Model description of a two-dimensional electrostatic particle-in-cell simulation parallelized with a graphics processing unit for plasma discharges

Hur, Min; Kim, Jin Seok; Song, In Cheol; Verboncoeur, John P.; Lee, Hae June

doi:10.1088/2516-1067/ab0918

Cited by 25 publications

(25 citation statements)

References 18 publications

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“…Studies on various kinetic effects in 2D CCP structures have recently been reported, even for high‐pressure regimes. [ 7, 9–18 ]…”

Section: Introductionmentioning

confidence: 99%

“…Studies on various kinetic effects in 2D CCP structures have recently been reported, even for high-pressure regimes. [7,[9][10][11][12][13][14][15][16][17][18] This study analyzed the transition between nonlocal and local kinetics in CCP equipment using a 2D GPU PIC simulation with various control parameters. The spatial profiles of density, flux, power absorption, and collisions have been observed for the variation of gas pressure, gap distance, and driving voltage.…”

Section: Introductionmentioning

confidence: 99%

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Two‐dimensional analysis for the transition from nonlocal to local electron kinetics and its effect on the spatial uniformity of a capacitively coupled plasma

Kim

Park

et al. 2022

Plasma Processes & Polymers

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In capacitively coupled plasmas (CCPs) operated under various pressure conditions in semiconductor manufacturing processes, the transition in discharge characteristics is observed depending on local or nonlocal electron kinetics. A two‐dimensional (2D) particle‐in‐cell (PIC) simulation is required because the one‐dimensional PIC method cannot capture the effect of device structures and because fluid models cannot treat the self‐consistent change in the energy distributions. Using a 2D PIC simulation parallelized with a graphics processing unit, we investigated the transition of electron kinetics for the variation of the driving voltage, gas pressure, the gap distance between upper and lower electrodes, and the sidewall condition. Moreover, the mechanism for electron energy relaxation in a CCP is elucidated to develop a method to improve the process uniformity.

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“…Studies on various kinetic effects in 2D CCP structures have recently been reported, even for high‐pressure regimes. [ 7, 9–18 ]…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two‐dimensional analysis for the transition from nonlocal to local electron kinetics and its effect on the spatial uniformity of a capacitively coupled plasma

Kim

Park

et al. 2022

Plasma Processes & Polymers

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“…Various parallel computing methods such as the message-passing interface (MPI), open multiprocessing (OpenMP), and GPUs have been implemented to reduce the computational load. In this study, we used paralleled 2-D PIC simulation with a GPU [19]. The information related to the particles is allocated to the memory in a way that is optimized for the GPU.…”

Section: Model Descriptionmentioning

confidence: 99%

Kinetic Analysis of Electrode Heating Effects in a Torr-Regime Capacitively Coupled Plasma Reactor: 2-D Particle-in-Cell Simulation Study

Park

Kim

et al. 2022

IEEE Trans. Plasma Sci.

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In the semiconductor industry, the electrode of a capacitively coupled plasma deposition reactor is often heated with the aim of process optimization. Based on chemical kinetics, a heated electrode can modulate the film properties or can enhance the growth rates of deposited thin films. Because the source gas undergoes rapid expansion in the hotter region near the electrode, the heated electrode is responsible for lowering the source density near the corresponding sheath. Thus, spatial variations in the kinetic parameters of the plasma such as the electron energy probability functions (EEPFs), ion energy distribution functions (IEDFs), and surface fluxes of ions can be controlled by changing the electrode temperature. Our simulation results indicated that a higher electrode temperature causes the direct ionization rate to increase, while the step-ionization rate decreases. In addition, the use of a heated electrode was observed to decrease the difference between the EEPF of the reactor center and that of the reactor edge. The improved consistency of the EEPF distribution implies that the homogeneity of the film quality between the center and edge of the wafer can be enhanced by improving the uniformity of the composition ratio of species.

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“…A significant benefit is that this model can track the detailed kinetic motion of charged species and their consequential physical features; however, the kinetic model is computationally expensive. Recently, with the rapid development of computational power using graphic processing units (GPUs), the advantages of kinetic models have been augmented by GPU-based particle-in-cell Monte Carlo collision simulations to provide valuable insights into the fundamental nature of charged species behaviors in complex plasma systems [19][20][21][22][23]. The fluid model represents the behavior of plasma species as fluid equations derived from the Boltzmann equation, which is coupled with Maxwell's equation, describing plasma in terms of averaged macroscopic quantities using the balance of continuity, momentum, and energy for each species in the plasma.…”

Section: Introductionmentioning

confidence: 99%

Computational approach for plasma process optimization combined with deep learning model

Bae

Park³

et al. 2023

J. Phys. D: Appl. Phys.

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As semiconductor device structures become more complex and sophisticated, the formation of finer and deeper patterns is required. To achieve a higher yield for mass production as the number of process steps increases and process variables become more diverse, process optimization requires extensive engineering effort to meet the target process requirements, such as uniformity. In this study, we propose an efficient process design framework that can efficiently search for optimal process conditions by combining deep learning (DL) with plasma simulations. To establish the DL model, a dataset was created using a two-dimensional (2D) hybrid plasma equipment model (HPEM) code for an argon inductively coupled plasma (ICP) system under a given process window. The DL model was implemented and trained using the dataset to learn the functional relationship between the process conditions and their consequential plasma states, which was characterized by 2D field data. The performance of the DL model was confirmed by comparison of the output with the ground truth, validating its high consistency. Moreover, the DL results provide a reasonable interpretation of the fundamental features of plasmas and show a good correlation with the experimental observations in terms of the measured etch rate characteristics. Using the designed DL, an extensive exploration of process variables was conducted to find the optimal processing condition using the multi-objective particle swarm optimization (MOPSO) algorithm for the given objective functions of high etch rate and its uniform distribution. The obtained optimal candidates were evaluated and compared to other process conditions experimentally, demonstrating a fairly enhanced etch rate and uniformity at the same time. The proposed computational framework substantially reduced trial-and-error repetitions in tailoring process conditions from a practical perspective. Moreover, it will serve as an effective tool to narrow the processing window, particularly in the early stages of development for advanced equipment and processes.

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Model description of a two-dimensional electrostatic particle-in-cell simulation parallelized with a graphics processing unit for plasma discharges

Cited by 25 publications

References 18 publications

Two‐dimensional analysis for the transition from nonlocal to local electron kinetics and its effect on the spatial uniformity of a capacitively coupled plasma

Two‐dimensional analysis for the transition from nonlocal to local electron kinetics and its effect on the spatial uniformity of a capacitively coupled plasma

Kinetic Analysis of Electrode Heating Effects in a Torr-Regime Capacitively Coupled Plasma Reactor: 2-D Particle-in-Cell Simulation Study

Computational approach for plasma process optimization combined with deep learning model

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