Multi-diagnostic experimental validation of 1d3v PIC/MCC simulations of low pressure capacitive RF plasmas operated in argon

An understanding of the plasma dynamics of radio-frequency (RF) hollow cathode discharges (HCDs) at low to moderate pressures is important due to their wide range of applications. A HCD consists of a hollow cylindrical cavity in the RF-powered cathode separated from a grounded electrode by a dielectric. In RF HCDs, RF sheath heating can play a significant role in plasma production in addition to secondary electrons. In this study, a single hollow cathode hole is modeled using the particle-in-cell/Monte Carlo collision (PIC-MCC) technique at low pressure, where kinetic effects are important. Characterization of a single hollow cathode using PIC-MCC simulation is, however, computationally expensive. For improved computational efficiency, a neural network modeling framework has been developed using the temporal variations of applied RF voltages as input and the electrode current as output. A space-filling design for computational experiments is used, where the variables include the RF voltage at the fundamental frequency, RF voltage at the second harmonic, and their phase difference. The predictions of the electrode current using the trained neural network model compare well with the results of the PIC/MCC simulations, but at a significantly lower computational cost. The neural network model predicts the current very well inside the training domain, and reasonably well even outside the training domain considered in this study.

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.

We investigate the effects of secondary electrons (SEs), induced by electrons impinging on the electrodes, on the characteristics of low-pressure single-frequency capacitively coupled plasmas (CCPs) by particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. In a recent PIC/MCC simulation study, that incorporated a realistic description of the electron-surface interaction, such electron-induced SEs (δ-electrons) were found to have a remarkable impact on the ionization dynamics and the plasma parameters in argon at 0.5 Pa and 6.7 cm gap between SiO2 electrodes (Horváth et al 2017 Plasma Sources Sci. Technol. 26 124001). At such low pressure and at high voltage amplitudes, the ion-induced SEs (γ-electrons) emitted at one electrode can reach the opposite electrode with high energies, where, depending on the surface material and surface conditions, they can induce the emission of a high number of δ-electrons, which can cause significant ionization and a higher plasma density. Here, we study the influence of δ-electrons on the ionization dynamics and plasma parameters at various pressures and voltage amplitudes, assuming different SE yields for ions (γ-coefficient) in single-frequency 13.56 MHz argon discharges. The emission of SEs by electron impact is found to be an important plasma-surface process at low pressures, between 0.5 Pa and 3 Pa. Both the gas pressure and the value of the γ-coefficient are found to affect the role of δ-electrons in shaping the discharge characteristics at different voltage amplitudes. Their effect on the ionization dynamics is most striking at low pressures, high voltage amplitudes and high values of the γ-coefficient. However, in the whole parameter regime investigated here, the realistic description of the electron-surface interaction significantly alters the computed plasma parameters, compared to results obtained based on a simple model for the description of the electron-surface interaction, widely used in PIC/MCC simulations of low-pressure CCPs.

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.

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.

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.

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.

In particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations of capacitively coupled plasmas (CCPs), the plasma-surface interaction is generally described by a simple model in which a constant secondary electron emission coefficient (SEEC) is assumed for ions bombarding the electrodes. In most PIC/MCC studies of CCPs, this coefficient is set to γ = 0.1, independent of the energy of the incident particle, the electrode material, and the surface conditions. Here, the effects of implementing energy-dependent secondary electron yields for ions, fast neutrals, and taking surface conditions into account in PIC/MCC simulations is investigated. Simulations are performed using self-consistently calculated effective SEECs, , for ‘clean’ (e.g., heavily sputtered) and ‘dirty’ (e.g., oxidized) metal surfaces in single- and dual-frequency discharges in argon and the results are compared to those obtained by assuming a constant secondary electron yield of for ions. In single-frequency (13.56 MHz) discharges operated under conditions of low heavy particle energies at the electrodes, the pressure and voltage at which the transition between the α- and γ-mode electron power absorption occurs are found to strongly depend on the surface conditions. For ‘dirty’ surfaces, the discharge operates in α-mode for all conditions investigated due to a low effective SEEC. In classical dual-frequency (1.937 MHz + 27.12 MHz) discharges significantly increases with increasing low-frequency voltage amplitude, , for dirty surfaces. This is due to the effect of on the heavy particle energies at the electrodes, which negatively influences the quality of the separate control of ion properties at the electrodes. The new results on the separate control of ion properties in such discharges indicate significant differences compared to previous results obtained with different constant values of γ.

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.

The particle-in-cell Monte Carlo collision (PIC-MCC) model is an essential way to investigate the kinetic behaviors of low-temperature plasmas, but usually, it is hugely time consuming in simulating atmospheric radio frequency (RF) plasmas. In this study, a deep neural network (DNN) with multiple hidden layers is developed to predict the kinetic discharge characteristics of atmospheric RF plasmas. The results obtained from the PIC-MCC model are used as the training dataset for the DNN, and the well-trained DNN is able to efficiently yield various kinetic behaviors of atmospheric RF discharges with very high precision. The validation of the results predicted by the DNN algorithm is performed by comparing them with the simulation results directly from the PIC-MCC model. Compared with the time-consuming PIC-MCC simulations, the well-trained DNN takes only 0.01 s to yield the essential kinetic characteristics of atmospheric RF discharges, which saves seven orders of magnitude of computation time compared with the traditional PIC-MCC simulation. The predicted data show that the discharge current of atmospheric RF discharges increases monotonically with the driving frequency at a given applied voltage, and as the driving frequency increases, the electric field in the sheath region is strongly enhanced with the sheath region shrinks and the bulk plasma region expanding. Additionally, the electron energy distribution function (EEDF) can be accurately predicted by DNN; moreover, as the driving frequency increases, the low-energy electrons can be transformed into medium-energy electrons, leading to a transition of the EEDF from a three-temperature distribution to a Maxwellian distribution from the DNN prediction. The study indicates that the well-trained DNN is a promising tool for plasma simulation with very high efficiency and accuracy compared with the PIC-MCC model with huge computational costs, which could provide enough kinetic results to further understand the discharge behaviors in atmospheric RF discharges.

Special Issue on Numerical Modelling of Low‐Temperature Plasmas for Various Applications – Part I: Review and Tutorial Papers on Numerical Modelling Approaches

Summary form only given. We developed 1d3v Particle in Cell/Monte Carlo Collision (PIC/MCC) numerical code for the Radio-Frequency (RF) capacitive glow discharge. This method includes the solution of the Lorentz force equation for the motion of super particles and the Poisson equation for the electric field. Collisions between the particles are modeled with the Monte Carlo method. In this process, the elastic and charge exchange collisions between the ion-neutral pairs, as well as the elastic, excitation and ionization collisions between the electron-neutral pairs are taken into account. Test calculations were carried out for the plasma of RF discharge. Numerical code was validated by comparison with the published simulation results. Parallelization of this code was performed and the efficiency in time was studied. This efficiency was also analyzed according to increasing number of cores in a cluster.

The ignition process of a pulse modulated capacitively coupled argon discharge driven simultaneously by two radio frequency voltages [12.5 MHz (high frequency) and 2.5 MHz (low frequency, LF)] is investigated by multifold experimental diagnostics and particle in cell / Monte Carlo collision simulations. In particular, (i) the effects of the LF voltage amplitude measured at the end of the pulse-on period, VL,end , on the spatiotemporal distribution of the electron impact excitation rate determined by phase resolved optical emission spectroscopy, and (ii) the electrical parameters acquired by analyzing the measured waveforms of the plasma current and voltage, are studied. Computed electrical parameters and spatio-temporal excitation maps show a good qualitative agreement with the experimental results. Especially, various breakdown mechanisms are found at different VL,end . At low values of VL,end , the ‘RF-avalanche’ mode (volume process) dominates the electron multiplication process. By increasing VL,end , the ionization caused by the volume electrons is suppressed and the electron loss at the electrodes is enhanced, leading to a delayed ignition. At higher values of VL,end , the avalanche ionization is significantly enhanced by ion-induced secondary electron emission at the electrodes, so that the ignition is significantly advanced.

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

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.