The origin of Bohm diffusion, investigated by a comparison of different modelling methods

Previously, a microplasma was discovered in the rear gap of a sliding contact. This plasma is called a ‘triboplasma’, the behaviour of which obeys the Paschen law in a gas discharge. The generation of the triboplasma has been explained to be generated by discharging of ambient air due to the intense electric field caused by tribocharging, based on the experimental findings.In this report, the mechanism of triboplasma generation is theoretically analysed using the particle-in-cell/Monte Carlo collision (PIC/MCC) simulation method for the triboplasma generated in the tribosystem, where a diamond pin slides against a sapphire disc in ambient air. Two-dimensional sideward density distributions of the electrons, ions and ions in the rear gap of the sliding contact are obtained theoretically by the PIC/MCC method. These calculated particle distributions coincided well with the triboplasma distributions experimentally observed. The previously proposed triboplasma generation due to gas discharging is verified theoretically using the PIC/MCC simulation method.

Self-organized striated structures of the plasma emission have recently been observed in capacitive radio-frequency CF4 plasmas by phase resolved optical emission spectroscopy (PROES) and their formation was analyzed and understood by particle in cell/Monte Carlo collision (PIC/MCC) simulations (Liu et al 2016 Phys. Rev. Lett. 116 255002). The striations were found to result from the periodic generation of double layers due to the modulation of the densities of positive and negative ions responding to the externally applied RF potential. In this work, an in-depth analysis of the formation of striations is given, as well as the effect of the driving frequency on the plasma parameters, such as the spatially modulated charged species densities, the electric field, and the electron power absorption is studied by PROES measurements, PIC/MCC simulations, and an ion–ion plasma model. The measured spatio-temporal electronic excitation patterns at different driving frequencies show a high degree of consistency with the simulation results. The striation gap (i.e., the distance between two ion density maxima) is found to be inversely proportional to the driving frequency. In the presence of striations the minimum ( ) ion densities in the bulk region exhibit an approximately quadratic increase with the driving frequency. For these densities, the eigenfrequency of the ion–ion plasma is near the driving frequency, indicating that a resonance occurs between the positive and negative ions and the oscillating electric field inside the plasma bulk. The maximum ion densities in the plasma bulk are found not to exhibit a simple dependence on the driving frequency, since these ion densities are abnormally enhanced within a certain frequency range due to the ions being focused into the ‘striations’ by the spatially modulated electric field inside the bulk region.

Understanding the spatio-temporal dynamics of charged particles in low pressure radio frequency capacitively coupled plasmas (CCP) is the basis for knowledge based process development in these plasma sources. Due to the importance of kinetic non-local effects the particle in cell/Monte Carlo collision (PIC/MCC) simulation became the primary modeling approach. However, due to computational limitations most previous PIC/MCC simulations were restricted to spatial resolution in one dimension. Additionally, most previous studies were based on oversimplified treatments of plasma-surface interactions. Overcoming these problems could clearly lead to a more realistic description of the physics of these plasma sources. In this work, the effects of the reactor geometry in combination with realistic heavy particle and electron induced secondary electron emission coefficients (SEEC) on the charged particle dynamics are revealed by GPU based 2D3V PIC/MCC simulations of argon discharges operated at 0.5 Pa and at a high voltage amplitude of 1000 V. The geometrical reactor asymmetry as well as the SEECs are found to affect the power absorption dynamics and distribution functions of electrons and ions strongly by determining the sheath voltages and widths adjacent to powered and grounded surface elements as well as via the self-excitation of the plasma series resonance. It is noticed that secondary electrons play important roles even at low pressures. Electron induced secondary electrons (δ-electrons) are found to cause up to half of the total ionization, while heavy particle induced secondary electrons (γ-electrons) do not cause much ionization directly, but induce most of the δ-electron emission from boundary surfaces. The fundamental insights obtained into the 2D-space resolved charged particle dynamics are used to understand the formation of energy distribution functions of electrons and ions for different reactor geometries and surface conditions.

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.

We present numerical kinetic modeling of generation and evolution of the plasma produced as a result of resonance enhanced multiphoton ionization (REMPI) in Argon gas. The particle-in-cell/Monte Carlo collision (PIC/MCC) simulations capture non-equilibrium effects in REMPI plasma expansion by considering the major collisional processes at the microscopic level: elastic scattering, electron impact ionization, ion charge exchange, and recombination and quenching for metastable excited atoms. The conditions in one-dimensional (1D) and two-dimensional (2D) formulations correspond to known experiments in Argon at a pressure of 5 Torr. The 1D PIC/MCC calculations are compared with the published results of local drift-diffusion model, obtained for the same conditions. It is shown that the PIC/MCC and diffusion-drift models are in qualitative and in reasonable quantitative agreement during the ambipolar expansion stage, whereas significant non-equilibrium exists during the first few 10 s of nanoseconds. 2D effects are important in the REMPI plasma expansion. The 2D PIC/MCC calculations produce significantly lower peak electron densities as compared to 1D and show a better agreement with experimentally measured microwave radiation scattering.

The spatio-temporal ionization and excitation dynamics in low-pressure radiofrequency (RF) discharges operated in neon are studied and a detailed comparison of experimental and kinetic simulation results is provided for a wide parameter regime. Phase resolved optical emission spectroscopy (PROES) measurements and 1d3v particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations are performed in a geometrically symmetric capacitively coupled plasma (CCP) reactor at driving frequencies ranging from 3.39 MHz to 13.56 MHz, pressures between 60 Pa and 500 Pa, at a peak-to-peak voltage of 330 V. We examine the applicability of PROES (which provides information about the spatio-temporal distribution of the electron-impact excitation dynamics from the ground state into the Ne 2p1 state) to probe the discharge operation mode in neon (which is determined by the spatio-temporal distribution of the ionization dynamics). We find that the spatio-temporal excitation rates measured by PROES are in a good agreement with the excitation rates obtained from the PIC/MCC simulations, for all the discharge conditions studied here. However, the ionization dynamics is found to be significantly different from the excitation dynamics under most of the discharge conditions studied here, especially at higher values of the driving frequency and lower values of the pressure, when energetic heavy particle induced secondary electrons (γ-electrons) are more likely to ionize than to excite. PROES does not probe the discharge operation mode under these conditions. At a fixed frequency and peak-to-peak voltage, the spatio-temporal distribution of the ionization rate obtained from PIC/MCC simulations shows a transition of the discharge operation mode from the α-mode to the γ-mode by increasing the pressure. However, PROES fails to show this transition. While in the spatio-temporal distribution of the excitation rate obtained from the PROES measurements and the PIC/MCC simulations the α-peak (the intensity maximum at the bulk side of the expanding sheath edge) is dominant and a γ-peak (a maximum near the edge of the fully expanded sheath) becomes visible only at high values of the pressure or at the lowest frequency of 3.39 MHz, a γ-peak is visible in the ionization rate for all operation conditions, and it dominates the ionization in the vast majority of the cases investigated.

Various spectral line emissions are often used for the experimental characterization of low-temperature plasmas. For a better understanding of the relation between the plasma characteristics and optical emission spectra, first-principle numerical simulations for low-pressure radio-frequency driven capacitively-coupled plasmas (CCPs) of argon have been performed by coupling one-dimensional particle-in-cell/Monte Carlo collision (PIC/MCC) simulations with a global collisional-radiative model (CRM). The only ionization and excitation mechanisms included in the PIC/MCC simulations of this study are the electron-impact ionization and excitations of the ground-state Ar atoms, as done commonly, whereas the electron-impact ionization of metastable states and other ionization mechanisms are also included in the CRM to account for the optical emission spectra. The PIC/MCC coupled CRM provides the emission spectra, which are then compared with experimental data obtained from the corresponding Ar CCPs with a gas pressure ranging from 2 Pa to 100 Pa. The comparison has shown good agreement for pressures up to about 20 Pa but increasingly notable deviations at higher pressures. The deviation is ascribed to the missing consistency between the PIC/MCC simulations and CRM at higher pressures, where the ionization from the metastable states is more dominant than that from the ground states, indicating a significant change in the electron energy distribution function due to the electron collisions with excited Ar atoms at higher pressures.

A Cartesian-coordinate two-dimensional electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) plasma simulation code is presented, including a new treatment of charge balance at dielectric boundaries. It is used to simulate an Ar plasma in a symmetric radiofrequency capacitively-coupled parallel-plate reactor with a thick (3.5 cm) dielectric side-wall. The reactor size (12 cm electrode width, 2.5 cm electrode spacing) and frequency (15 MHz) are such that electromagnetic effects can be ignored. The dielectric side-wall effectively shields the plasma from the enhanced electric field at the powered-grounded electrode junction, which has previously been shown to produce locally enhanced plasma density (Dalvie et al 1993 Appl. Phys. Lett. 62 3207–9; Overzet and Hopkins 1993 Appl. Phys. Lett. 63 2484–6; Boeuf and Pitchford 1995 Phys. Rev. E 51 1376–90). Nevertheless, enhanced electron heating is observed in a region adjacent to the dielectric boundary, leading to maxima in ionization rate, plasma density and ion flux to the electrodes in this region, and not at the reactor centre as would otherwise be expected. The axially-integrated electron power deposition peaks closer to the dielectric edge than the electron density. The electron heating components are derived from the PIC/MCC simulations and show that this enhanced electron heating results from increased Ohmic heating in the axial direction as the electron density decreases towards the side-wall. We investigated the validity of different analytical formulas to estimate the Ohmic heating by comparing them to the PIC results. The widespread assumption that a time-averaged momentum transfer frequency, vm, can be used to estimate the momentum change can cause large errors, since it neglects both phase and amplitude information. Furthermore, the classical relationship between the total electron current and the electric field must be used with caution, particularly close to the dielectric edge where the (neglected) pressure gradient term becomes significant.

The Particle In Cell/Monte Carlo Collisions (PIC/MCC) simulation was used for the calculation of electron and ion currents to a spherical Langmuir (electrostatic) probe. This simulation took into account the collisions of collected charged particles with neutral gas particles around the probe and it can calculate the probe currents at higher neutral gas pressures. The improvements of usual simulation techniques enabled to speed up the simulation and to calculate the probe current even for neutral gas pressures above 1 kPa. The simulations were carried out for two cases: i) probe with radius of 0.5 mm in non‐thermal plasma with high electron temperature, ii) probe with radius of 10 µm in afterglow plasma with low electron temperature. The influence of probe radius on electron probe current was also studied. The simulations showed that thick sheath limit of OML theory provides incorrect values of probe current for probes with radii larger than 200 µm at plasma parameters considered even at very low neutral gas pressures. The probe characteristics were calculated for probe with 0.5 mm radius for pressures up to 500 Pa and for probe with 10 μm radius for pressures up to 3 kPa. The influence of collisions on electron and ion probe current was demonstrated and the procedure for determination of electron and ion densities from the probe measurement at higher pressures was developed. The results from PIC/MCC simulations were compared with results from continuum theory. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effects of electron induced secondary electron (SE) emission from SiO2 electrodes in single-frequency capacitively coupled plasmas (CCPs) are studied by particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations in argon gas at 0.5 Pa for different voltage amplitudes. Unlike conventional simulations, we use a realistic model for the description of electron-surface interactions, which takes into account the elastic reflection and the inelastic backscattering of electrons, as well as the emission of electron induced SEs (δ-electrons). The emission coefficients corresponding to these elementary processes are determined as a function of the electron energy and angle of incidence, taking the properties of the surface into account. Compared to the results obtained by using a simplified model for the electron-surface interaction, widely used in PIC/MCC simulations of CCPs, which includes only elastic electron reflection at a constant probability of 0.2, strongly different electron power absorption and ionization dynamics are observed. We find that ion induced SEs (γ-electrons) emitted at one electrode and accelerated to high energies by the local sheath electric field propagate through the plasma almost collisionlessly and impinge on the opposing sheath within a few nanoseconds. Depending on the instantaneous local sheath voltage these energetic electrons are either reflected by the sheath electric field or they hit the electrode surface, where each γ-electron can generate multiple δ-electrons upon impact. These electron induced SEs are accelerated back into the plasma by the momentary sheath electric field and can again generate δ-electrons at the opposite electrode after propagating through the plasma bulk. Overall, a complex dynamics of γ- and δ-electrons is observed including multiple reflections between the boundary sheaths. At high voltages, the electron induced SE emission is found to strongly affect the plasma density and the ionization dynamics and, thus, it represents an important plasma-surface interaction that should be included in PIC/MCC simulations of CCPs under such conditions.

The electron cyclotron resonance (ECR) effect in a weakly magnetized capacitively coupled radio frequency (RF) plasma was previously observed with optical emission spectroscopy (OES) in experiments and analyzed by particle-in-cell/Monte Carlo collision (PIC/MCC) simulations (Zhang et al 2022 Plasma Sources Sci. Technol. 31 07LT01). When the electron cyclotron frequency equals the RF driving frequency, the electron can gyrate in phase with the RF electric field inside the plasma bulk, being continuously accelerated like microwave ECR, leading to prominent increases in the electron temperature and the excitation or ionization rate in the bulk region. Here, we study further the basic features of the RF ECR and the effects of the driving frequency and the gas pressure on the RF ECR effect by OES and via PIC/MCC simulations. Additionally, a single electron model is employed to aid in understanding the ECR effect. It is found that the maximum of the measured plasma emission intensity caused by ECR is suppressed by either decreasing the driving frequency from 60 MHz to 13.56 MHz or increasing the gas pressure from 0.5 Pa to 5 Pa, which shows a qualitative agreement with the change of the excitation rate obtained in the simulations. Besides, the simulation results show that by decreasing the driving frequency the electron energy probability function (EEPF) changes from a convex to a concave shape, accompanied by a decreased electron temperature in the bulk region. By increasing the gas pressure, the EEPF and the electron temperature show a reduced dependence on the magnitude of the magnetic field. These results suggest that the ECR effect is more pronounced at a higher frequency and a lower gas pressure, primarily due to a stronger bulk electric field, together wih a shorter gyration radius and lower frequency of electron–neutral collisions.

The electron bounce resonance heating (BRH) in dual-frequency capacitively coupled plasmas operated in oxygen is studied by different experimental methods and a particle-in-cell/Monte Carlo collision (PIC/MCC) simulation, and compared with the electropositive argon discharge. In comparison with argon, the experimental results show that in an oxygen discharge the resonance peaks in positive-ion density and light intensity tend to occur at larger electrode gaps. Moreover, at electrode gaps L > 2.5 cm, the positive-ion (and electron) density and the light emission drop monotonically in the oxygen discharge upon increasing L, whereas they rise (after an initial drop) in the argon case. At resonance gap the electronegativity reaches its maximum due to the BRH. All these experimental observations are explained by PIC/MCC simulations, which show that in the oxygen discharge the bulk electric field becomes quite strong and is out of phase with the sheath field. Therefore, it retards the resonance electrons when traversing the bulk, resulting in a suppressed BRH. Both experiment and simulation results show that this effect becomes more pronounced at lower high-frequency power, when the discharge mode changes from electropositive to electronegative. In a pure oxygen discharge, the BRH is suppressed with increasing pressure and almost diminishes at 12 Pa. Finally, the driving frequency significantly affects the BRH, because it determines the phase relation between bulk electric field and sheath electric field.

The power absorption mechanisms of charged particles during the ignition of pulsed dual radio-frequency (12.5 MHz/2.5 MHz) capacitively coupled argon plasmas at different gas pressures are investigated by multi-fold experimental diagnostics and particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. All the experimental results, including the evolution of the macroscopic plasma and electrical parameters, and the spatiotemporal distribution of the electron-impact excitation rate during the ignition process are well reproduced by the PIC/MCC simulations. It is found that by increasing the pressure, the plasma ignition occurs more rapidly and meanwhile the RF power dissipation is significantly enhanced during the ignition phase. At the beginning of the ignition phase electrons dissipate energy rapidly via ionization and excitation, leading to an overshoot of the optical emission intensity (OEI) and the RF power dissipation, while the ion energy absorption rate is relatively low and grows slowly. When the OEI and the RF power deposition overshoot, the charge density increases and accordingly the electron and especially the ion power absorption rate is enhanced due to an enhanced electric field within the space charge regions near the electrodes. During the post-ignition phase the sheaths form and the energy dissipated to the ions surpasses that dissipated to the electrons. At low pressure, e.g. 30 Pa, the electron power absorption mainly occurs inside the bulk region and the electron excitation and ionization dynamics resemble each other. By contrast, at higher pressure, e.g. 60 Pa and 120 Pa, the excitation and ionization dynamics behave differently, i.e. the excitation is mainly produced by high-energy electrons generated due to the expanding sheath and the drift electric fields inside the bulk region, while the ionization generated by γ-electrons is mainly located at the edge of the fully expanded sheaths.

For interpreting the production mechanism of surface-wave plasmas sustained along a metal rod, electromagnetic simulation on the electromagnetic field distributions and particle-in-cell/Monte Carlo collision (PIC/MCC) simulation of the ionization process are present. The results show that the enhanced electric field of surface plasmon polaritons (SPPs) can be excited in the ion sheath layer between the negative-voltage metal rod and the surface-wave plasmas, which is responsible for maintaining the plasma discharge. Moreover, the spatio-temporal evolutions of plasma density and electric fields are simulated by the PIC/MCC model. It is further suggested that the expanded ion sheath layer can extend the length of plasma domain by increasing the plasma absorbed energy from SPPs.

The electron heating mode transitions in capacitively coupled CF4 discharges were studied by synergistically using two diagnostic methods in combination with Particle-in-Cell/Monte Carlo collision (PIC/MCC) simulations. Based on the method of phase resolved optical emission spectroscopy of trace rare gas, the spatiotemporal evolutions of energetic electrons were presented. The time-average electron density at the discharge center was measured by using a hairpin probe. All the experimental results were compared with those obtained from PIC/MCC simulations. Two different electron heating modes were observed depending on the discharge conditions: (1) the α mode (or electropositive mode), in which the electron heating maximum occurs near the sheath boundary, dominated by the sheath electric field during its expansion phase, (2) the drift-ambipolar (DA) mode (or electronegative mode), in which the electron heating maxima occur inside the entire bulk plasma and near the collapsing sheath edge, dominated by the drift field inside the bulk and the ambipolar fields near the collapsing sheath edge, respectively. The transitions between the two modes were presented when changing the rf power, working pressure and driving frequency.By increasing the power, the heating mode experiences a transition from DA to α mode. This is ascribed to the fact that at high powers, the sheath heating is enhanced, leading to a drastic decrease in the electronegativity, and consequently the DA electric field is significantly reduced. By increasing the pressure, a heating mode transition from a pure α mode, then a combination of α and DA modes, finally into a DA mode is induced. We found that the mode transition is much more sensitive to the change of working pressure than that of rf power. When increasing the pressure, there is an evident enhancement in the electron attachment, which can generate the negative ions and deplete the electrons, resulting in a higher electronegativity as well as a higher DA field, and therefore the excitation and ionization in the bulk are enhanced. The driving frequency is found to significantly affect the electronegativity, i.e. as the driving frequency increases, the discharge becomes more electropositive, and the sheath heating (α mode) dominates. Furthermore, we conclude that as the driving frequency is increased, the pressure, at which the mode transition occurs, is increased, while the power, at which the mode transition occurs, is decreased.