Particle-in-cell modeling of low pressure, high voltage capacitively coupled Ar plasmas.
Abstract not provided.
Lietz, Amanda↗
SEARCH · Engineering Papers
Results for “capacitively coupled plasma”
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Effects of macroparticle weighting in axisymmetric particle-in-cell Monte Carlo collision simulations
In this paper, the effects of macroparticle (MP) weighting on the plasma discharge, particularly near the centerline, are investigated using a two-dimensional axisymmetric particle-in-cell Monte Carlo collision (PIC/MCC) model. A variable MP weight according to the radial position of the MPs is employed to maintain sufficient number of MPs near the centerline of the plasma source. Finally, the plasma density obtained from the PIC/MCC simulations for low-pressure (25–100 mTorr) capacitively coupled plasmas is found to be artificially large when the MP weight near the centerline is not well resolved, demonstrating the need for particle convergence studies for axisymmetric PIC/MCC simulations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Validation Studies using ELK and the Open-Source MOOSE Framework Application Zapdos for Electromagnetic Coupled Plasma Simulation
An open source simulation platform that captures electromagnetics, plasma chemistry, and fluid treatment of the plasma domain would be a powerful tool for studying low temperature plasma (LTP) phenomena. Within the Multiphysics Object-Oriented Simulation Environment (MOOSE) open source framework, ELK, CRANE, and Zapdos are combined to provide open source simulation capability for the LTP community. This talk presents continued validation of the general electromagnetic (EM) simulation tool ELK (Electromagnetic Library for Kinetics & fluids). Previous validation efforts focused on simulating standard waveguide and antenna benchmarks in vacuum and linear dielectrics, but ELK has since been coupled with the MOOSE-based plasma fluid application Zapdos [Lindsay et al 2016 J. Phys. D: Appl. Phys. 49 235204] to perform radio-frequency (rf) capacitively coupled plasma (CCP) system simulation. Plasma validation efforts initially focused on electrostatic benchmarks to demonstrate ELK-Zapdos code coupling and then moved to electromagnetic benchmarks based on interesting geometries and conditions (VHF effects in a CCP reactor, microwave heating, etc.). Results and progress in these efforts will be summarized and discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges
It is recognized that standing wave effects appearing in large-area, very-high-frequency capacitively coupled plasma (CCP) reactors cause center-high plasma non-uniformity. Using a high-frequency magnetic probe, we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56, 30, and 60 MHz. The design, principle, calibration, and validation of the probe are described in detail. Spatial structures of the harmonics of the magnetic field, determined by the magnetic probe, were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition, providing insights into the behavior of nonlinear harmonics. At a low driving frequency, i.e. 13.56 MHz, no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible. Here, the harmonic magnetic field/current was found to increase dramatically with the driving frequency, due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency, leading to the enhancements of the ohmic heating and the plasma density in the bulk, specifically at the electrode center. At a high driving frequency, i.e. 60 MHz, the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure, with the main peak on axis, and one or more minor peaks between the electrode center and the edge, contributing to the center-high profile of the plasma density.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Importance of gas heating in capacitively coupled radiofrequency plasma-assisted synthesis of carbon nanomaterials
In pursuit of diamond nanoparticles, a capacitively-coupled radio frequency flow-through plasma reactor was operated with methane-argon gas mixtures. Signatures of the final product obtained microscopically and spectroscopically indicated that the product was an amorphous form of graphite. This result was consistent irrespective of combinations of the macroscopic reactor settings. To explain the observed synthesis output, measurements of C 2 and gas properties were carried out by laser-induced fluorescence and optical emission spectroscopy. Strikingly, the results indicated a strong gas temperature gradient of 100 K per mm from the center of the reactor to the wall. Based on additional plasma imaging, a model of hot constricted region (filamentation region) was then formulated. It illustrated that, while the hot constricted region was present, the bulk of the gas was not hot enough to facilitate diamond sp 3 formation: characterized by much lower reaction rates, when compared to sp 2 , sp 3 formation kinetics are expected to become exponentially slow. This result was further confirmed by experiments under identical conditions but with a H 2 /CH 4 mixture, where no output material was detected: if graphitic sp 2 formation was expected as the main output material from the methane feedstock, atomic hydrogen would then be expected to etch it away in situ, such that the net production of that sp 2 -hybridized solid material is nearly a zero. Finally, the crucial importance of gas heating was corroborated by replacing RF with microwave source whereby facile sp 3 production was attained with H 2 /CH 4 gas mixture.
36 MATERIALS SCIENCE↗
Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges
Abstract It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage V L on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage V L at 2 MHz varies from 0 to 700 V while the HF voltage V H at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. V L = 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as V L increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher V L , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔEbecomes wider with the increase of V L . The IEDF at the radial center of the powered electrode exhibits a broader ΔEthan that at the edge. For the IADF, an increased V L results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.
Physics↗
Voltage waveform tailoring for high aspect ratio plasma etching of SiO 2 using Ar/CF 4 /O 2 mixtures: Consequences of ion and electron distributions on etch profiles
The quality of high aspect ratio (HAR) features etched into dielectrics for microelectronics fabrication using halogen containing low temperature plasmas strongly depends on the energy and angular distribution of the incident ions (IEAD) onto the wafer, as well as potentially that of the electrons (EEAD). Positive ions, accelerated to high energies by the sheath electric field, have narrow angular spreads and can penetrate deeply into HAR features. Electrons typically arrive at the wafer with nearly thermal energy and isotropic angular distributions and so do not directly penetrate deeply into features. These differences can lead to positive charging of the insides of the features that can slow etching rates and produce geometric defects such as twisting. In this work, we computationally investigated the plasma etching of HAR features into SiO 2 using tailored voltage waveforms in a geometrically asymmetric capacitively coupled plasma sustained in an Ar/CF 4 /O 2 mixture at 40 mTorr. The tailored waveform consisted of a sinusoidal wave and its higher harmonics with a fundamental frequency of 1 MHz. We found that some degree of control of the IEADs and EEADs is possible by adjusting the phase of higher harmonics φ through the resulting generation of electrical asymmetry and electric field reversal. However, the IEADs and EEADs cannot easily be separately controlled. The control of IEADs and EEADs is inherently linked. The highest quality feature was obtained with a phase angle φ = 0° as this value generated the largest (most negative) DC self-bias and largest electric field reversal for accelerating electrons into the feature. That said, the consequences of voltage waveform tailoring (VWT) on etched features are dominated by the change in the IEADs. Although VWT does produce EEADs with higher energy and narrower angular spread, the effect of these electrons on the feature compared to thermal electrons is not large. Finally, this smaller impact of VWT produced EEADs is attributed to thermal electrons being accelerated into the feature by electric fields produced by the positive in-feature charging.
47 OTHER INSTRUMENTATION↗
Electron density measurements and calculations in a helium capacitively-coupled radio-frequency plasma
We report a comparison of inferred electron density (n e ) in a He capacitively-coupled plasma, deduced from laser-collision induced fluorescence measurements, with values computed using a hybrid simulation framework based on particle-in-cell/Monte Carlo collisions simulations and a fluid model for excited He atoms. The studies were carried out for gas pressures between 50 mTorr and 1000 mTorr and peak-to-peak radio-frequency (13.56 MHz) voltages between 150 V and 350 V, in a highly symmetric source equipped with plane-parallel electrodes. A good agreement is found between the experimental and modeling results for n e except at the lowest operating voltages and gas pressures. The (effective) electron temperature (T e ) values derived by the two methods agree as well reasonably within the plasma bulk. The simulation results are used to compare the density distributions of He + and various He excited levels and their major populating and de-populating channels at 100 mTorr and 1000 mTorr.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Scaling of silicon nanoparticle growth in low temperature flowing plasmas
Low temperature plasmas are an emerging method to synthesize high quality nanoparticles (NPs). An established and successful technique to produce NPs is using a capacitively coupled plasma (CCP) in cylindrical geometry. Although a robust synthesis technique, optimizing or specifying NP properties using CCPs, is challenging. In this paper, results from a computational investigation for the growth of silicon NPs in flowing inductively coupled plasmas (ICPs) using Ar/SiH 4 gas mixtures of up to a few Torr are discussed. ICPs produce more locally constrained and quiescent plasma potentials. These positive plasma potentials produce an electrostatic trap for negatively charged NPs, which can significantly extend the residence time of NPs in the plasma, which in turn provides a controllable period for particle growth. The computational platforms used in this study consist of a two-dimensional plasma hydrodynamics model, a three-dimensional nanoparticle growth and trajectory tracking model, and a molecular dynamics simulation for deriving reactive sticking coefficients of silane radicals on Si NPs. Trends for the nanoparticle growth as a function of SiH 4 inlet fraction, gas residence time, energy deposition per particle, pressure, and reactor diameter are discussed. The general path for particle synthesis is the trapping of small NPs in the positive electrostatic potential, followed by entrainment in the gas flow upon reaching a critical particle size. Optimizing or controlling NP synthesis then depends on the spatial distribution of plasma potential, the density of growth species, and the relative time that particles spend in the electrostatic trap and flowing through higher densities of growth species upon leaving the trap.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Verification and validation of the open-source plasma fluid code: Zapdos
Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10 -2 to 10 -4 , while the convergence’s slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry and metastable density measurements by planar laser-induced fluorescence imaging. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Furthermore, probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at https://github.com/shannon-lab/zapdos.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Toward the origins of binding energy shifts and “satellites” formation during plasma-XPS measurements
In-plasma x-ray photoelectron spectroscopy (plasma-XPS) emerges as a powerful platform for real-time, in situ chemical analysis under conditions relevant to semiconductor processing and other plasma-enabled technologies. This study investigates the origins of binding energy (BE) shifts and the formation of “satellite” peaks observed during plasma-XPS measurements across conductive, dielectric, and gas-phase systems. Using a standard laboratory-based ambient pressure XPS apparatus coupled with an alternating current (AC)-driven capacitively coupled plasma source, we demonstrate that metastable surface species, such as transient Au oxides, can be detected during plasma exposure, revealing chemical states that are hardly accessible using conventional ultrahigh vacuum (UHV) XPS. In dielectric samples (e.g., undoped diamond, sapphire), we observe pressure- and plasma-type-dependent BE shifts of more than 50 eV, attributed to x-ray-induced and plasma-mediated surface charging. These shifts are mitigated at higher pressures/plasmas or in electronegative plasmas (e.g., O 2 ), the latter due to enhanced charge compensation mechanisms involving slow negative ions. For gas-phase species, AC-plasma excitation leads to spectral broadening and the emergence of “satellite” peaks with energy separations of a few electron volts, linked to oscillating local plasma potentials in the probing volume. Furthermore, these findings highlight the complex and important interplay between plasma parameters, surface charging, and local electric fields in shaping XPS spectra. Overall, plasma-XPS emerges as a critical metrological tool for probing transient surface chemistry, with implications for semiconductor processing, material synthesis, and plasma diagnostics.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Accelerating kinetic plasma simulations with machine-learning-generated initial conditions
Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.
Artificial neural networks↗
Scaling of atomic layer etching of SiO 2 in fluorocarbon plasmas: Transient etching and surface roughness
Fabricating sub-10 nm microelectronics places plasma processing precision at atomic dimensions. Atomic layer etching (ALE) is a cyclic plasma process used in semiconductor fabrication that has the potential to remove a single layer of atoms during each cycle. In self-limiting ideal ALE, a single monolayer of a material is consistently removed in each cycle, typically expressed as EPC (etch per cycle). In plasma ALE of dielectrics, such as SiO 2 and Si 3 N 4 , using fluorocarbon gas mixtures, etching proceeds through deposition of a thin polymer layer and the process is not strictly self-terminating. As a result, EPC is highly process dependent and particularly sensitive to the thickness of the polymer layer. In this paper, results are discussed from a computational investigation of the ALE of SiO 2 on flat surfaces and in short trenches using capacitively coupled plasmas consisting of a deposition step (fluorocarbon plasma) and an etch step (argon plasma). We found that ALE performance is a delicate balance between deposition of polymer during the first half cycle and etching (with polymer removal) during the second half cycle. In the absence of complete removal of the overlying polymer in each cycle, ALE may be transient as the polymer thickness grows with each cycle with a reduction in EPC until the thickness is too large to enable further etching. Small and statistical amounts of polymer left from a previous cycle can produce statistical variation in polymer thickness on the next cycle, which in turn can lead to a spatially dependent EPC and ALE roughness. Based on synergy between T i (sputtering time) and T p (passivation time), dielectric ALE can be described as having three modes: deposition, roughening surface (transitioning to etch-stop), and smooth surface with steady-state EPC.
Materials Science↗
Positive charging of grains in an afterglow plasma is enhanced by ions drifting in an electric field
In a plasma, the polarity of a dust grain's charge is typically negative, but it can reverse and become positive in an afterglow, when the power sustaining the plasma is switched off. This positive charging, which occurs in the afterglow's first few milliseconds, is studied for grains much larger than a few nm. It is hypothesized that the positive charging is enhanced by the presence of a dc electric field, which causes ions to drift through the neutral gas. A larger value of the reduced electric field E/N leads to a larger ion kinetic energy and thus a greater collection of positive charge on a grain. The maximum possible positive charge is attained if the grain's surface potential rises to match the ion kinetic energy, at a time before ions have departed and the grain's charge becomes frozen. Thereafter, when vacuum conditions prevail, the grain will retain its positive residual charge. In an experiment, dust grains were electrically levitated in a capacitively coupled plasma until the power was abruptly turned off. In the afterglow, grains fell faster than expected due to gravity alone, indicating a downward electric force, in the presence of a remaining dc electric field. Acceleration measurements yielded repeatable results for the residual charge's value, which was of the order +10 4 e and increased with E/N, supporting the hypothesis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Independent Electron and Ion Energy Distribution Control for Semiconductor Processing Phase I Final Technical Report
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Mapping electron density with laser collision induced fluorescence in a helium capacitively coupled radio frequency plasma
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Bentz, Brian Zahler↗
Electron density measurements and calculations in a helium capacitively-coupled radio-frequency plasma
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Donko, Zoltan↗
Data set of fully kinetic simulations of capacitively-coupled radio-frequency plasma discharges in argon
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Fierro, Andrew Steven [Sandia National Laboratorie↗