A new combined PIC-MCC approach is developed for accurate and fast simulation of a radio frequency discharge at low gas pressure and high density of plasma. Test calculations of transition between different modes of electron heating in a ccrf discharge in helium and argon show a good agreement with experimental data.
We demonstrate high efficiency of the combined PIC-MCC algorithm, especially for the collisionless regime of electron heating.
Two-dimensional capacitively coupled radio frequency discharge in methane is simulated by PIC-MCC method. The results were obtained in pressure range 50-300 mTorr and voltage range 40-180 V for discharge frequency 13.56 MHz. The electron energy and electron--methane reaction rates spatial distributions show existence of two regimes of discharge glow: a) with active sheaths, when electrons are hot in electrode sheaths and cold in the middle of discharge so the electron-neutral reactions strongly dominate in sheaths regions; b) with volume domination, when the electron energy is more uniform and…
Particle-in-cell with Monte Carlo collisions (PIC/MCC) is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form (electrostatic, one-dimensional geometry, and explicit time integration), it can properly describe a wide variety of complex, non-local, non-linear phenomena in electrical gas discharges at the microscopic level with high accuracy. However, being a numerical model working with discretized temporal and (partially) spatial coordinates, its stable and accurate operation l…
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 modelling 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 modelling results using the classical drift-diffusion approximation and benchmark results obtained by PIC/…
Resonantly Driven Electron Bernstein Waves in Magnetized Low-Pressure Capacitive Discharges
School of Physical Sciences, UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai（孟买大学物理科学学院，UM-DAE基础科学卓越中心）；Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴哈国家研究所）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
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. 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 increas…
The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current of low pressure capacitive radio frequency (RF) discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation…
We benchmark and analyze the error of energy conservation (EC) scheme for Particle in cell/Monte-Carlo Couple (PIC/MCC) algorithms by a radio frequency discharging simulation. The plasma heating behaviors and electron distributing functions obtained by 1D simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some "numerical cooling" be…
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas the heavy species are modeled within a fluid description. Validity of the popular drift-diffusion approximation is verified against a "full" fluid model accounting for the ion inertia and a fully kinetic PIC/MCC code for ions as well as electrons. The fluid models require knowledge of the momentum exchange frequency and dependence of the ion mobilities on the…
We report the existence of an enhanced operating regime for a high-frequency, low-pressure capacitively coupled plasma (CCP) discharge in the presence of a weak magnetic field applied parallel to the electrodes. Our PIC-MCC simulations show that the plasma density and ion flux values exhibit a sharp peak when the electron cyclotron frequency equals half of the applied RF frequency. The physical mechanism responsible for this behaviour is traced to a synchronization between the oscillatory motion of the electrode sheath edge and the motion of a set of electrons reflected by this sheath. These e…
Using Monte Carlo Collisions (MCC) method, we have performed simulations of ion velocity distribution functions (IVDF) taking into account both elastic collisions and charge exchange collisions of ions with atoms in uniform electric fields for argon and helium background gases. The simulation results are verified by comparison with the experiment data of the ion drift velocities and the ion transverse diffusion coefficients in argon and helium. The recently published experimental data for the first seven coefficients of the Legendre polynomial expansion of the ion energy and angular distributi…
Azimuthal structures in cylindrical Penning discharge are studied with 2D3V radial-azimuthal PIC/MCC model with the axial magnetic field. The discharge is self-consistently supported by ionization due to the axial injection of electrons. It is shown that the steady-state discharge can be supported in two different regimes with different type of observed azimuthal structures. The transition between the regimes is controlled by the mechanism of the energy input to the discharge. In the first regime (low energy of the injected electrons), with the pronounced $m=1$ spoke activity, the power input …
In most PIC/MCC simulations of radio frequency capacitively coupled plasmas (CCPs) several simplifications are made: (i) fast neutrals are not traced, (ii) heavy particle induced excitation and ionization are neglected, (iii) secondary electron emission from boundary surfaces due to neutral particle impact is not taken into account, and (iv) the secondary electron emission coefficient is assumed to be constant, i.e. independent of the incident particle energy and the surface conditions. Here we question the validity of these simplifications under conditions typical for plasma processing applic…
This paper is a simulation based investigation of the effect of elastic collisions and effectively elastic-like excitation collisions between electrons and background neutrals on the dynamics of a cylindrically trapped electron cloud that also has an ion contaminant mixed in it. Effects of the collisions on the instability are evident from alteration in the growth rate and energetics of the ion resonance instability caused by the presence of background neutrals as compared to a vacuum background. Further in order to understand if the non-ionizing collisions can independently be a cause of dest…
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 9…
An argon-xenon (Ar/Xe) plasma is used as a model system for complex plasmas. Based on this system, symmetric low-pressure capacitively coupled radio-frequency discharges are examined utilizing Particle-In-Cell/Monte Carlo Collisions (PIC/MCC) simulations. In addition to the simulation, an analytical energy balance model fed with the simulation data is applied to analyze the findings further. This work focuses on investigating the ion dynamics in a plasma with two ion species and a gas mixture as background. By varying the gas composition and driving voltage of the single-frequency discharge, f…
Non-self-sustained electric discharge and electric breakdown were triggered and guided by a train of picosecond UV pulses overlapped with a long free-running UV pulse of a hybrid Ti:Sapphire-KrF laser facility. Photocurrent sustained by this train is two orders of magnitude higher, and electric breakdown distance is twice longer than those for the discharge triggered by the long UV pulse only.
The propagation mechanisms of plasma streamers have been observed and investigated in a surface dielectric barrier discharge (SDBD) using 2D particle in cell simulations. The investigations are carried out under a simulated air mixture, 80\% N$_2$ and 20\% O$_2$, at atmospheric pressure, 100$\,$kPa, under both DC conditions and a pulsed DC waveform that represent AC conditions. The simulated geometry is a simplification of the symmetric and fully exposed SDBD resulting in the simultaneous ignition of both positive and negative streamers on either side of the Al$_2$O$_3$ dielectric barrier. In …
We employ a particle-in-cell Monte Carlo collision/particle-particle particle-mesh (PIC-MCC/PPPM) simulation to study the plasma flow around and the charge distribution of a three-dimensional dust cluster in the sheath of a low-pressure rf argon discharge. The geometry of the cluster and its position in the sheath are fixed to the experimental values, prohibiting a mechanical response of the cluster. Electrically, however, the cluster and the plasma environment, mimicking also the experimental situation, are coupled self-consistently. We find a broad distribution of the charges collected by th…
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…
The crucial role that Ions Energy Distribution Function (IEDF) at the electrodes plays in plasma processing of semiconductor materials demands that this quantity be predicted with high accuracy and with low noise levels in any plasma simulator. In this work, an efficient Particle-in-cell/Monte-Carlo (PIC/MC) simulator is developed to model IEDF at the electrodes of electronegative plasma discharges. The simulator uses an effective method to increase the number of MC particles in regions of low particle density by splitting the particles and by adjusting their statistical weight. This statistic…
Simulation Studies of Resonant Excitation of Electron Bernstein Waves in Capacitive Discharges
School of Physical Sciences, UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai（孟买大学基础科学卓越中心物理学院）；Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
During the initial phase of microwave (MW) power launch inside a MW discharge ion source (MDIS), plasma and the electric fields are evolved with time together in the plasma volume. The spatio-temporal evolution pattern in the cavity of a MDIS is reported here, highlighting the role of these electric fields on power coupling processes. Evolution of electric field and so power coupling processes are calculated using Finite Element Method (FEM). Unlike PIC/MCC or hybrid fluid, here FEM model uses time dependent Poisson solver through drift-diffusion approach. In presence of plasma gradient in the…
The effects of the discharge voltage on the formation and nature of electric field transients in a symmetric, collisionless, very high frequency, capacitively coupled plasma are studied using a self-consistent particle-in-cell (PIC) simulation code. At a driving frequency of 60 MHz and 5 mTorr of argon gas pressure, the discharge voltage is varied from 10V to 150 V for a fixed discharge gap. It is observed that an increase in the discharge voltage causes filamentation in the electric field transients and to create multiple higher harmonics in the bulk plasma. Correspondingly, higher harmonics,…
Electron emission from the boundary is ubiquitous in capacitively coupled plasma (CCP) and precipitates nonnegligible influences on the discharge properties. Here we present the PIC-MCC simulation of an Ohmic-dominant heating mode of capacitively coupled plasma where the stochastic heating vanishes and only Ohmic heating sustains the discharge, due to sheath inversion by boundary electron emission. The inverted CCP features negative sheath potential without Bohm presheath, hence excluding plasma heating due to sheath edge oscillation. The particle and energy transport of the proposed heating m…
Both fluid and particle models are commonly used to simulate streamer discharges. In this paper, we quantitatively study the agreement between these approaches for axisymmetric and 3D simulations of positive streamers in air. We use a drift-diffusion-reaction fluid model with the local field approximation and a PIC-MCC (particle-in-cell, Monte Carlo collision) particle model. The simulations are performed at 300 K and 1 bar in a 10 mm plate-plate gap with a 2 mm needle electrode. Applied voltages between 11.7 and 15.6 kV are used, which correspond to background fields of about 15 to 20 kV/cm. …
Radio-frequency-driven atmospheric pressure plasma jets (RF APPJs) play an essential role in many technological applications. This work studies the characteristics of these discharges in the so-called non-neutral regime where the conventional structure of a quasi-neutral bulk and an electron depleted sheath does not develop, and the electrons are instead organized in a drift-soliton-like structure that never reaches quasi-neutrality. A hybrid particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation is set up, which combines a fully kinetic electron model via the PIC/MCC algorithm with a dr…
Formation of near-cathode plasma at the instant of breakdown of the air gap was studied by the methods of picosecond laser probing. It was demonstrated that 1-2 ns after a sharp rise of the current through the discharge gap dense plasma clots with Ne~10^20 cm^-3 and dNe/dx ~ 10^24 cm^-4 are formed on the cathode surface. It was shown that these highly ionized regions lead to initiation and development of the spark channel originating from the cathode. We propose that the observed formations correspond to erosive plasma formed from the cathode material.
Very high frequency (VHF) driven capacitive discharges are now being increasingly adopted for plasma-based materials processing due to their high processing rates and lower substrate damage. Past studies related to complex plasma dynamics and higher harmonics generation in such systems were limited to constant voltage/current conditions, whereas, industrial systems are mostly driven by constant power density sources. In the present study, using particle-in-cell (PIC) simulation, we explore the dynamics of collisionless symmetric capacitive discharges that is operated at constant power densitie…
The high order fluid model developed in the preceding paper is employed here to study the propagation of negative planar streamer fronts in pure nitrogen. The model consists of the balance equations for electron density, average electron velocity, average electron energy and average electron energy flux. These balance equations have been obtained as velocity moments of Boltzmann's equation and are here coupled to the Poisson equation for the space charge electric field. Here the results of simulations with the high order model, with a PIC/MC (Particle in cell/Monte Carlo) model and with the fi…
The process of electron multiplication through the bouncing-like accelerated motion of electrons inside nanovoids formed owing to external electric fields in bulk liquid water is investigated using Monte Carlo simulations in Geant4-DNA. Our results show that the initial charge developed at the metal/liquid interface can be multiplied and expanded along the direction of the external electric field on a picosecond timescale, owing to collision-free interiors of the nanoruptures. Characteristic features of two different electron multiplication mechanisms are revealed and characterized. We find th…
We study the use of frequency upconversion schemes of near-IR picosecond laser pulses and compare their ability to guide and trigger electric discharges through filamentation in air. Upconversion, such as Second Harmonic Generation, is favorable for triggering electric discharges for given amount of available laser energy, even taking into account the losses inherent to frequency conversion. We focus on the practical question of optimizing the use of energy from a given available laser system and the potential advantage to use frequency conversion schemes.
Long wavelength plasma non-uniformities rotating in the azimuthal direction ("rotating spokes") have been observed in a number of experiments on Hall thrusters or magnetron discharges. We use a two-dimensional (2D), axial-azimuthal Particle-In-Cell Monte Carlo Collisions (PIC-MCC) model to study the formation of instabilities in a direct current (dc) magnetron discharge under conditions close to recent experiments. In spite of the simplified 2D geometry of the model, the simulations can reproduce the main features of the experimental results. At a given position above the cathode, correspondin…
Recently, S Patil et al. have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio-frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their Particle-in-Cell (PIC) simulations show, that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied RF frequency for a given fixed voltage. In the present work we take a detailed look at this phenome…
A particle-in-cell (PIC) simulation study is performed to investigate the discharge asymmetry, higher harmonic generations and electron heating mechanism in a low pressure very high frequency capacitively coupled plasma (CCP) excited by a saw-tooth like current waveform. Two current densities, 50 A/m2 and 100 A/m2 are chosen for a constant gas pressure of 5 mTorr in argon plasma. The driving frequency is varied from 13.56 MHz to 54.24 MHz. At a lower driving frequency, high frequency modulations on the instantaneous sheath edge position at the grounded electrode are observed. These high freque…
The self-excitation of Plasma Series Resonance (PSR) oscillations plays an important role in the electron heating dynamics in Capacitively Coupled Radio Frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the Electrical Asymmetry Effect, i.e. by varying the total number of harmonics and tuning the phase …
Breakdown voltages of a capacitively coupled radio frequency argon discharge at 27 MHz are studied. We use a one-dimensional electrostatic PIC code to investigate the effect of changing the secondary emission properties of the electrodes on the breakdown voltage, particularly at low pd values. Simulation results are compared with the available experimental results and a satisfactory agreement is found.
The low-frequency rotating plasma instability (spoke) in the ISCT200 thruster operating in the wall-less configuration was simulated with a 3 dimensional PIC MCC code. In the simulations an m = 1 spoke rotating with a velocity of 6.5 km/s in the ExB direction was observed. The rotating electron density structure in the spoke is accompanied by a strongly depleted region of the neutral gas, which clearly shows that the spoke instability is of an ionization nature, similar to the axial breathing mode oscillations. In the simulation the electron cross-field transport through the spoke core was cau…
The Particle-in-Cell (PIC) method was used to study two different ion thruster concepts - Stationary Plasma Thrusters (SPT) and High Efficiency Multistage Plasma Thrusters (HEMP-T), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particle fluxes on the thrusters channel surfaces. In both cases, PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts. The simulations demonstrated that the new HEMP thruster co…
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 [Y.-X. Liu, et al. Phys. Rev. Lett. 116, 255002 (2016)]. 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 f…
