Bulletin of the American Physical Society
74th Annual Gaseous Electronics Conference
Volume 66, Number 7
Monday–Friday, October 4–8, 2021;
Virtual: GEC Platform
Time Zone: Central Daylight Time, USA
Session CT14: Modeling Verification and Validation |
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Chair: Tugba Piskin, University of Michigan Room: Virtual GEC platform |
Tuesday, October 5, 2021 8:00AM - 8:15AM |
CT14.00001: Validation of Hybrid Electron Particle-In-Cell (PIC)-Ion Fluid Plasma Simulation Methodology for Low Pressure Capacitively Coupled Plasma (CCP) Chambers Sathya S Ganta, Shahid Rauf, Peng Tian, Kallol Bera, Manuel Schröder, Ihor Korolov, Julian Schulze Low-pressure (< 30 mTorr) capacitively coupled plasma (CCP) plasma sources provide the energetic sheaths that are vital in high-energy dielectric etching and high-quality film deposition applications. The kinetic behavior of electrons at low pressure cannot be adequately captured in the widely used fluid plasma models. The particle in cell (PIC) simulation methodology that accurately captures plasma behavior in this pressure range incurs prohibitively high computational cost especially when the chamber dimensions are large. In this paper, we present a hybrid PIC fluid simulation methodology where electrons are assumed to be particles while ions are treated as fluid where computational cost is reduced substantially due to reduced number of particles. The hybrid simulation methodology is compared against full PIC methodology for verification and the results are validated using experimental data. Ar, O2, and their mixtures are simulated in a low-pressure axisymmetric single and dual-frequency RF powered CCP chamber. In this chamber, ion currents and ion energy distribution functions are measured at the grounded electrode using relatively calibrated field energy analyzer sensors for different process conditions along with the corresponding bulk plasma density at different radial positions using a Langmuir probe. We validate our hybrid PIC-fluid simulations using these measurements and discuss the computational advantages and disadvantages of the proposed methodology over full PIC modeling. |
Tuesday, October 5, 2021 8:15AM - 8:30AM |
CT14.00002: Validation and Verification Methods for the Open Source Code: Zapdos Corey S DeChant, Casey T Icenhour, Grayson Gall, Shane Keniley, Alexander D Lindsay, Davide Curreli, Steven Shannon Zapdos is an open source, multi-fluid plasma code based in MOOSE (Multiphysics Object Oriented Simulation Environment). Validation and verification studies were done within three broad studies. First, temporal and spatial convergence studies were conducted by using the method of manufactured solutions (MMS), where different coupling configurations were tested. Second, Zapdos results were compared to previous simulations for a push-pull RF discharge of argon in the GEC reference cell for 1 Torr in 1D, and 1 Torr and 100 mTorr in 2D. Finally, a parametric study was done for argon at varying pressure and voltage for RF discharges at 13.56 MHz in a GEC reference cell and compared to previous experimental results for electron and metastable densities that used microwave interferometry and laser-induced fluorescence, respectively. The MMS study results resembled the expected theoretically convergence trends with electron mean energy being particular sensitive. The comparisons to previous simulations matched within reason. Current experiment validation results follow previous experimental trend, with some deviation for pressure near 100 mTorr. A possible reason for those deviations could be due to the current assumptions within Zapdos based on the fluid approximation of plasmas. |
Tuesday, October 5, 2021 8:30AM - 8:45AM |
CT14.00003: Particle-in-cell modeling and experimental diagnosis of dual-frequency capacitively-coupled oxygen discharge Han Luo, Peng Tian, Jason Kenney, Shahid Rauf, Julian Schulze, Ihor Korolov Low-pressure capacitively coupled plasmas (CCP) have been used extensively in the semiconductor industry for various processing applications. The ability of CCP in generating highly energetic ions with moderate dissociation and ionization makes it a key technology for the etching of dielectric materials. As the feature sizes become smaller and the cost of experiments increases, it becomes crucial to characterize processing characteristics using numerical modeling. This work focuses on ion energy distribution functions (IEDF) in a dual-frequency O2 CCP. The influence of processing conditions on IEDF is examined using both particle-in-cell (PIC) modeling and IEDF measurement using a retarding field ion energy analyzer. PIC modeling is also used to understand the critical underlying physical processes that influence the IEDF. The 1D PIC simulations and the corresponding experimental measurements were done at different pressures, RF voltages, and the frequency of the low-frequency source. The elastic and charge exchange ion-neutral reactions are found vital to capture the low energy ion population in the IEDF at higher pressures. Improvements in the model that allowed better agreement with experiments are discussed. |
Tuesday, October 5, 2021 8:45AM - 9:00AM |
CT14.00004: Analytical model for estimating plasma parameters in a planar diode Haomin Sun, Jian Chen, Alexander V Khrabrov, Igor Kaganovich, David Smith, Svetlana Selezneva, Dmytro Sydorenko We report the analytical model for estimating the electron temperature and number density in the plasma of a planar diode by considering the energy and particle balance equations. In a planar diode, two groups of electrons are present: an electron beam emitted from the cathode and cold electrons trapped in the plasma bulk. An electron beam emitted from a cathode excites plasma waves which can heat cold electrons in the bulk via particle-wave interactions. The resulting equation for the cold electron temperature contains six terms, including the energy exchange in the elastic, and inelastic (excitation and ionization) collisions between the cold electrons and neutrals, the energy exchange in the Coulomb collisions between cold and beam electrons, wave heating, and the wall losses of energetic electrons to the anode. We compare the results of the analytical theory with that of the particle-in-cell simulations using EDIPIC code and find a good agreement. The analytical model also shows that the heating term due to the Coulomb collisions with beam electrons and the energy loss to the anode are dominant, and they mostly balance each other, whereas the energy exchange due to the collisions with neutrals and wave heating are small and can be omitted. By coupling the energy balance equation with the particle balance equation, we can solve for both the number density and electron temperature as functions of the current density, electrode distance, pressure, and applied voltage. This model has been validated against past experiments and a good agreement was found. |
Tuesday, October 5, 2021 9:00AM - 9:15AM |
CT14.00005: Effect of dynamic particle reweighting on plasma swarm parameters in the particle-in-cell code Aleph Taylor H Hall, Jeremiah Boerner, Zakari Eckert, Russell Hooper, Jose Pacheco Aleph is a particle-in-cell (PIC) code developed at Sandia National Laboratories for the simulation of a large range of plasma systems. Aleph uses unstructured mesh geometries and contains a rich collection of capabilities for performing electric field solves, plasma chemistry using direct-simulation Monte Carlo (DSMC), plasma-surface interactions, and plasma-photon processes. This large suite of capabilities makes Aleph a robust tool for studying a variety of non-equilibrium plasmas, such as corona discharges, DC glow discharges, vacuum arc breakdown, and dielectric barrier discharges. Beyond these functionalities, Aleph also incorporates a novel dynamic reweighting algorithm capable of modifying computational particle weights on a per-element basis with options that enable the user to optimize performance and accuracy. To ensure that reweighting preserves accurate collisional properties, a set of zero-dimensional simulations were performed to examine a range of swarm parameters for a hydrogen plasma. Aleph simulation results, both with and without electron impact ionization, compare favorably with the two-term Boltzmann solver Bolsig+. Finally, Aleph’s reweighting algorithm is shown to maintain a high degree of accuracy over a large range of particle reweighting strategies. |
Tuesday, October 5, 2021 9:15AM - 9:30AM |
CT14.00006: Particle-In-Cell Modeling of Capacitively Coupled Argon Discharges in a Wide Range of Frequencies Saurabh H Simha, Sergey Macheret, Jonathan Poggie, Igor Kaganovich, Alexander V Khrabrov Radio-frequency capacitively coupled discharges in argon were simulated in a wide range of frequencies using a one-dimensional Particle-In-Cell/ Monte Carlo Collision technique. The principal goal was to study the changes in electron heating modes with increase in RF frequency. The simulation results were compared with experimental data for a fixed voltage of 80 V (peak-to-peak) and frequencies ranging from 13.56 MHz to 57 MHz. At 50 mTorr, a bi-Maxwellian energy distribution function was observed at the center of the domain. The frequency dependence of centerline electron number density and the effective electron temperature obtained by integrating the distribution function were compared to experimental results and a matching trend was observed. |
Tuesday, October 5, 2021 9:30AM - 9:45AM |
CT14.00007: 2D simulation of the positive streamer in SF6: effect of high attachment rate in atmospheric and sub atmospheric pressures. Francis Boakye-Mensah, Nelly Bonifaci, Rachelle Hanna, Innocent Niyonzima, Igor Timoshkin In high voltage applications, pressurized SF6, a highly electronegative gas is used. Understanding physical mechanisms leading to breakdown of this insulating medium are of utmost importance for designing fast switching electrical equipment. Breakdown in SF6 at atmospheric pressure occurs via a streamer-leader transition. This is difficult to achieve numerically with current simulation models limited to streamer studies which are suitable for low pressures. This work presents an attempt to understand streamer discharges in the gas using a plasma fluid model implementation in COMSOL® Multiphysics at 0.1 and 1 bar. The effect of the high electronegativity of SF6 is evaluated by comparing streamers in SF6 to that in Air on the axes of electric field distribution, electron and ion densities profiles, streamer velocity and diameter for a cathode directed streamer in 2D axisymmetric point to plane configuration. Depending on pressure, a reduction or loss of the conduction path between the streamer head and the tip of the needle electrode is obtained in SF6 as opposed to a near consistent electron density profile in the streamer channel for air. This showcases the high influence of attachment in SF6 at lower reduced electric fields in comparison to air. |
Tuesday, October 5, 2021 9:45AM - 10:00AM |
CT14.00008: Experimental Validation of Particle-in-Cell/Monte Carlo Collision simulation coupled with Collisional Radiative Model by Optical Emission Spectroscopy Fatima Jenina T Arellano, Zoltan Donko, Peter Hartmann, Tsanko Vaskov Tsankov, Uwe Czarnetzki, Satoshi Hamaguchi Capacitively-coupled radio-frequency (RF) Ar plasma experiments with optical emission spectroscopy (OES) measurements were used to validate a 1D Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulation code with a Collisional Radiative Model (CRM). The CRM based on the first 14 levels of argon provided the line intensities using the electron energy distribution function (EEDF) obtained from the PIC/MCC simulation. The experiments were performed in a plasma source with symmetric parallel-plate stainless steel electrodes having a gap distance of 4 cm and a radius of 7.1 cm enclosed inside a cylindrical quartz chamber wall. The peak-to-peak voltage applied to the powered electrode ranged between 200 and 500 V, and the gas pressure varied from 1.5 to 120 Pa. OES spectra were acquired from the central region of the plasma. The validity of the simulation model was tested by comparing the electrical current (EC) and spectral line intensities obtained from both experiments and simulations. The resulting OES and EC comparison showed good agreement between the measurements and calculations in general. Moreover, the line intensities were found to be highly sensitive to changes in the EEDF. The extent of the agreement between the experiment and simulation corroborated with the nonintrusive OES and EC measurements gives us a well-defined level of confidence in using the simulation as a virtual metrology tool to predict plasma parameters that are usually difficult or even impossible to be obtained experimentally. |
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