The paper provides a tutorial to the conceptual layout of a self-consistently coupled Particle-In-Cell/Test-Particle model for the kinetic simulation of sputtering transport in capacitively coupled plasmas at low gas pressures. It explains when a kinetic approach is actually needed and which numerical concepts allow for the inherent nonequilibrium behavior of the charged and neutral particles. At the example of a generic sputtering discharge both the fundamentals of the applied Monte Carlo methods as well as the conceptual details in the context of the sputtering scenario are elaborated on. Finally, two in the context of sputtering transport simulations often exploited assumptions, namely on the energy distribution of impinging ions as well as on the test particle approach, are validated for the proposed example discharge.
The processes of injection of a sputtered-and-ionized working material into the pulsed reflex discharge plasma have been considered at the initial stage of dense gas-metal plasma formation. A calculation model has been proposed to estimate the parameters of the sputtering mechanism for the required working material to be injected into the discharge. The data obtained are in good accordance with experimental results.
Discharges with crossed electric and magnetic fields are known to develop instabilities that are crucial in the transport of charged particles. Sputtering magnetrons are no exception. While most recent studies focused on traveling ionization zones in high power impulse magnetron sputtering, we show here fast camera images of magnetron discharges at very low current. A single drifting ionization zone is always present, even down to the threshold current of about 10 mA.
The discharges in high power impulse magnetron sputtering (HiPIMS) have been reported to consist of azimuthally inhomogeneous plasma with locally increased light emission. The luminous zones seemingly travel around the racetrack and are implicated in generation of the high ion kinetic energies observed in HiPIMS. We show that the inhomogeneities smooth out at high discharge current to yield azimuthally homogeneous plasma. This may have implications for the spatial and kinetic energy distribution of sputtered particles, and therefore also on the thin films deposited by high power impulse magnet…
The sputtering of inside wall components of tokamaks can lead to the injection of supersaturated vapour in the plasma edge. The resulting condensation favours the formation of clusters which can give rise to solid particulates by further accretion. Sputtering discharges are proposed to have highlight on the formation of carbonaceous dust observed in the tokamaks with graphite based wall components. The flux of the sputtered carbon atoms is evaluated in the conditions of our laboratory discharges as well as the evolution of their energy distribution. It is shown that a cooling mechanism occurs …
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,…
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…
We investigate the energy and angular distributions of the ions reaching the electrodes in low-pressure, capacitively coupled oxygen radio-frequency discharges. These distributions, as well as the possibilities of the independent control of the ion flux and the ion energy are analysed for different types of excitation: single- and classical dual-frequency, as well as valleys- and sawtooth-type waveforms. The studies are based on kinetic, particle-based simulations that reveal the physics of these discharges in great details. The conditions cover weakly collisional to highly collisional domains…
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 study the properties of a capacitive 13.56 MHz discharge properties with a mixture of Ar/C2H2 taking into account the plasmochemistry and growth of heavy hydrocarbons. A hybrid model was developed to combine the kinetic description for electron motion and the fluid approach for negative and positive ions transport and plasmochemical processes. A significant change of plasma parameters related to injection of 5.8% portion of acetylene in argon was observed and analyzed. We found that the electronegativity of the mixture is about 30%. The densities of negatively and positively charged heavy h…
Parameters of a high frequency capacitive discharge in argon in axially symmetric chambers of different geometries are studied in experiments and by means of two-dimensional kinetic modeling by the Particle-in-Cell method. It is demonstrated that a change in the ratio of the areas of the driven and grounded electrodes can substantially increase the ion energy on the electrode practically without disturbing the plasma parameters. Particular attention is paid to studying the self-bias voltage and the ion distribution function on the electrode for gas pressures ranging from 15 to 70 mTorr. The re…
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）
We use the one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 to explore the charged particle densities, the electronegativity, the electron energy probability function (EEPF), and the electron heating mechanism in a single frequency capacitively coupled oxygen discharge when the applied voltage amplitude is varied. We explore discharges operated at 10 mTorr, where electron heating within the plasma bulk (the electronegative core) dominates, and at 50 mTorr where sheath heating dominates. At 10 mTorr the discharge is operated in combined drift-ambipolar (DA) and …
The effect of micron-sized particles on a low-pressure capacitively-coupled rf discharge is studied both experimentally and using numerical simulations. In the laboratory experiments, microparticle clouds occupying a considerable fraction of the discharge volume are supported against gravity with the help of the thermophoretic force. The spatiotemporally resolved optical emission measurements are performed with different arrangements of microparticles. The numerical simulations are carried out on the basis of a one-dimensional hybrid (fluid-kinetic) discharge model describing the interaction b…
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…
In this work, we present the results of simulations carried out for N2-H2 capacitively coupled radio-frequency discharges, running at low pressure (0.3-0.9 mbar), low power (5-20 W), and for amounts of H2 up to 5 pct. Simulations are performed using a hybrid code that couples a two-dimensional time-dependent fluid module, describing the dynamics of the charged particles in the discharge, to a zero-dimensional kinetic module, that solves the Boltzmann equation and describes the production and destruction of neutral species. The model accounts for the production of several vibrationally and elec…
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…
The effect of surface quenching coefficients of $O_2(a^{1}Δg)$ and $O_2(b^{1}Σg^{+})$ on capacitively coupled $Ar$/$O_2$ discharge: A global/equivalent circuit model study
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics, Dalian University of Technology（大连理工大学激光、离子和电子束材料改性教育部重点实验室物理学院）
Using particle-in-cell simulation technique, we investigate the plasma and ionization asymmetry, electron and ion energy distribution function in capacitive discharges excited by tailored waveforms. At a base frequency of 13.56 MHz, three different waveforms namely, sinusoidal, saw-tooth, and square are applied for a constant current density of 50 A/m2 and 5 mTorr argon gas pressure. The simulation results show that the square waveform produces the highest plasma density in the discharge, whereas maximum asymmetry is observed for plasma excited by sawtooth like waveform. Both square and sawtoo…
The influence of charge trap states in the dielectric boundary material on capacitively coupled radio frequency plasma discharge is investigated with theory and Particle in cell/Monte Carlo Collision simulation. It is found that the trap states of the wall material manipulated discharge properties mainly through the varying ion induced secondary electron emission (SEE) coefficient in response to dynamic surface charges accumulated within solid boundary. A comprehensive SEE model considering surface charging is established first, which incorporates the valence band electron distribution, electr…
The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomen…
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…
External matching networks are crucial and necessary for operating capacitively coupled plasmas in order to maximize the absorbed power. Experiments show that external circuits in general heavily interact with the plasma in a nonlinear way. This interaction has to be taken into account in order to be able to design suitable networks, e.g., for plasma processing systems. For a complete understanding of the underlying physics of this coupling, a nonlinear simulation approach which considers both the plasma and the circuit dynamics can provide useful insights. In this work, the coupling of an equ…
A system of automated computerized Langmuir probe measurements is used in order to determine the plasma parameters in a plasma reactor constructed for cleaning of metallic artifacts by RF discharge. A compensated probe insures the suppression of the RF interference. The probe data are collected using a commercial data acquisition unit connected to a portable computer. The raw data are processed using wavelet transforms techniques which assures the de-noising of the probe signal without distortion of the probe I-V characteristic. The first and second derivatives of the I-V characteristic are de…
Experimental investigation of an electronegative cylindrical capacitively coupled geometrically asymmetric plasma discharge with an axisymmetric magnetic field
We apply the Ionization Region Model (IRM) and the Orsay Boltzmann equation for ELectrons coupled with Ionization and eXcited states kinetics (OBELIX) model to study the electron kinetics of a high power impulse magnetron sputtering (HiPIMS) discharge. In the IRM the bulk (cold) electrons are assumed to exhibit a Maxwellian energy distribution and the secondary (hot) electrons, emitted from the target surface upon ion bombardment, are treated as a high energy tail, while in the OBELIX the electron energy distribution is calculated self-consistently using an isotropic Boltzmann equation. The tw…
An 18-level argon collisional radiative model (CRM) suitable for low pressure was established. The model can be solved by combining the optical emission spectroscopy (OES) with Langmuir probe calibration. In the capacitively coupled plasmas (CCPs) with different frequency and power, the electron temperature and density obtained by the model were compared with those measured by Langmuir probe. It is found that the calibration point at any frequency or power is suitable for the fixed pressure. This method was then applied to the diagnosis of triple-frequency (TF) CCPs, it is shown that the high …
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…
A self-consistent particle-in-cell simulation study is performed to investigate the effect of driving frequency on the electric field non-linearity, electron heating mechanism and electron energy distribution function (EEDF) in a low pressure symmetric capacitively coupled plasma (CCP) discharge at a constant electron plasma frequency. The driving frequency is varied from 27.12 MHz to 100 MHz for a discharge gap of 3.2 cm in argon at a gas pressure of 1 Pa. The simulation results provide insight of higher harmonic generations in a CCP system for a constant electron response time. The spatio-te…
In this manuscript, a fluid model is utilized to calculate the density of plasma species assuming geometrically symmetric Ar/CF4 Radiofrequency Capacitively Coupled Plasmas. The electrodes are driven by a sinusoidal waefront with an amplitude of 200 V and a frequency of 13.56 MHz. The gap between the electrodes is 5cm. The plasma species density is calculated as a function of the gas pressure, electron temperature, and the gas composition. In a good agreement with recent experimental results, $CF^+_3$ and F are dominant for all considered simulation parameters. The results explain the pathways…
We use the one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 to explore the influence of the surface quenching of the singlet delta metastable molecule O$_2$(a$^1Δ_{\rm g}$) on the electron heating mechanism, and the electron energy probability function (EEPF), in a single frequency capacitively coupled oxygen discharge. When operating at low pressure (10 mTorr) varying the surface quenching coefficient in the range 0.00001 -- 0.1 has no influence on the electron heating mechanism and electron heating is dominated by drift-ambipolar (DA) heating in the plasma bu…
Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently develope…
The dynamical characteristics of a single frequency low pressure capacitively coupled plasma (CCP) device under varying applied RF voltages and driving frequencies are studied using particle-in-cell/Monte Carlo collision simulations. An operational regime is identified where for a given voltage the plasma density is found to remain constant over a range of driving frequencies and to then increase rapidly as a function of the driving frequency. The threshold frequency for this mode transition as well as the value of the constant density is found to increase with an increase in the applied volta…
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）
In this article, the stability of a complex plasma monolayer levitating in the sheath of the poweredelectrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Com-pared to earlier studies, a better integration of the experimental results and theory is achieved byoperating with actual experimental control parameters such as the gas pressure and the dischargepower. It is shown that for a given microparticle monolayer at a fixed discharge power there existtwo threshold pressures: (i) above a specific pressure p cryst , the monolayer always crystallises; (ii)below …
Following requirements of the plasma processing industry for increasing throughput, capacitively coupled plasma reactors with large area electrodes driving by very high frequency sources have been proposed. However, such reactors with plasmas inside support modes which can negatively influence the uniformity in the ion fluxes or the average energy of the ions impinging on the substrates, which is an essential requirement of the industry. It is shown when the popular electrostatic approximation used for description of the fields in capacitively coupled plasmas (CCP) breaks down and when these m…
One-dimensional particle-in-cell simulation is used to simulate the capacitively coupled argon plasma for a range of driving frequency from 13.56 MHz to 100 MHz. The argon chemistry set can, selectively, include two metastable levels enabling multi-step ionization and metastable pooling. The results show that the plasma density decreases when metastable atoms are included with higher discrepancy at higher excitation frequency. The contribution of multistep ionization to overall density increases with excitation frequency. The electron temperature increases with the inclusion of metastable atom…
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…
- We made use of a combination of three models that describe plasma equilibrium, cluster kinetics and aerosol dynamics in order to investigate solid carbonaceous dust formation in a DC gas discharge where the carbon source is provided by a graphite cathode sputtering. This enabled us to determine the time-evolution of some of the particle characteristics, e., g. total density, mean-diameter, average-charge as function of the sputtering yield. We showed that for few minutes discharge duration, the particle density reaches 10 7-10 8 cm-3 , the particle mean diameter is approximately 40 nm and th…
We conducted experimental studies and computer simulations of standing striations in capacitive coupled plasma in Argon gas. Standing striations were observed at frequencies 3.6, 8.4 and 19.0 MHz, in a pressure range 0.05-10 Torr, tube radius R=1.1 cm, for a certain range of discharge currents (plasma densities). Numerical simulations revealed similar nature of standing striations in CCP and moving striations in DC discharges under similar discharge conditions. Comparison of computer simulations with experimental observations helped clarify the nature of these striations. The non-linear depend…
Revisiting Electron Heating in Capacitively Coupled Plasma (CCP) Discharges: A Nonlinear Dynamics Perspective
Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；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）
This paper reports experiments on self$-$excited dust acoustic waves (DAWs) and its propagation characteristics in a magnetized rf discharge plasma. The DAWs are spontaneously excited in dusty plasma after adding more particles in the confining potential well and found to propagate in the direction of streaming ions. The spontaneous excitation of such low-frequency modes is possible due to the instabilities associated with streaming ions through the dust grain medium. The background E-field and neutral pressure determine the stability of excited DAWs. The characteristics of DAWs strongly depen…
We use the one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 to explore the properties and the origins of both the electric field and electron power absorption within the plasma bulk for a capacitively coupled oxygen discharge operated at 10 and 100 mTorr for 45 mm of gap distance. The properties of the electric field at three different time slices as well as time averaged have been explored considering the moments of the Boltzmann equation. The electron power absorption is distinctly different at these operating pressures. The most relevant contributions to the…
The mixing of N2 with H2 leads to very different plasmas from pure N2 and H2 plasma discharges. Numerous issues are therefore raised involving the processes leading to ammonia (NH3) formation. The aim of this work is to better characterize capacitively-coupled radiofrequency plasma discharges in N2 with few percents of H2 (up to 5 pct), at low pressure (0.3 to 1 mbar) and low coupled power (3 to 13 W). Both experimental measurements and numerical simulations are performed. For clarity, we separated the results in two complementary parts. The actual one (first part), presents the details on the…
Cleaning of contamination of optical surfaces by amorphous carbon (a-C) is highly relevant for extreme ultraviolet (EUV) lithography. We have studied the mechanisms for a-C removal from a Si surface. By comparing a-C removal in a surface wave discharge (SWD) plasma and an EUV-induced plasma, the cleaning mechanisms for hydrogen and helium gas environments were determined. The C-atom removal per incident ion was estimated for different sample bias voltages and ion fluxes. It was found that H2 plasmas generally had higher cleaning rates than He plasmas: up to seven times higher for more negative…
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…
Physics-separating artificial neural networks for predicting sputtering and thin film deposition of AlN in Ar/N$_2$ discharges on experimental timescales
Ruhr University Bochum（波鸿鲁尔大学）；Kiel University（基尔大学）
