Gaseous Electronics Conference Research Articles

Electrical characteristics of the GEC reference cell at low pressure: a two-dimensional PIC/MCC modeling study

The electrical characteristics of the Gaseous Electronics Conference reference cell at low pressures are investigated using a two-dimensional electrostatic implicit particle-in-cell/Monte Carlo collision model in cylindrical coordinates. The coupling between the complex reactor geometry and the external circuit is included via an equivalent capacitance calculated from the electric energy density and the charge conservation equation. The results of this model are compared with experimental measurements and other model calculations and show agreement. The plasma series resonance effect, closely related to electron heating, is observed in this numerical simulation of a strongly asymmetric reactor at low pressures. The plasma kinetics of the capacitively coupled discharge and details of the external circuit response, including electrical waveforms and higher-order harmonics, are discussed at different pressures, which provides important insights for understanding the power coupling mechanisms in capacitively coupled discharges.

Effects of collision-enhanced charging on dust crystal

Numerical simulations of monolayer dust crystals in a radio frequency (RF) complex plasma were performed to examine the crystal structure and quantify the effects of including the collision-enhanced ion current in the charging model. A gaseous electronics conference (GEC) cell similar to a previous experimental work was modeled for a range of RF voltages, using a continuum description for the plasma and a particle description for dust grains. The time history of each dust grain was monitored. The dust charge was computed using both the orbital motion limited and the collision-enhanced charging (CEC) model applicable to the sheath region. The dust model accounted for the electric force, ion drag force, neutral drag force, gravity, and the ion wake. The CEC model produced a lower charge and lower electric force which agreed better with the experimental data. Then dust crystals composed of 40–100 grains were modeled and the levitation height and inter-particle spacing of the resulting crystals was examined. Including the collision-enhanced current reduced the inter-particle spacing but only had a minor effect on the levitation height.

SOMAFOAM: An OpenFOAM based solver for continuum simulations of low-temperature plasmas

We report the development of SOMAFOAM, a finite volume framework for performing continuum simulations of low-temperature plasmas. The primary goal of this work is to discuss the features of SOMAFOAM along with representative results provided as examples for a range of operating conditions and geometries. This includes plasma and plasma–dielectric systems operating in direct current, radio frequency, and microwave regimes from pressures as low as 100 mTorr to atmospheric pressure. The code has several useful features including the ability to run massively parallel simulations using arbitrary geometries, structured/unstructured meshes, choice of models such as drift–diffusion/full-momentum at runtime, and species-dependent timesteps to name a few. The verification/validation studies presented include comparison with previously published continuum simulations (low-pressure direct current and radio frequency plasma), with experiments (Gaseous Electronics Conference Reference Cell and microwave microplasma ignited in a split ring resonator), and previously published kinetic simulations (low-pressure radio frequency plasma). Other examples provided include a direct current atmospheric pressure microplasma bounded by dielectric sidewalls and a helium–nitrogen plasma ignited using a needle electrode facing a dielectric. The performance of the code is also discussed with serial and distributed memory parallel runs demonstrated up to 512 cores. The design and implementation of the code in a modular object-oriented framework allows for easy extension and seamless coupling with other codes and can be expected to play an important role in both academia and industry.

Dust as probes: Determining confinement and interaction forces.

Complex plasmas are interesting systems as the charged dust can self-assemble into different types of ordered structures. To understand the mechanisms which govern the transitions from one type of structure to another, it is necessary to know both the dust charge and the confining electric fields within the environment, parameters which are difficult to measure independently. As dust is usually confined in a plasma sheath where the ions stream from the bulk plasma to the negative lower electrode, the problem is further complicated by the ion wake field, which develops downstream of the dust grains in a flowing plasma. The differences in local ion density caused by the wake field change the equilibrium dust charge and shielding distance of the dust grains, and thus affect the interaction between grains. Here we use a molecular dynamics simulation of ion flow past dust grains to investigate the interaction between the dust particles and ions. We consider a long vertical chain of particles confined within a glass box placed on the lower electrode of a Gaseous Electronics Conference rf reference cell. We apply the model iteratively to self-consistently determine the dust charge, electric field, and ion density along the length of the chain as well as the ion flow speed. Simulation results indicate that the ion flow speed within the box is subsonic.

On uniformity and non-local transport in low pressure capacitively coupled plasmas

Low pressure (<30 mTorr) capacitively coupled plasmas (CCP) are important for many plasma processing applications. Due to high energy of electrons in these plasmas and long electron mean free path, kinetic phenomena dominate the electron behavior. A multi-dimensional particle-in-cell (PIC) model is utilized to study the physics of sub-100 mTorr Ar CCPs in this article. A one-dimensional model for helium plasma in the 30–300 mTorr pressure range is first used to benchmark the PIC code against published results by Turner et al [2013 Phys. Plasmas 013507]. The article then focuses on two-dimensional modeling of the gaseous electronics conference (GEC) reference cell in cylindrical geometry. Computed ion density and DC bias voltage at 100 mTorr are compared to available experimental data for a range of radio frequency voltages, demonstrating good agreement. The validated model is used to examine Ar plasmas in the GEC reference cell in the 12.5–100 mTorr pressure range. It is found that the peak in ion and electron densities is near the electrode edge at 100 mTorr due to strong electric field there. As the gas pressure decreases, the peak in plasma density moves to the chamber center. This change in plasma spatial profile is linked to kinetic behavior of electrons, both regarding plasma production and transport in the plasma. Time-dependent results are used to illustrate that electron current at 25 mTorr is mainly kinetic and carried by beam electrons generated by expanding sheaths.

Development of a Massively Parallelized Fluid-Based Plasma Simulation Code With a Finite-Volume Method on an Unstructured Grid

A massively parallelized unstructured-grid plasma simulation code based on a multifluid plasma model has been developed and validated. The code uses a collocated cell-centered finite-volume method and is designed to simulate intermediate low-pressure and atmospheric-pressure (AP) plasma sources with complex machine geometries. One of the novel features of this code is that it is implemented in a highly flexible computational platform named ultrafast massively parallel processing (ultraMPP), which allows straightforward addition and integration of different partial differential equation (PDE) solvers in a self-consistent manner. As to the numerical methods, the Scharfetter–Gummel scheme is adopted to handle the drift-diffusion flux of electrons, whereas the Harten–Lax-van Leer (HLL)-type approximate Riemann solver is used to handle the convection terms of ion momentum equations. For discretization of the diffusion terms in an unstructured grid, the Taylor expansion is used to deal with the effects of nonorthogonality of the cells, and the cell-center gradient is calculated using a least-squares method. The simulation code with a local-field approximation (LFA) was validated for two cases of AP plasmas as well as a case of an argon capacitively coupled plasma generated in a Gaseous Electronic Conference (GEC) reference cell with local mean energy approximation (LMEA) at intermediate low pressure. The simulation results were found to be in good agreement with the previously published experimental and simulation data.

Plasma-Enhanced Chemical Vapor Deposition of Silicon Films at Low Pressure in GEC Reference Cell

A self-consistent fluid simulation of inductively coupled plasma-enhanced chemical vapour deposition (ICP-CVD) using silane, argon, and hydrogen mixture is presented. The model solves the continuity equations for charged species, the drift-diffusion equations to describe their transport and the electron energy balance equation, coupled with Maxwell’s and Poisson’s equations, using COMSOL Multiphysics software. In order to obtain a better comprehending of the discharge parameters, a discharge in a Gaseous Electronics Conference cell (GEC) reactor is simulated. In this study, the GEC reactor with five-turn inductive coils is driven at a radio frequency of 13.56 MHz in order to sustain the plasma discharge at low temperature for a mixture of SiH4/Ar/H2, with an intial gas pressure fixed at 20 mTorr. The simulations yield the profile of plasma components such as electron density and temperature as well as the electrical potential in the centre of the discharge during silicon films deposition. The effects of external settings, such as chamber pressure, applied power and hydrogen dilution, on the growth rate of the silicon films deposited by ICP-CVD are then investigated. It is shown that the increase of the applied power from 1000 to 3000 W and the gas pressure from 10 to 40 mTorr results in a moderate increase in the deposition rate of the silicon films, whereas the increase in the dilution of the hydrogen in the mixture produces its decrease.

Mapping the Plasma Potential in a Glass Box

Modeling the dynamics of charged dust particles, confined in a glass box placed on the lower electrode of a Gaseous Electronics Conference cell, requires that the interactions between the charged dust, plasma, and boundaries need to be accounted for in a self-consistent manner. The charged lower electrode affects the plasma conditions throughout the glass box, altering the electron and ion densities and temperatures within the plasma sheath. These plasma characteristics determine the charge collected on the walls of the surrounding glass box, the electric potential within the glass box, the dust charge, and ultimately the dynamics of the dust. This paper describes the steps taken to build a simple model of the relationship between the plasma conditions and the potential within the box as well as the expected dust charge near the center of the box. The calculated potential and dust charge are used to construct acceleration maps for the dust, which are compared to experimentally measured acceleration of the dust within the box.

Temperature measurement of a dust particle in a RF plasma GEC reference cell

The thermal motion of a dust particle levitated in a plasma chamber is similar to that described by Brownian motion in many ways. The primary difference between a dust particle in a plasma system and a free Brownian particle is that in addition to the random collisions between the dust particle and the neutral gas atoms, there are electric field fluctuations, dust charge fluctuations, and correlated motions from the unwanted continuous signals originating within the plasma system itself. This last contribution does not include random motion and is therefore separable from the random motion in a ‘normal’ temperature measurement. In this paper, we discuss how to separate random and coherent motions of a dust particle confined in a glass box in a Gaseous Electronic Conference (GEC) radio-frequency (RF) reference cell employing experimentally determined dust particle fluctuation data analysed using the mean square displacement technique.

A hybrid model for low pressure inductively coupled plasmas combining a fluid model for electrons with a plasma-potential-dependent energy distribution and a fluid-Monte Carlo model for ions

A hybrid plasma model is utilized for the simulation of inductively coupled plasmas (ICPs). It consists of a plasma fluid model coupling fluid with Maxwell’s equations and a Monte Carlo (MC) particle tracing model utilized for the calculation of the ion mobility in high electrostatic fields (sheaths). The model is applied to low pressure Argon plasma in the gaseous electronics conference (GEC) reference cell. Following measurements of electron energy distribution function (EEDF) in low pressure ICPs, a three-temperature EEDF is considered; it is formulated with a generalized equation and depends on the local plasma potential. The use of a predefined formula for the EEDF entails a low computational cost: All parameters affected by the EEDF are calculated as functions of the plasma potential and the mean electron energy once and before the solution of the model. The model results are validated by a comparison with spatially resolved (on axial and radial distance) measurements of electron density, electron temperature, and plasma potential. Both the calculation of the ion mobility by the MC model and the consideration of the three-temperature EEDF are critical for the accuracy of the model results. The very good agreement of the model results with the measurements and the low computational cost in combination with the flexibility of the code utilized for the numerical solution manifest the potential of the hybrid plasma model for the simulation of low pressure ICPs.

Analysis of magnetic field plasma interactions using microparticles as probes.

The interaction between a magnetic field and plasma close to a nonconductive surface is of interest for both science and technology. In space, crustal magnetic fields on celestial bodies without atmosphere can interact with the solar wind. In advanced technologies such as those used in fusion or spaceflight, magnetic fields can be used to either control a plasma or protect surfaces exposed to the high heat loads produced by plasma. In this paper, a method will be discussed for investigating magnetic field plasma interactions close to a nonconductive surface inside a Gaseous Electronics Conference reference cell employing dust particles as probes. To accomplish this, a magnet covered by a glass plate was exposed to a low power argon plasma. The magnetic field was strong enough to magnetize the electrons, while not directly impacting the dynamics of the ions or the dust particles used for diagnostics. In order to investigate the interaction of the plasma with the magnetic field and the nonconductive surface, micron-sized dust particles were introduced into the plasma and their trajectories were recorded with a high-speed camera. Based on the resulting particle trajectories, the accelerations of the dust particles were determined and acceleration maps over the field of view were generated which are representative of the forces acting on the particles. The results show that the magnetic field is responsible for the development of strong electric fields in the plasma, in both horizontal and vertical directions, leading to complex motion of the dust particles.

Dusty plasma cavities: Probe-induced and natural.

A comprehensive exploration of regional dust evacuation in complex plasma crystals is presented. Voids created in three-dimensional crystals on the International Space Station have provided a rich foundation for experiments, but cavities in dust crystals formed in ground-based experiments have not received as much attention. Inside a modified Gaseous Electronics Conference rf cell, a powered vertical probe was used to clear the central area of a dust crystal, producing a cavity with high cylindrical symmetry. Cavities generated by three mechanisms are examined. First, repulsion of micrometer-sized particles by a negatively charged probe is investigated. A model of this effect developed for a dc plasma is modified and applied to explain experimental data in rf plasma. Second, the formation of natural cavities is surveyed; a radial ion drag proposed to occur due to a curved sheath is considered in conjunction with thermophoresis and a flattened confinement potential above the center of the electrode. Finally, cavity formation upon increasing the probe potential above the plasma floating potential is justified by a combination of ion drag and sheath edge modification. The cavities produced by these methods appear similar, but each is shown to be facilitated by fundamentally different processes.

Two-Dimensional Numerical Study on Characterization of Low-Pressure Capacitively Coupled Argon Discharges

This paper presents an investigation of argon capacitively coupled plasma at low pressure. A two-dimensional, time-dependent fluid model is used to describe the production, transport, and destruction of electrons and positive ions. The model is solved for a GEC(gaseous electronics conference) Cell reactor type (with 4cm diameter and 2.5cm interelectrode distance) operating at frequency 13.56MHz, pressure 1Torr and applied voltage 1000V, in pure argon. Two-dimensional distributions are presented in the stationary state, including electron temperature and species density i.e. electron, ion and metastable atom. The electric field and electric potential at different phases in one RF cycle is also studied.

Comparisons of sets of electron–neutral scattering cross sections and swarm parameters in noble gases: II. Helium and neon

This paper is the second of a series of four reports, describing work carried in 2011 in the context of the Plasma Data Exchange Project with the Gaseous Electronics Conference, devoted to intercomparisons between different sets of electron–neutral scattering cross sections from ground-state noble gas atoms, in the energy range from thermal to about 1 keV. The present work compares cross section sets for helium and neon, determined independently, which are available on the open access LXCat website (www.lxcat.laplace.univ-tlse.fr/). The cross sections are used as input data in an electron Boltzmann solver or in Monte Carlo simulations, to calculate different swarm parameters (transport parameters and rate coefficients). The calculated quantities are compared with measurements to assess the quality of the cross sections in providing data for modelling low-temperature plasmas or analysing experiments. The paper includes several appendices prepared by co-authors to the work, presenting details on how the various cross section datasets were compiled or evaluated.

Comparisons of sets of electron–neutral scattering cross sections and swarm parameters in noble gases: I. Argon

This paper describes work done in the context of the Gaseous Electronics Conference (GEC) Plasma Data Exchange Project (PDEP) as discussed in the preface to this cluster issue. The purposes of this paper and its companion papers are to compare sets of cross sections for electron scattering from ground-state noble gas atoms in the energy range from thermal to about 1 keV and to comment on their applicability for plasma modelling. To these ends, we present in this paper intercomparisons of the nine independently derived sets of cross sections for electron scattering from ground-state argon atoms that have been posted in databases on the LXCat open-access website (www.lxcat.laplace.univ-tlse.fr). We show electron transport, excitation and ionization coefficients (swarm parameters) calculated using these cross section data in Boltzmann solvers and we compare calculated values with measurements. For the most part, the cross section sets have been compiled by co-authors on this paper and appendices giving details about how the various cross sections datasets were compiled have been written by the individual co-authors. Additional appendices discuss our criteria for selection of experimental data to be included in the comparisons and give a brief overview of the methods used here for solving the Boltzmann equation.

Comparisons of sets of electron–neutral scattering cross sections and swarm parameters in noble gases: III. Krypton and xenon

This paper, the third in a series of three, describes work carried in the context of Plasma Data Exchange Project of the Gaseous Electronics Conference (PDEP-GEC) to compare electron collision cross-sections sets from ground-state, noble gases atoms and to check their consistency with measured swarm parameters. Such consistency is a minimum requirement if the cross-section data are to be used for modelling low-temperature plasmas. In this paper, we present intercomparisons of the independently compiled sets of electron cross-sections from ground-state, neutral Kr and Xe atoms presently available on the LXCat open-access website (www.lxcat.laplace.univ-tlse.fr). Swarm parameters (reduced mobility, characteristic energy, reduced longitudinal diffusion coefficient, reduced ionization coefficient) calculated in a Boltzmann solver or Monte Carlo simulation using these cross-sections sets are compared with experimental data, also available online on the LXCat site.

Helical structures in vertically aligned dust particle chains in a complex plasma

Self-assembly of structures from vertically aligned, charged dust particle bundles within a glass box placed on the lower, powered electrode of a Gaseous Electronics Conference rf reference cell were produced and examined experimentally. Self-organized formation of one-dimensional vertical chains, two-dimensional zigzag structures, and three-dimensional helical structures of triangular, quadrangular, pentagonal, hexagonal, and heptagonal symmetries are shown to occur. System evolution is shown to progress from a one-dimensional chain structure, through a zigzag transition to a two-dimensional, spindlelike structure, and then to various three-dimensional, helical structures exhibiting multiple symmetries. Stable configurations are found to be dependent upon the system confinement, γ(2)=(ω(0h)/ω(0v))(2) (where ω(0h,v) are the horizontal and vertical dust resonance frequencies), the total number of particles within a bundle, and the rf power. For clusters having fixed numbers of particles, the rf power at which structural phase transitions occur is repeatable and exhibits no observable hysteresis. The critical conditions for these structural phase transitions as well as the basic symmetry exhibited by the one-, two-, and three-dimensional structures that subsequently develop are in good agreement with the theoretically predicted configurations of minimum energy determined employing molecular dynamics simulations for charged dust particles confined in a prolate, spheroidal potential as presented theoretically by Kamimura and Ishihara [Kamimura and Ishihara, Phys. Rev. E 85, 016406 (2012)].

Vertical Interaction Between Dust Particles Confined in a Glass Box in a Complex Plasma

In this experiment, falling particle trajectories within and without a glass box placed on the lower electrode in a Gaseous Electronics Conference reference cell are recorded and analyzed, and the electrostatic forces exerted on the dust particles are measured and compared. Experimental results show that, for particles falling in a complex plasma with no glass box, only a single force balance point (i.e., the position where the gravitational force is balanced by the electrostatic force) exists in the vertical direction while, for particles falling inside a glass box, this force balance spans an extended vertical range.

Study and Optimization of PECVD Films Containing Fluorine and Carbon Layered with Diamond Like Carbon Films as Ultra Low Dielectric Constant Interlayer Dielectrics

ABSTRACTLayered dielectric films comprising of Diamond like Carbon (DLC) and Amorphous Fluorocarbon (a:C-F) were generated using three different stack configurations for ultra low dielectric constant (ULK) applications. These include a DLC – a:C-F – DLC sandwich, a:C-F – DLC topcoat only and an annealed a:C-F – DLC topcoat only film stack. These films were subsequently evaluated for thickness, dielectric constant, contact angle, surface roughness and chemical structure using IR analysis. Thermal stability was analyzed after annealing in Argon ambient at 400°C for 1 hour. Deposition conditions were optimized for film thickness, roughness, dielectric constant and contact angle using Minitab by tuning process pressure, substrate temperature and FRR. The modified Gaseous Electronics Conference (mGEC) reference cell was used to deposit DLC films using CH4 and Argon as precursors. Structural properties of the deposited thin film were studied using laser excitation of 633 nm in a Jobin Yvon Labram high-resolution micro-Raman spectrometer. Multiple points on each sample were analyzed in terms of the disordered carbon (D-peak) and graphitic carbon (G-peak). The thin film of DLC was subsequently annealed in Ar ambient for 1 hr at 400°C and analyzed. Commercially available graphing software was utilized to deconvolute peaks and the ratio of their intensities as well as the shift in their positions were determined to characterize the as-deposited and annealed film. The film was further characterized using AFM, FTIR, XRD, goniometry and electrical testing. Average film roughness as measured by AFM was less than 1 nm, the k-value was 2.5 and the contact angle with water was 42°. A:C-F films were separately deposited using CF4 and Si2H6 (5% by volume in He) as precursors in a UNAXIS PECVD system. Films deposited using substrate temperatures between 120°C – 200°C, chamber pressure of 300 and 500 mTorr and power of 100 W were independently evaluated in terms of their electrical, physical, structural and optical properties prior to layering with DLC films. After process optimization, seven unique process conditions generated promising layered films with k-values between 1.69 and 1.95. Of these, only one film exhibited very low shrinkage rates acceptable for semiconductor device processing.

Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

A plasma–sheath transition analysis requires a reliable mathematical expression for the plasma potential profile Φ(x) near the sheath edge xs in the limit ɛ≡λD/ℓ=0 (where λD is the Debye length and ℓ is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation (ɛ=0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys. D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann’s formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since “the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity” [Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann’s general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and “water-bag” ion source velocity distributions. We find the potential profile near the plasma–sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to “practical infinity.” While within limits of “very low” and “relatively high” ion source temperatures, the potential is proportional to the space coordinate powered by rational numbers α=1/2 and α=2/3, with medium ion source temperatures. We found α between these values being a non-rational number strongly dependent on the ion source temperature. The range of the non-rational power-law turns out to be a very narrow one, at the expense of the extension of α=2/3 region towards unexpectedly low ion source temperatures.