a complete spatio-temporal description of electron power absorption. The discharge undergoes an electron power absorption mode transition from the drift-ambipolar- to the striation-mode at phi(0) = 180 V. Although Ohmic power absorption is found to be the dominant electron power absorption mechanism in the parameter range considered, the electron power absorption mode transition can be inferred from the behaviour of the spatio-temporally averaged ambipolar power absorption as a function of the voltage amplitude. Furthermore, it is shown, that as a consequence of the presence of striations, the temporal modulation of the electron density leads to a temporal modulation of the ambipolar electric field, which is responsible for the striated structures of various physical quantities related to electrons, such as the electron temperature and the ionization source function.

Plasma simulations are powerful tools for understanding fundamental plasma science phenomena and for process optimization in applications. To ensure their quantitative accuracy, they must be validated against experiments. In this work, such an experimental validation is performed for a 1d3v particle-in-cell simulation complemented with the Monte Carlo treatment of collision processes of a capacitively coupled radio frequency plasma driven at 13.56 MHz and operated in neon gas. In a geometrically symmetric reactor the electron density in the discharge center and the spatio-temporal distribution of the electron impact excitation rate from the ground into the Ne 2p_1 state are measured by a microwave cutoff probe and phase resolved optical emission spectroscopy, respectively. The measurements are conducted for electrode gaps between 50 mm and 90 mm, neutral gas pressures between 20 mTorr and 50 mTorr, and peak-to-peak values of the driving voltage waveform between 250 V and 650 V. Simulations are performed under identical discharge conditions. In the simulations, various combinations of surface coefficients characterising the interactions of electrons and heavy particles with the anodized aluminium electrode surfaces are adopted. We find, that the simulations using a constant effective heavy particle induced secondary electron emission coefficient of 0.3 and a realistic electron-surface interaction model (which considers energy-dependent and material specific elastic and inelastic electron reflection, as well as the emission of true secondary electrons from the surface) yield results which are in good quantitative agreement with the experimental data.

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.

The physical characteristics of an argon discharge excited by a single-frequency harmonic waveform in the low-intermediate pressure regime (5–250 Pa) are investigated using particle-in-cell/Monte Carlo collisions simulations. It is found that, when the pressure is increased, a non-negligible bulk electric field develops due to the presence of a ‘passive bulk’, where a plateau of constant electron density forms. As the pressure is increased, the ionization in the bulk region decreases (due to the shrinking of the energy relaxation length of electrons accelerated within the sheaths and at the sheath edges), while the excitation rate increases (due to the increase of the bulk electric field). Using the Fourier spectrum of the discharge current, the phase shift between the current and the driving voltage waveform is calculated, which shows that the plasma gets more resistive in this regime. The phase shift and the (wavelength-integrated) intensity of the optical emission from the plasma are also obtained experimentally. The good qualitative agreement of these data with the computed characteristics verifies the simulation model. Using the Boltzmann term analysis method, we find that the bulk electric field is an Ohmic field and that the peculiar shape of the plasma density profile is partially a consequence of the spatio-temporal distribution of the ambipolar electric field.

Particle-in-cell/Monte Carlo collisions simulations are performed to study the effects of electron induced secondary electrons (SEs) in single-frequency (13.56 MHz) capacitively coupled oxygen discharges operated in the low-pressure regime ( <1 Pa). A comparison of the plasma parameters is presented based on different surface models in the simulations. Both for electrons and ions, simple and realistic approaches are used to model their interactions with the electrode material. The simple approaches use constant coefficients (electron reflection, SE emission), irrespectively of the discharge conditions and the surface properties, while the realistic surface coefficients are functions of the energy of the particles hitting the electrode and depend on the surface properties. When electron induced secondary electron emission (SEE) is accounted for, a complex electron emission and ionization dynamics of ion induced γ- and electron induced δ-electrons is found. When both the electron and ion induced SEE is described by energy dependent surface coefficients, an exponential increase of the plasma density and the O2(a1Δg) metastable concentration is observed by increasing the driving voltage amplitude, as well as a strong decrease of the electronegativity of the discharge and a transition of the discharge operation mode from the drift-ambipolar mode to the α-mode are found to take place.

Phase resolved optical emission spectroscopy (PROES) measurements combined with 1d3v particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations are used to study the electron power absorption and excitation/ionization dynamics in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases. The study is performed for a geometrically symmetric CCP reactor with a gap length of 2.5 cm at a driving frequency of 10 MHz and a peak-to-peak voltage of 350 V. The pressure of the gas mixture is varied between 15 Pa and 500 Pa, while the neon/oxygen concentration is tuned between 10% and 90%. For all discharge conditions, the spatio-temporal distributions of the electron-impact excitation rate from the Ne ground state into the Ne 2p(5)3p(0) state measured by PROES and obtained from PIC/MCC simulations show good qualitative agreement. Based on the emission/excitation patterns, multiple operation regimes are identified. Localized bright emission features at the bulk boundaries, caused by local maxima in the electronegativity are found at high pressures and high O-2 concentrations. The relative contributions of the ambipolar and the Ohmic electron power absorption are found to vary strongly with the discharge parameters: the Ohmic power absorption is enhanced by both the high collisionality at high pressures and the high electronegativity at low pressures. In the wide parameter regime covered in this study, the PROES measurements are found to accurately represent the ionization dynamics, i.e. the discharge operation mode. This work represents also a successful experimental validation of the discharge model developed for neon-oxygen CCPs.

The magnetized drift-ambipolar (‘m-DA’) electron power absorption mode and a sequence of structural transitions, including the formation of an electropositive core where the electron density is much higher than the negative ion density, are identified in a magnetized capacitive Radio-Frequency (RF) plasma of a strongly electronegative gas, CF 4 . The m-DA mode is caused by a magnetic enhancement of the bulk electric field due to the attenuation of the electron transport and plasma conductivity across the magnetic field. This leads to the formation of ionization maxima at distinct axial positions and a local trapping of electrons by the magnetic field as a function of its strength.

In this paper, we describe an efficient, massively parallel GPU implementation strategy for speeding up one-dimensional electrostatic plasma simulations based on the Particle-in-Cell method with Monte-Carlo collisions. Relying on the Roofline performance model, we identify performance-critical points of the program and provide optimised solutions. We use four benchmark cases to verify the correctness of the CUDA and OpenCL implementations and analyse their performance properties on a number of NVIDIA and AMD cards. Plasma parameters computed with both GPU implementations differ not more than 2% from each other and respective literature reference data. Our final implementations reach over 2.6 Tflop/s sustained performance on a single card, and show speed up factors of up to 200 (when using 10 million particles). We demonstrate that GPUs can be very efficiently used for simulating collisional plasmas and argue that their further use will enable performing more accurate simulations in shorter time, increase research productivity and help in advancing the science of plasma simulation.

The particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation approach has become a standard and well-established tool in studies of capacitively coupled radio frequency (RF) plasmas. While code-to-code benchmarks have been performed in some cases, systematic experimental validations of such simulations are rare. In this work, a multi-diagnostic experimental validation of 1d3v electrostatic PIC/MCC simulation results is performed in argon gas at pressures ranging from 1 Pa to 100 Pa and at RF (13.56 MHz) voltage amplitudes between 150 V and 350 V using a custom built geometrically symmetric reference reactor. The gas temperature, the electron density, the spatio-temporal electron impact excitation dynamics, and the ion flux-energy distribution at the grounded electrode are measured. In the simulations, the gas temperature and the electrode surface coefficients for secondary electron emission and electron reflection are input parameters. Experimentally, the gas temperature is found to increase significantly beyond room temperature as a function of pressure, whereas constant values for the gas temperature are typically assumed in simulations. The computational results are found to be sensitive to the gas temperature and to the choice of surface coefficients, especially at low pressures, at which non-local kinetic effects are prominent. By adjusting these input parameters to specific values, a good quantitative agreement between all measured and computationally obtained plasma parameters is achieved. If the gas temperature is known, surface coefficients for different electrode materials can be determined in this way by computationally assisted diagnostics. The results show, that PIC/MCC simulations can describe experiments correctly, if appropriate values for the gas temperature and surface coefficients are used. Otherwise significant deviations can occur.

Particle based simulations are indispensable tools for numerical studies of charged particle swarms and low-temperature plasma sources. The main advantage of such approaches is that they do not require any assumptions regarding the shape of the particle velocity/energy distribution function (VDF/EDF), but provide these basic quantities of kinetic theory as a result of the computations. Additionally, they can provide, e.g. transport coefficients, under arbitrary time and space dependence of the electric/magnetic fields. For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the particle-in-cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has become an important tool during the past decades. In particular, for radio-frequency (RF) capacitively coupled plasma (CCP) systems PIC/MCC is perhaps the primary simulation tool these days. This approach is able to describe discharges over a wide range of operating conditions, and has largely contributed to the understanding of the physics of CCPs operating in various gases and their mixtures, in chambers with simple and complicated geometries, driven by single- and multi-frequency (tailored) waveforms. PIC/MCC simulation codes have been developed and maintained by many research groups, some of these codes are available to the community as freeware resources. While this computational approach has already been present for a number of decades, the rapid evolution of the computing infrastructure makes it increasingly more popular and accessible, as simulations of simple systems can be executed now on personal computers or laptops. During the past few years we have experienced an increasing interest in lectures and courses dealing with the basics of particle simulations, including the PIC/MCC technique. In a response to this, the current paper (i) provides a tutorial on the physical basis and the algorithms of the PIC/MCC technique and (ii) presents a basic (spatially one-dimensional) electrostatic PIC/MCC simulation code, whose source is made freely available in various programming languages. We share the code in C/C++ versions, as well as in a version written in Rust, which is a rapidly emerging computational language. Our code intends to be a ‘starting tool’ for those who are interested in learning the details of the PIC/MCC technique and would like to develop the ‘skeleton’ code further, for their research purposes. Following the description of the physical basis and the algorithms used in the code, a few examples of results obtained with this code for single- and dual-frequency CCPs in argon are also given.

External magnetic fields impose diverse effects on low-temperature plasmas. We study these in a low-pressure capacitively coupled radio frequency plasma in argon via self-consistent kinetic simulations. The primary effect of the transversal magnetic field, that manifests itself in the trapping of electrons at lower excitation frequencies and, thus, in an increase of the plasma density as a function of the magnetic field, is overruled at higher excitation frequencies by the attenuation of the self-excitation of plasma series resonance oscillations and the attenuation of non-linear electron resonance heating, which lead to a reduced plasma density. At higher magnetic fields the plasma density increases again due to (i) a longer interaction time between the electrons and the edges of the expanding sheaths and (ii) the electric field reversals that develop at the collapsing sheath edges to overcome the trapping of electrons and accelerate them towards the electrodes.

We present a detailed analysis of electron trajectories within the sheath regions of capacitively coupled plasmas excited by radio-frequency voltage waveforms at low pressures. Complex features inside the sheaths are identified in several physical quantities, which are sculptured by the trajectories of bouncing energetic electrons (predominantly ion induced secondary electrons) under the influence of the spatio-temporally varying electric field. Based on a systematic parameter variation the generation of the various features as a function of surface processes is explained and the trajectories of electrons of different origin are identified.

Low pressure single- or dual-frequency capacitively coupled radio frequency (RF) plasmas are frequently used for high-aspect ratio (HAR) dielectric etching due to their capability to generate vertical ion bombardment of the wafer at high energies. Electrons typically reach the wafer at low energies and with a wide angular distribution during the local sheath collapse. Thus, in contrast to positive ions, electrons cannot propagate deeply into HAR etch features and the bottom as well as the sidewalls of such trenches can charge up positively, while the mask charges negatively. This causes etch stops and distortion of profile shapes. Here, we investigate low pressure, high voltage capacitively coupled RF argon gas discharges by Particle-In-Cell/Monte Carlo collisions simulations and demonstrate that this problem can be solved by Voltage Waveform Tailoring, i.e. the velocity and angular distribution of electrons impacting on the electrodes can be tuned towards high velocities and small angles to the surface-normal, while keeping the energies of the impacting ions high. The applied voltage waveforms consist of a base frequency of 400 kHz with 10 kV amplitude and a series of higher harmonics. A high frequency component at 40 or 60 MHz is used additionally. Square voltage waveforms with different rise-times are examined as well. We show that high fluxes of electrons towards the wafer at normal velocities of up to 2.2 x 10(7) m s(-1) (corresponding to 1.4 keV energy) can be realized.