Particle in cell/Monte Carlo collision analysis of the problem of identification of impurities in the gas by the plasma electron spectroscopy method

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.

In this paper, a one-dimensional (1-D) particle in cell-Monte Carlo collisions (PIC-MCC) model is developed to study the process of post-arc sheath expansion. In this model, both electrons and ions are treated as particles with their thermal velocities obeying the Maxwell-Boltzmann velocity distribution. The model takes the collision effects of ion-neutral (charge exchange collision and momentum exchange collision), and electron-neutral (scatter collision, excitation collision and ionization collision) into consideration. The simulation results are also compared with that calculated by the classical continuous transition model (CTM). In present work, the influence of some important factors, e.g. the density of initial residual plasma, the density of background metal vapor, the rising rate of transient recovery voltage (TRV) on the sheath expanding process are investigated.

Comparative studies of capacitively coupled radio-frequency discharges in helium and argon at pressures between 10 and 80 Pa are presented applying two different fluid modeling approaches as well as two independently developed particle-in-cell/Monte Carlo collision (PIC/MCC) codes. The focus is on the analysis of the range of applicability of a recently proposed fluid model including an improved drift-diffusion approximation for the electron component as well as its comparison with fluid modeling results using the classical drift-diffusion approximation and benchmark results obtained by PIC/MCC simulations. Main features of this time- and space-dependent fluid model are given. It is found that the novel approach shows generally quite good agreement with the macroscopic properties derived by the kinetic simulations and is largely able to characterize qualitatively and quantitatively the discharge behavior even at conditions when the classical fluid modeling approach fails. Furthermore, the excellent agreement between the two PIC/MCC simulation codes using the velocity Verlet method for the integration of the equations of motion verifies their accuracy and applicability.

The left branch of the Paschen curve for helium gas is studied both experimentally and by means of particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. The physical model incorporates electron, ion, and fast atom species whose energy-dependent anisotropic scattering on background neutrals, as well as backscattering at the electrodes, is properly accounted for. For the range of breakdown voltage 15 kV≤Vbr≤130 kV, a good agreement is observed between simulations and available experimental results for the discharge gap d = 1.4 cm. The PIC/MCC model is used to predict the Paschen curve at higher voltages up to 1 MV, based on the availability of input atomic data. We find that the pd similarity scaling does hold and that above 300 kV, the value of pd at breakdown begins to increase with increasing voltage. To achieve good agreement between PIC/MCC predictions and experimental data for the Paschen curve, it is essential to account for impact ionization by fast atoms (produced in charge exchange) and ions and for anisotropic scattering of all species on background atoms. With the increase of the applied voltage, energetic fast atoms progressively dominate in the overall ionization rate. The model makes this clear by predicting that breakdown would occur even without electron- and ion-induced ionization of the background gas, due to ionization by fast atoms backscattered at the cathode, and their high production rate in charge exchange collisions. Multiple fast neutrals per ion are produced when the free path is small compared to the electrode gap.

A parallel 1d3v Particle in Cell/Monte Carlo Collision (PIC/MCC) code was derived and applied for the investigation of the formation of photoplasma in sodium vapor. The effects of particle weighting and the Courant number on the computed plasma properties were examined, and the convergence of the numerical method with respect to these parameters was demonstrated. Simulations were carried out for the stepwise spatial profile of the resonant sodium atoms density. The basic plasma parameters (such as eedf, iedf, atomic and molecular ion and electron densities, and electric field and potential) were computed. The results of the PIC/MCC simulations were compared to those obtained from the fluid model. Simulations revealed a strong spatial non-uniformity in the electron density and the electric potential over the computational domain that provides evidence in favour of photovoltaic conversion of light energy into electrical energy.

The plasma density radial profiles in capacitive discharges driven over a wide frequency range (60–220 MHz) are measured by a floating double probe, and the results measured at 60 MHz are compared with those obtained from the electrostatic models, i.e. particle in cell/Monte Carlo collision (PIC/MCC) and the fluid models. It was found that at low pressure the plasma density peaks at the center of the reactor, while it peaks at the electrode edge at high pressure, indicating that the power deposition transitions from ‘non-local’ to ‘local’ with increasing pressure. The plasma radial profiles obtained from the PIC/MCC simulation and fluid model show a qualitative agreement with the experiment at low pressure and high pressure, respectively. This is primarily due to the fact that at low pressure the fluid model substantially under-predicts sheath heating, which, however, is the main electron heating mechanism at low pressure. So the total power into electrons and therefore the plasma density is also under-predicted. In contrast, the PIC/MCC model takes into account these electron collisionless heating effects at low pressure, and thus the plasma density is enhanced in the central region of electrodes. At high pressure, due to local power deposition, both the experiment and fluid simulation show that as rf power increases, a density peak at the electrode edge appears, indicating an enhancement in edge field. Compared with the electrostatic case, at a higher frequency, the plasma density profile is determined by electromagnetic (EM) effects, especially the standing wave effect. To be specific, we found that the standing wave effect exhibits multi-node structure within the electrode at 130 MHz or above, and the wavelength becomes smaller as the excitation frequency increases. At high excitation frequency and high pressure, the rf power is mainly deposited at the electrode periphery due to the fact that the EM waves are strongly damped when they propagate from the discharge edge to the center. In addition, our experimental results show that the standing wave wavelength increases with rf power.

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.

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.

This paper reports that a simulation of glow discharge in pure helium gas at the pressure of 1.333 × 103 Pa under a high-voltage nanosecond pulse is performed by using a one-dimensional particle-in-cell Monte Carlo collisions (PIC-MCC) model. Numerical modelling results show that the cathode sheath is much thicker than that of anode during the pulse discharge, and that there exists the phenomenon of field reversal at relative high pressures near the end of the pulse, which results from the cumulative positive charges due to their finite mobility during the cathode sheath expansion. Moreover, electron energy distribution function (EEDF) and ion energy distribution function (IEDF) have been also observed. In the early stage of the pulse, a large amount of electrons can be accelerated above the ionization threshold energy. However, in the second half of the pulse, as the field in bulk plasma decreases and thereafter the reverse field forms due to the excessive charges in cathode sheath, although the plasma density grows, the high energy part of EEDF decreases. It concludes that the large volume non-equilibrium plasmas can be obtained with high-voltage nanosecond pulse discharges.

The gas desorbed from the dielectric surface has a great influence on the characteristics of microwave breakdown on the vacuum side of the dielectric window. In this paper, the dielectric surface breakdown is described by using the electromagnetic particle-in-cell-Monte Carlo collision (PIC-MCC) model. The process of desorption of gas and its influence on the breakdown characteristics are studied. The simulation results show that, due to the accumulation of desorbed gas, the pressure near the dielectric surface increases in time, and the breakdown mechanism transitions from secondary electron multipactor to collision ionization. More and more electrons generated by collision ionization drift to the dielectric surface, so that the amplitude of self-organized normal electric field increases in time and sometimes points to the dielectric surface. Nevertheless, the number of secondary electrons emitted in each microwave cycle is approximately equal to the number of primary electrons. In the early and middle stages of breakdown, the attenuation of the microwave electric field near the dielectric surface is very small. However, the collision ionization causes a sharp increase in the number density of electrons, and the microwave electric field decays rapidly in the later stage of breakdown. Compared with the electromagnetic PIC-MCC simulation results, the mean energy and number of electrons obtained by the electrostatic PIC-MCC model are overestimated in the later stage of breakdown because it does not take into account the attenuation of microwave electric field. The pressure of the desorbed gas predicted by the electromagnetic PIC-MCC model is close to the measured value, when the number of gas atoms desorbed by an incident electron is taken as 0.4.

The structure of a capacitively coupled high-pressure glow (HPG) discharge in high-purity helium is investigated using a detailed one-dimensional modeling approach. Impurity effects are modeled using trace amounts of nitrogen gas in helium. Average electron temperatures and densities for the HPG discharge are similar to their low-pressure counterpart. Helium-dimer ions dominate the discharge structure for sufficiently high-current densities, but model impurity nitrogen ions are found to be dominant for low-discharge currents. Helium dimer metastable atoms are found to be the dominant metastable species in the discharge. The high collisionality of the HPG plasma results in significant discharge potential drop across the bulk plasma region, electron Joule heating in the bulk plasma, and electron elastic collisional losses. High collisionality also results in very low ion-impact energies of order 1 eV at the electrode surfaces.

It has been shown that self-sustained normal dc atmospheric pressure glow discharge (APGD) in helium exists in a large range of current values from 100 µA to 10 A. The plasma of this discharge is weakly ionized (one thousandth part of a per cent) and is non-equilibrium. The plasma non-equilibrium degree in the positive column depends on the discharge current values. Parameters of the cathode region stay constant over the whole current range of normal APGD.

A wide variety of plasma phenomena have been investigated during the past decades using the particle-in-cell/Monte Carlo collisions (PIC/MCC) method. As an important component of the PIC/MCC method, solving Poisson’s equation is crucial for the accuracy and efficiency of calculations. Different acceleration techniques for solving finite difference discretization Poisson’s equation are investigated and compared, including direct method, iterative method, multigrid (MG) method, parallel computing and inherited initial value. The charge density distribution with a known analytical solution is used to validate the algorithm and code. The optimal relaxation factor for the successive over-relaxation (SOR) method in 2D Poisson’s equation with unequal grid node numbers in different dimensions is derived, which is only related to the dimension with the largest grid number. Although there will be a ‘more optimal’ relaxation factor deviated from in some simulation cases, selecting the optimal relaxation factor derived always leads to a not slow solving speed. However, when SOR is used in MG for smoothing, the optimal relaxation factor will shift to 0.5–1.2 from the theoretical optimal value derived with the increase of MG levels. By comparing the convergence order under different relaxation factors and MG levels, the suitable MG level is proposed as log2[min(N x , N y )]−2. Combining the optimal SOR relaxation factor, MG, parallel computing and inherited initial values, the computational cost may decrease by 5 orders of magnitude than that by the simple Gaussian elimination (GE). Based on the optimal acceleration techniques mentioned above, a benchmark simulation case electron cyclotron drift instability (ECDI) in magnetized plasmas was run to further validate the developed PIC/MCC code. The distributions of electric field in the x-direction, electron density and electron temperature are all consistent with the literatures. This paper provides a reference for the acceleration strategy selection for solving Poisson’s equation quickly in plasma simulations.

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.